The document outlines the course contents for MTH 201 Biometry. It covers topics such as designing experiments, analysis of variance, experimental designs including completely randomized design, randomized complete block design, Latin square design, and factorial experiments. It provides examples of key concepts such as treatments, experimental units, randomization, replication, and blocking. The document also gives an example of a potential film canister experiment to demonstrate these fundamental design principles.
The document discusses different experimental design techniques including completely randomized design (CRD), randomized block design (RBD), and Latin square design (LSD). It provides examples of how each design can be applied and compares their advantages and disadvantages. Key principles of experimental design are randomization, replication, and local control. The goal of design of experiments is to control insignificant variables and attribute results only to the experimental variables.
This document summarizes key aspects of different types of experimental designs:
1) Completely Randomized Design (CRD) is used when experimental material is limited and homogeneous. It has a simple layout but provides no local control for environmental variation.
2) Randomized Block Design (RBD) controls for environmental variation between blocks but only in one direction. It allows for more treatments than CRD.
3) Latin Square Design (LSD) controls variation in two directions by arranging treatments in rows and columns. It provides more accurate results than CRD and RBD for a small number of treatments.
4) Split Plot Design (SPD) studies multiple factors simultaneously at different levels of precision by dividing plots into
Multiple Linear Regression II and ANOVA IJames Neill
Explains advanced use of multiple linear regression, including residuals, interactions and analysis of change, then introduces the principles of ANOVA starting with explanation of t-tests.
This document provides an overview of different types of statistical tests used for data analysis and interpretation. It discusses scales of measurement, parametric vs nonparametric tests, formulating hypotheses, types of statistical errors, establishing decision rules, and choosing the appropriate statistical test based on the number and types of variables. Key statistical tests covered include t-tests, ANOVA, chi-square tests, and correlations. Examples are provided to illustrate how to interpret and report the results of these common statistical analyses.
This document discusses data transformation techniques for statistical analysis. It explains that if measurement data is not normally distributed or has unequal variances, transformation is necessary. It then outlines steps to test for normality in SPSS. The document focuses on three common transformations: logarithmic for count data with a wide range, square root for rare count events, and arcsine for proportional or percentage data to make distributions normal. Examples and formulas are provided for each transformation.
The Mann Witney U Test in statistics is related to a testing without considering any assumption as to the parameters of frequently distributed of a valueless hypothesis. It is similar to the value selected randomly from one sample, can be higher than or lesser than a value selected randomly from a second sample. Copy the link given below and paste it in new browser window to get more information on Mann Whitney U Test:- http://www.transtutors.com/homework-help/statistics/mann-whitney-u-test.aspx
Blocking is a technique used in experimental design to account for nuisance factors that may impact the response variable but are not of interest to the experimenter. A balanced incomplete block design (BIBD) is a type of randomized block design where each block contains some but not all of the treatments being tested, and each treatment appears an equal number of times across blocks. This design allows blocking to remove nuisance variability while still testing experimental units on all treatments. The statistical analysis of a BIBD involves checking that the design is properly balanced and analyzing the results to determine the effects of factors and their interactions on the response variable. An example is provided of a chemical catalyst experiment using a BIBD to test multiple catalyst materials across different reactor batches
The document discusses different experimental design techniques including completely randomized design (CRD), randomized block design (RBD), and Latin square design (LSD). It provides examples of how each design can be applied and compares their advantages and disadvantages. Key principles of experimental design are randomization, replication, and local control. The goal of design of experiments is to control insignificant variables and attribute results only to the experimental variables.
This document summarizes key aspects of different types of experimental designs:
1) Completely Randomized Design (CRD) is used when experimental material is limited and homogeneous. It has a simple layout but provides no local control for environmental variation.
2) Randomized Block Design (RBD) controls for environmental variation between blocks but only in one direction. It allows for more treatments than CRD.
3) Latin Square Design (LSD) controls variation in two directions by arranging treatments in rows and columns. It provides more accurate results than CRD and RBD for a small number of treatments.
4) Split Plot Design (SPD) studies multiple factors simultaneously at different levels of precision by dividing plots into
Multiple Linear Regression II and ANOVA IJames Neill
Explains advanced use of multiple linear regression, including residuals, interactions and analysis of change, then introduces the principles of ANOVA starting with explanation of t-tests.
This document provides an overview of different types of statistical tests used for data analysis and interpretation. It discusses scales of measurement, parametric vs nonparametric tests, formulating hypotheses, types of statistical errors, establishing decision rules, and choosing the appropriate statistical test based on the number and types of variables. Key statistical tests covered include t-tests, ANOVA, chi-square tests, and correlations. Examples are provided to illustrate how to interpret and report the results of these common statistical analyses.
This document discusses data transformation techniques for statistical analysis. It explains that if measurement data is not normally distributed or has unequal variances, transformation is necessary. It then outlines steps to test for normality in SPSS. The document focuses on three common transformations: logarithmic for count data with a wide range, square root for rare count events, and arcsine for proportional or percentage data to make distributions normal. Examples and formulas are provided for each transformation.
The Mann Witney U Test in statistics is related to a testing without considering any assumption as to the parameters of frequently distributed of a valueless hypothesis. It is similar to the value selected randomly from one sample, can be higher than or lesser than a value selected randomly from a second sample. Copy the link given below and paste it in new browser window to get more information on Mann Whitney U Test:- http://www.transtutors.com/homework-help/statistics/mann-whitney-u-test.aspx
Blocking is a technique used in experimental design to account for nuisance factors that may impact the response variable but are not of interest to the experimenter. A balanced incomplete block design (BIBD) is a type of randomized block design where each block contains some but not all of the treatments being tested, and each treatment appears an equal number of times across blocks. This design allows blocking to remove nuisance variability while still testing experimental units on all treatments. The statistical analysis of a BIBD involves checking that the design is properly balanced and analyzing the results to determine the effects of factors and their interactions on the response variable. An example is provided of a chemical catalyst experiment using a BIBD to test multiple catalyst materials across different reactor batches
A researcher assigns 33 subjects to 3 groups receiving dietary information via different modes: an online website, a nurse practitioner, or a video. The researcher measures 3 dependent variables related to the presentation: difficulty, usefulness, and importance. MANOVA is an appropriate analysis to determine if the modes of presentation have a significant effect on a combination of the dependent variables, while accounting for correlations between them. The researcher can use MANOVA to test whether the interactive website is superior to the other modes in conveying the information in a comprehensive yet cost-effective manner.
presentation of factorial experiment 3*2D-kay Verma
This document describes a three-level factorial experiment with two factors: variety and spacing. It discusses main effects, interaction effects, and types of factorial experiments. The experiment uses three varieties of crops planted at three different spacing levels, for a total of nine treatment combinations. The results are analyzed to determine the sum of squares and averages for each variety and spacing level, as well as the interaction between variety and spacing.
The document describes a randomized complete block design (RCBD) experimental method. RCBD involves comparing treatments (e.g. fertilizers) applied to experimental units (e.g. corn crops) grouped into blocks (e.g. fields). Treatments are randomly assigned to experimental units within each block. RCBD controls for variability between blocks (e.g. differences in soil between fields) to isolate the effect of treatments. It provides more precise results than a completely randomized design when blocks are homogeneous within and heterogeneous between.
This document provides information on using SPSS for educational research. It discusses descriptive statistics, common statistical issues in research, procedures for creating a SPSS data file and conducting descriptive analyses. It also explains how to perform t-tests, analysis of variance (ANOVA), frequencies analysis and other statistical tests in SPSS. The document is intended as a guide for researchers on applying various statistical analyses in SPSS.
v When to Choose a Statistical Tests OR When NOT to Choose? v Parametric vs. Non-Parametric Tests (Comparison)
v Parameters to check when Choosing a Statistical Test:
- Distribution of Data
- Type of data/Variable
- Types of Analysis (What’s the hypothesis)
- No of groups or data-sets
- Data Group Design
v Snapshot of all statistical test and “How” to Choose using above parameters v Explanation using Examples:
- Mann Whitney U Test
- Wilcoxon Sign Rank Test
- Spearman’s co-relation
- Chi-Square Test
v Conclusion
MANOVA is an extension of ANOVA that allows for analysis of multiple dependent variables. It tests whether changes in independent variables have statistically significant effects on two or more dependent variables. If the MANOVA results indicate significance, then individual ANOVA tests must be examined to determine which dependent variable(s) are driving the effect. A key advantage is the ability to analyze multiple outcomes simultaneously, while controlling for increased complexity and loss of degrees of freedom with additional variables.
This document discusses principles of experimental design. It covers the aims of experiments including developing new products or processes or improving existing ones. It discusses types of experiments and defines DOE (design of experiments). It outlines the phases of experimental design including treatment design, experiment design, and analysis design. It provides examples of treatment design objectives like screening, quantifying, optimization, and theory. It also discusses concepts like one-variable and two-way factorial experiments, experimental units, replicates, randomization, and analysis of variance.
SPSS is a statistical software package used for interactive or programmed data analysis. It can perform complex data analysis and statistics with simple commands. Originally called the Statistical Package for the Social Sciences when it was first created in 1968, SPSS is now owned by IBM. The default window in SPSS contains a data editor with two sheets - the data view sheet displays raw data while the variable view sheet defines metadata for each variable. SPSS allows users to easily enter, clean, manage and analyze data to derive useful information for making informed decisions.
A Latin square design assigns treatments to rows and columns so that each treatment appears once in each row and column. This allows controlling for two sources of variation: rows and columns. An example describes using a Latin square to study the effects of different protein sources and levels on rat weight gain. Treatments are assigned to letters in the square. Advantages are controlling two variables, but disadvantages are experiments become large with many treatments and statistical analysis is complicated.
Multinomial logisticregression basicrelationshipsAnirudha si
This document provides an overview of multinomial logistic regression. It discusses how multinomial logistic regression compares multiple groups through binary logistic regressions. It describes how to interpret the results, including evaluating the overall relationship between predictors and the dependent variable and relationships between individual predictors and the dependent variable. Requirements and assumptions of the analysis are explained, such as the dependent variable being non-metric and cases-to-variable ratios. Methods for evaluating model accuracy and usefulness are also outlined.
ANOVA (analysis of variance) and mean differentiation tests are statistical methods used to compare means or medians of multiple groups. ANOVA compares three or more means to test for statistical significance and is similar to multiple t-tests but with less type I error. It requires continuous dependent variables and categorical independent variables. There are different types of ANOVA including one-way, factorial, repeated measures, and multivariate ANOVA. Key assumptions of ANOVA include normality, homogeneity of variance, and independence of observations. The F-test statistic follows an F-distribution and is used to evaluate the null hypothesis that population means are equal.
Experiments
A Quick History of Design of Experiments
Why We Use Experimental Designs
What is Design of Experiment
How Design of Experiment contributes
Terminology
Analysis Of Variation (ANOVA)
Basic Principle of Design of Experiments
Some Experimental Designs
This presentation discusses the procedure involved in two-way mixed ANOVA design. The procedure has been discussed by solving a problem using SPSS functionality.
A repeated measures ANOVA is used to test whether a single group of people change over time by comparing distributions from the same group at different time periods, rather than comparing distributions from different groups. The overall F-ratio reveals if there are differences among time periods, and post hoc tests identify exactly where the differences occurred. In contrast, a one-way ANOVA compares distributions between two or more different groups to determine if there are statistical differences between them.
This document outlines the preface, objectives, description, requirements and references for a course on experimental design. The course focuses on using statistical techniques to solve problems in agricultural, environmental and biological sciences. It covers principles of experimental design, analysis of variance (ANOVA) for one-way and two-way classifications, and introduces SPSS software for conducting statistical analyses. The objective is for students to learn how to design experiments and analyze and interpret results.
This document explains the key differences between observational and experimental studies. Observational studies involve observing phenomena as they occur naturally, while experimental studies involve manipulating variables and determining their effects. It defines related concepts like independent and dependent variables, treatment and control groups. It notes advantages of experimental studies like controlling subject selection and variable manipulation, and disadvantages like artificial settings and potential confounding variables.
Hypothesis testing involves proposing and testing hypotheses, or predictions, about relationships between variables. There are four main types of hypotheses: null, alternative, directional, and non-directional. The null hypothesis proposes no relationship between variables, while the alternative hypothesis contradicts the null. Directional hypotheses predict the nature of a relationship, while non-directional hypotheses do not. Common statistical tests used for hypothesis testing include the z-test, t-test, chi-square test, and F-test. Hypothesis testing is a crucial part of the scientific method for assessing theories through empirical observation.
This document summarizes key aspects of the randomized complete block design (RCBD). It begins by introducing blocking to account for nuisance factors. It then describes how to conduct an experiment as an RCBD, including assigning treatments to blocks and analyzing the data. Statistical models for the RCBD are presented along with equations for estimating parameters and testing hypotheses. Residual plots are discussed for checking assumptions. The document concludes by covering additional RCBD topics like interactions, sample size choice, and estimating missing values.
A document on design of experiments (DOE) is summarized as follows:
DOE is a systematic method to determine the relationship between factors affecting a process and its output. Experiments involve the systematic collection of data with a focus on the design itself rather than results. Factors that can be modified are called controllable inputs or x-factors, while uncontrollable inputs cannot be changed. Hypothesis testing uses statistical methods to determine significant factors. Blocking and replication are used to reduce unwanted variations and estimate random error. Interactions occur when the simultaneous influence of two variables on a third is not additive. Well-designed experiments can optimize processes and solve problems.
Here is a piece of detailed information about the experimental design used in the field of statistics. This also features some information on the three most widely accepted and most widely used designs.
A researcher assigns 33 subjects to 3 groups receiving dietary information via different modes: an online website, a nurse practitioner, or a video. The researcher measures 3 dependent variables related to the presentation: difficulty, usefulness, and importance. MANOVA is an appropriate analysis to determine if the modes of presentation have a significant effect on a combination of the dependent variables, while accounting for correlations between them. The researcher can use MANOVA to test whether the interactive website is superior to the other modes in conveying the information in a comprehensive yet cost-effective manner.
presentation of factorial experiment 3*2D-kay Verma
This document describes a three-level factorial experiment with two factors: variety and spacing. It discusses main effects, interaction effects, and types of factorial experiments. The experiment uses three varieties of crops planted at three different spacing levels, for a total of nine treatment combinations. The results are analyzed to determine the sum of squares and averages for each variety and spacing level, as well as the interaction between variety and spacing.
The document describes a randomized complete block design (RCBD) experimental method. RCBD involves comparing treatments (e.g. fertilizers) applied to experimental units (e.g. corn crops) grouped into blocks (e.g. fields). Treatments are randomly assigned to experimental units within each block. RCBD controls for variability between blocks (e.g. differences in soil between fields) to isolate the effect of treatments. It provides more precise results than a completely randomized design when blocks are homogeneous within and heterogeneous between.
This document provides information on using SPSS for educational research. It discusses descriptive statistics, common statistical issues in research, procedures for creating a SPSS data file and conducting descriptive analyses. It also explains how to perform t-tests, analysis of variance (ANOVA), frequencies analysis and other statistical tests in SPSS. The document is intended as a guide for researchers on applying various statistical analyses in SPSS.
v When to Choose a Statistical Tests OR When NOT to Choose? v Parametric vs. Non-Parametric Tests (Comparison)
v Parameters to check when Choosing a Statistical Test:
- Distribution of Data
- Type of data/Variable
- Types of Analysis (What’s the hypothesis)
- No of groups or data-sets
- Data Group Design
v Snapshot of all statistical test and “How” to Choose using above parameters v Explanation using Examples:
- Mann Whitney U Test
- Wilcoxon Sign Rank Test
- Spearman’s co-relation
- Chi-Square Test
v Conclusion
MANOVA is an extension of ANOVA that allows for analysis of multiple dependent variables. It tests whether changes in independent variables have statistically significant effects on two or more dependent variables. If the MANOVA results indicate significance, then individual ANOVA tests must be examined to determine which dependent variable(s) are driving the effect. A key advantage is the ability to analyze multiple outcomes simultaneously, while controlling for increased complexity and loss of degrees of freedom with additional variables.
This document discusses principles of experimental design. It covers the aims of experiments including developing new products or processes or improving existing ones. It discusses types of experiments and defines DOE (design of experiments). It outlines the phases of experimental design including treatment design, experiment design, and analysis design. It provides examples of treatment design objectives like screening, quantifying, optimization, and theory. It also discusses concepts like one-variable and two-way factorial experiments, experimental units, replicates, randomization, and analysis of variance.
SPSS is a statistical software package used for interactive or programmed data analysis. It can perform complex data analysis and statistics with simple commands. Originally called the Statistical Package for the Social Sciences when it was first created in 1968, SPSS is now owned by IBM. The default window in SPSS contains a data editor with two sheets - the data view sheet displays raw data while the variable view sheet defines metadata for each variable. SPSS allows users to easily enter, clean, manage and analyze data to derive useful information for making informed decisions.
A Latin square design assigns treatments to rows and columns so that each treatment appears once in each row and column. This allows controlling for two sources of variation: rows and columns. An example describes using a Latin square to study the effects of different protein sources and levels on rat weight gain. Treatments are assigned to letters in the square. Advantages are controlling two variables, but disadvantages are experiments become large with many treatments and statistical analysis is complicated.
Multinomial logisticregression basicrelationshipsAnirudha si
This document provides an overview of multinomial logistic regression. It discusses how multinomial logistic regression compares multiple groups through binary logistic regressions. It describes how to interpret the results, including evaluating the overall relationship between predictors and the dependent variable and relationships between individual predictors and the dependent variable. Requirements and assumptions of the analysis are explained, such as the dependent variable being non-metric and cases-to-variable ratios. Methods for evaluating model accuracy and usefulness are also outlined.
ANOVA (analysis of variance) and mean differentiation tests are statistical methods used to compare means or medians of multiple groups. ANOVA compares three or more means to test for statistical significance and is similar to multiple t-tests but with less type I error. It requires continuous dependent variables and categorical independent variables. There are different types of ANOVA including one-way, factorial, repeated measures, and multivariate ANOVA. Key assumptions of ANOVA include normality, homogeneity of variance, and independence of observations. The F-test statistic follows an F-distribution and is used to evaluate the null hypothesis that population means are equal.
Experiments
A Quick History of Design of Experiments
Why We Use Experimental Designs
What is Design of Experiment
How Design of Experiment contributes
Terminology
Analysis Of Variation (ANOVA)
Basic Principle of Design of Experiments
Some Experimental Designs
This presentation discusses the procedure involved in two-way mixed ANOVA design. The procedure has been discussed by solving a problem using SPSS functionality.
A repeated measures ANOVA is used to test whether a single group of people change over time by comparing distributions from the same group at different time periods, rather than comparing distributions from different groups. The overall F-ratio reveals if there are differences among time periods, and post hoc tests identify exactly where the differences occurred. In contrast, a one-way ANOVA compares distributions between two or more different groups to determine if there are statistical differences between them.
This document outlines the preface, objectives, description, requirements and references for a course on experimental design. The course focuses on using statistical techniques to solve problems in agricultural, environmental and biological sciences. It covers principles of experimental design, analysis of variance (ANOVA) for one-way and two-way classifications, and introduces SPSS software for conducting statistical analyses. The objective is for students to learn how to design experiments and analyze and interpret results.
This document explains the key differences between observational and experimental studies. Observational studies involve observing phenomena as they occur naturally, while experimental studies involve manipulating variables and determining their effects. It defines related concepts like independent and dependent variables, treatment and control groups. It notes advantages of experimental studies like controlling subject selection and variable manipulation, and disadvantages like artificial settings and potential confounding variables.
Hypothesis testing involves proposing and testing hypotheses, or predictions, about relationships between variables. There are four main types of hypotheses: null, alternative, directional, and non-directional. The null hypothesis proposes no relationship between variables, while the alternative hypothesis contradicts the null. Directional hypotheses predict the nature of a relationship, while non-directional hypotheses do not. Common statistical tests used for hypothesis testing include the z-test, t-test, chi-square test, and F-test. Hypothesis testing is a crucial part of the scientific method for assessing theories through empirical observation.
This document summarizes key aspects of the randomized complete block design (RCBD). It begins by introducing blocking to account for nuisance factors. It then describes how to conduct an experiment as an RCBD, including assigning treatments to blocks and analyzing the data. Statistical models for the RCBD are presented along with equations for estimating parameters and testing hypotheses. Residual plots are discussed for checking assumptions. The document concludes by covering additional RCBD topics like interactions, sample size choice, and estimating missing values.
A document on design of experiments (DOE) is summarized as follows:
DOE is a systematic method to determine the relationship between factors affecting a process and its output. Experiments involve the systematic collection of data with a focus on the design itself rather than results. Factors that can be modified are called controllable inputs or x-factors, while uncontrollable inputs cannot be changed. Hypothesis testing uses statistical methods to determine significant factors. Blocking and replication are used to reduce unwanted variations and estimate random error. Interactions occur when the simultaneous influence of two variables on a third is not additive. Well-designed experiments can optimize processes and solve problems.
Here is a piece of detailed information about the experimental design used in the field of statistics. This also features some information on the three most widely accepted and most widely used designs.
A randomized block design (RBD) is an experimental design where treatment factors are assigned to experimental units at random within each block. Blocking reduces variability between units by grouping similar units together. In an example RBD experiment comparing sales of new menu items, the restaurants were blocked by location to account for differences between locations. Statistical analysis found no significant difference between the mean sales of the three menu items, failing to reject the null hypothesis.
The document provides an overview of key concepts in research methodology and experimental design. It defines important terms like treatments, experimental units, replication, blocking, and randomization. It discusses the objectives of different types of experimental designs like completely randomized design (CRD), randomized complete block design (RCBD), Latin square design (LSD), and factorial designs. It also covers topics like sources of variation, analysis of variance (ANOVA), interaction effects, and split plot designs. The document is intended to help junior researchers understand fundamental principles of research methodology.
Parameter Optimization of Shot Peening Process of PMG AL2024 Alloy CoverIOSRJMCE
Shot peening leads to local plastic deformations in the near-surface regions, which result in the development of compressive residual stress and the improvement of surface hardness in the aerospace structural components. These properties can be enhanced by careful selection of the peening parameters. PMG Cover of AL2024 Aluminum Alloy is widely used in the generator manufacturing cover due to its high specific static strength. In this study a Taguchi Grey Relational Analysis is presented to optimize the surface properties of residual stress, micro hardness. The effects of four peening parameters (Shot Diameter, Shot Velocity, Impact Angle, Nozzle Distance) on micro hardness and residual stress are investigated Design of Experiment work is carried out by MINITAB 14 software tools of Taguchi Grey relational method, for getting excellent shot peening process parameter combination by MAT LAB R2009 software tools of advanced Optimization method as Genetic Algorithm, Simulated Annealing. Compare of the above reading for the investigation.
This document provides guidance on key concepts and skills for practical biology experiments, including:
1. Experimental design involves establishing a testable hypothesis with independent and dependent variables. Proper controls and minimizing random/systematic errors ensures fair and reliable tests.
2. Variables, controls, sample size, precision and accuracy must be considered. Results should be recorded in tables and graphs, then analyzed and conclusions made about whether the data supports the original hypothesis.
3. Proper scientific communication includes objective interpretation of results, evaluating sources of error, and stating how experiments could be improved. The conclusion relates directly back to the original hypothesis.
Hypothesis Testing and Experimental design.pptxAbile2
The document discusses hypothesis testing and experimental design. It explains that hypothesis testing involves designing a method to collect data to evaluate and accept or reject a hypothesis. Experimental design aims to minimize sources of variability except the treatment being tested. Key aspects of experimental design discussed include sample size, replication, controls, randomization, and interspersion of treatments. Different types of experimental designs are also outlined, including completely randomized designs, randomized complete block designs, and factorial designs.
The document discusses the key components of designing an experiment, including:
1) The independent variable that is purposefully manipulated.
2) The dependent variable that responds to changes in the independent variable.
3) Constants that could influence the experiment but are deliberately kept the same.
4) Having multiple levels of the independent variable and repeating trials at each level helps draw reliable conclusions.
This document outlines key concepts for designing and conducting effective biology experiments, including formulating a testable hypothesis, identifying independent and dependent variables, controlling other factors, collecting precise measurements, analyzing sources of error, interpreting results, and drawing valid conclusions. Key aspects are designing experiments to test hypotheses, minimizing random and identifying systematic errors to improve reliability and accuracy, and repeating experiments to verify findings.
Experimental design involves systematically manipulating variables to test hypotheses. There are three principles: randomization, replication, and reducing noise. A response variable is measured, while explanatory variables that may affect the response are investigated. Factors are categorical variables with levels, while covariates are continuous variables. Screening designs identify significant factors from many potential ones using full or fractional factorials. The objective and number of factors determine the appropriate design, such as randomized block, central composite, or Plackett-Burman designs for screening or response surface methods for optimization.
Experimental research involves systematically manipulating and controlling variables to determine their effect on other variables. It is commonly used in sciences to understand causal relationships. Key aspects of experimental research include sampling groups correctly, using control groups for comparison, conducting pilot studies to test the design, identifying and controlling confounding variables, and analyzing data quantitatively to draw valid conclusions about causal effects. Well-designed experiments allow researchers to explain phenomena through investigating cause-and-effect relationships.
Response of Watermelon to Five Different Rates of Poultry Manure in Asaba Are...IOSR Journals
The document discusses experimental research designs, specifically pretest-posttest designs. It begins by explaining true experimental designs that use control and experimental groups, with pretests and posttests to both groups.
It then discusses different pretest-posttest designs in more detail, including Solomon four group designs. The Solomon four group design involves four groups - two groups that receive a pretest and posttest, one that only receives a posttest, and one that only receives a pretest.
The document provides an example of how pretest-posttest designs could be used to study the effects of fertilizers in agriculture. It evaluates the internal and external validity of different experimental designs and their ability to control for confounding variables
The research question investigated the effect of the independent variable (IV) on the dependent variable (DV) in XXXX as measured by a specific method. The author hypothesized that if the IV was changed by specific values, the DV would change in a predictable way based on scientific theory and previous research. Experiments were conducted where the IV was systematically altered while controlling other variables, and the DV was measured. Statistical analysis of the results provided support for the hypothesis. While limitations were identified, overall the study contributed meaningful findings to the scientific question.
The research question investigated the effect of the independent variable (IV) on the dependent variable (DV) in XXXX as measured by a specific method. The author hypothesized that if the IV was changed by specific values, the DV would change in a predictable way based on scientific theory and previous research. Experiments were conducted where the IV was systematically altered while controlling other variables, and the DV was measured. Statistical analysis of the results provided support for the hypothesis. While limitations were identified, overall the study contributed meaningful findings to the scientific question.
Thanh Nguyen DB 6COLLAPSETop of FormNowadays, along with t.docxarnoldmeredith47041
Thanh Nguyen
DB 6
COLLAPSE
Top of Form
Nowadays, along with the development of technologies, scientists have invented a new technology for plants and foods. They called it GMO, and they introduced it with a lot of benefits. There is no doubt that GMO technology helps people a lot in increasing the quality of foods. It helps farmers stop wasting their time and money on pesticides. The two main types of GMO crops in use today are engineered to either produce their pesticides o be herbicide-tolerant. More than 80% of corn grown in the US is GMO Bt corn, which produces its own Bacillus thuringiensis insecticide. This has significantly reduced the need for spraying insecticides over cornfields, and dozens of studies have shown there are no environmental or health concerns with Bt corn. Scientists also proved that GMO foods are safe for humans, and they are improving the benefits of GMO foods every day. GMO foods also increase nutrition value, such as the "Golden Rice". The "Golden Rice" Nowadays, along with the development of technologies, scientists have invented a new technology for plants and foods. They called it GMO, and they introduced it with a lot of benefits. There is no doubt that GMO technology helps people a lot in increasing the quality of foods. It helps farmers stop wasting their time and money on pesticides. Scientists also proved that GMO foods are safe for humans, and they are improving the benefits of GMO foods every day. GMO foods also increase nutrition value, such as the "Golden Rice". The "Golden Rice” produces high levels of beta-carotene.] A report by Australia and New Zealand’s food safety regulator found that Golden Rice "is considered to be as safe for human consumption as food derived from conventional rice."
“GMOs - Top 3 Pros and Cons.” ProConorg Headlines, www.procon.org/headline.php?headlineID=005447.
EXAMPLE OF REPORT
Title: Effect of Enzyme Concentration on the Reaction Rate (Urease Enzyme)
Introduction
Enzymes are molecules of proteins that facilitate a chemical reaction without losing its
chemical structure (Madder, 2009). An enzyme will sometimes break a substrate into
products once the substrate attaches to the active site, which is the place in the enzyme
that…
Sometimes the higher concentration of substrates in a solution can result in more
interactions with the enzymes as collations between molecules are more likely.
This experiment has the objective of evaluating the effect of the concentration of
enzymes on the chemical reaction target by the enzyme. Our hypothesis is that the more
enzymes present interacting with a specific substrate the more activity will result.
Materials and Procedure
The molecule of urea was selected as the substrate on which the enzyme urease acted
upon resulting in two products: carbon dioxide and ammonia. The presence of ammonia
was measured by determining the pH of the solution where the reaction took place.
Urea solution contained a .
The document discusses key principles of experimental design:
(1) Replication is used to estimate experimental error by exposing multiple experimental units to the same treatment.
(2) Randomization ensures the experimental error estimate is valid by randomly assigning treatments to prevent bias.
(3) Local control reduces experimental error by standardizing treatment application and conditions to make experiments more efficient.
Experimental design is a way to carefully plan experiments in advance so that results are both objective and valid. Ideally, an experimental design should:
• Describe how participants are allocated to experimental groups. A common method is completely randomized design, where participants are assigned to groups at random. A second method is randomized block design, where participants are divided into homogeneous blocks (for example, age groups) before being randomly assigned to groups.
• Minimize or eliminate confounding variables, which can offer alternative explanations for the experimental results.
• Allows making inferences about the relationship between independent variables and dependent variables.
• Reduce variability, to make it easier to find differences in treatment outcomes.
Types of Experimental Design
1. Between Subjects Design.
2. Completely Randomized Design.
3. Factorial Design.
4. Matched-Pairs Design.
5. Observational Study
• Longitudinal Research
• Cross Sectional Research
6. Pretest-Posttest Design.
7. Quasi-Experimental Design.
8. Randomized Block Design.
9. Randomized Controlled Trial
10. Within subjects Design.
This document discusses various research designs used in nursing research. It defines research design as the plan or blueprint for conducting a study. Experimental designs aim to identify cause-effect relationships through manipulation of independent variables and use of control groups. True experiments allow the highest level of control but quasi-experiments and pre-experimental designs are also used when true experiments are not possible. Non-experimental designs observe variables without manipulation and are used when variables cannot be manipulated or experiments would be unethical.
A completely randomized design (CRD) randomly assigns experimental units to different treatment groups so each unit has an equal chance of receiving any treatment. Any variation between units receiving the same treatment is considered experimental error. CRDs are best for homogeneous experimental units where environmental effects can be controlled, like laboratories. They are rarely used for field experiments with more variation. Treatments are administered at different levels or amounts. The randomization process, advantages like simplicity, and sources of variation are outlined. Analysis of variance (ANOVA) can be used to test for significant differences between treatment groups.
The design of Farm cart 0011 report 1 2020musadoto
This report describes the best designing of a 200cc FARM CART MACHINE which will be useful to the farm fields due to the fact that, the purchase, repair and maintenance are affordable to all level of income earners. Despite the cost effectiveness of the machine, the report also tries to justify that the machine can be used multipurposely as it serves the purposes of been used as farm transport, mowering machine, boom spraying and or mini planter with two rows. All these can be achieved as long as the implements are attached with respect to the power capacity of the farm cart.
The report tells only the design and testing of machine excluding its farm implements design. Some best reviews from other study projects done by other people in the world provided a good reference for designing and implementation of this project. The project is initially costly because it needs to develop a prototype and test the different first ideas.
The project report describes the important of choosing to use the designed farm cart machine compared to other farm machines at the market which are most efficiently to be used by farmers in their fields.
The challenges are inevitable in any project, here in designing of this 200cc farm machine, the major issue is the funding because the fund for this project is from the pocket which is always insufficient as it depends to the meals and accommodation money distribution sponsored from the HIGH EDUCATION STUDENTS LOAN BOARD (HESLB) thus it takes longer to accomplish the project by waiting another quarter of the semester to continue with the project which affects the other part of normal life(in terms of meals and accommodation).
The report recommends that, the department of engineering sciences and technology and Sokoine University of Agriculture as a whole should invest into this technology by utilizing fully the idea and funding the project for more better improvement so as to attain the desired standard that can with stand the different farm field factors. These when taken into consideration there is a possibility to achieve the industrialization policy in our country and thereafter it is a better approach to modern agriculture.
IRRIGATION SYSTEMS AND DESIGN - IWRE 317 questions collection 1997 - 2018 ...musadoto
This document contains sample exam questions for a course on irrigation systems design. It includes multiple choice and short answer questions testing understanding of key irrigation concepts. Some example questions are on pump characteristics, calculating water requirements for drip and sprinkler systems, estimating consumptive water use, and determining system efficiencies. The document provides a compilation of past exam questions from 1997 to 2018 to help students prepare for tests.
CONSTRUCTION [soil treatment, foundation backfill, Damp Proof Membrane[DPM] a...musadoto
With reference to a construction site visited recently, describe in details key features
that can be observed on site as follows
Foundations backfilling, hardcore, soil treatment, DPM and BRC works prior
to pouring oversite concrete
CONSTRUCTION [soil treatment, foundation backfill, Damp Proof Membrane[DPM] and BRC for engineers (civil)
BASICS OF COMPUTER PROGRAMMING-TAKE HOME ASSIGNMENT 2018musadoto
Self- Check 1
Which of the following are Pascal reserved words, standard identifiers, valid identifiers, invalid identifiers?
end ReadLn Bill
program Sues‟s Rate
Start begin const
Y=Z Prog#2 &Up
First Name „MaxScores‟ A*B
CostaMesa,CA Barnes&Noble CONST
XYZ123 ThisIsALongOne 123XYZANSWER
ANSWERS
Paschal reserved words:
begin, end, program, Start, CONST, const
Standard identifiers:
ReadLn, „MaxScores‟, Bill, Rate
Valid identifiers:
XYZ123, ThisIsALongOne, A*B, Y=Z, CostaMesa, CA, First Name
Invalid identifiers:
123XYZ, Sues‟s, &UpFirstName, Barnes&Noble, Prog#2
Self- Check 2
Which of the following literal values are legal and what are their types? Which are illegal and why?
15 „XYZ‟ „*‟
$25.123 15; -999
.123 „x‟ “X”
„9‟ „-5‟ True
ANSWER:
The following values are legal and their type
Legal
Type
Illegal
15
Integer literal
$25.123
„XYZ‟
String Literal
.123
„X‟
Character Literal
„9‟
True
Boolean Literal
15;
-999
Integer Literal
-„5‟
Operator literal
„*‟
TP- Lecture 4.2
Self- Checked 1
Which of the following are valid program headings? Which are invalid and why?
(i) Program program; - INVALID using reserved ID
(ii) program 2ndCourseInCS; -INVALID because starts with digit
(iii) program PascalIsFun;- VALID program heading
(iv) program Rainy Day; -INVALID – contains space
Self- Checked 2
Rewrite the following code so that it has no syntax errors and follows the writing conventions we adopted
(i) Program SMALL;
VAR X, Y, Z : real;
BEGIN
Y := 15.0;
Z := -Y + 3.5;
X :=Y + z;
writeln (x, Y, z);
END.
ANSWER:
Program
ENGINEERING SYSTEM DYNAMICS-TAKE HOME ASSIGNMENT 2018musadoto
1. Read Chapter 4 – System Dynamics for Mechanical Engineers by Matthew Davies and Tony L. Schmitz and implement Examples 4.1 to 4.12 in Matlab.
2. Read Chapter 7 – System Dynamics for Mechanical Engineers by Matthew Davies and Tony L. Schmitz and implement Examples 7.1 to 7.11 in Matlab.
3. Read Chapter 9 – System Dynamics for Mechanical Engineers by Matthew Davies and Tony L. Schmitz and implement Examples 9.1 to 9.6 in Matlab.
4. Read Chapter 11 – System Dynamics for Mechanical Engineers by Matthew Davies and Tony L. Schmitz and implement Examples 11.1 to 11.7 in Matlab.
5. Read Chapter 2 - System Dynamics for Engineering Students: Concepts and Applications by Nicolae Lobontiu and attempt problem 2.18 (page 63).
6. Read Chapter 3 - System Dynamics for Engineering Students: Concepts and Applications by Nicolae Lobontiu and attempt problem 3.13 (pp 98 - 100).
7. Read Chapter 4 - System Dynamics for Engineering Students: Concepts and Applications by Nicolae Lobontiu and attempt problem 4.20 (page 146).
8. Read Chapter 5 - System Dynamics for Engineering Students: Concepts and Applications by Nicolae Lobontiu and attempt problems 5.15 (page 198), 5.21 (pp 199 - 200) and 5.27 (pp 201 – 202).
Hardeninig of steel (Jominy test)-CoET- udsmmusadoto
The document describes a Jominy end-quench test experiment to measure the hardenability of two steel samples. Steel samples A and C were heated to the austenite temperature and quenched with water at one end. Hardness measurements using the Rockwell C scale were taken at intervals along the samples. Sample A showed little variation in hardness, while hardness decreased with distance from the quenched end for sample C. A graph of hardness versus distance revealed that sample A has higher hardenability, retaining hardness further from the quenched end. The hardenability indices at 50HRC were determined to be 2mm, 5mm, and 6.5mm from the graph.
1.1 The aim of the experiment
The aim of the experiment is to test the usefulness of the ultrasonic waves, by passing them through different
solids one can find out a lot of physical properties like young’s modulus , defects, Poisson ratio, Velocity of
sound in respective material this is due to the response of the received ultrasonic waves.
1.2 Theory of experiment
Ultrasonic testing (UT) is a family of non-destructive testing (NDT) techniques based on the propagation of ultrasonic waves in the object or material tested. In most common UT applications, very short ultrasonic pulse-waves with center frequencies ranging from 0.1-15 MHz, and occasionally up to 50 MHz, are transmitted into materials to detect internal flaws or to characterize materials. A common example is ultrasonic thickness measurement, which tests the thickness of the test object, for example, to monitor pipework corrosion.
Ultrasonic testing is often performed on steel and other metals and alloys, though it can also be used on concrete, wood and composites, albeit with less resolution. It is used in many industries including steel and aluminium construction, metallurgy, manufacturing, aerospace, automotive and other transportation sectors.
Ae 219 - BASICS OF PASCHAL PROGRAMMING-2017 test manual solutionmusadoto
Whether the Pascal program is small or large, it must have a specific structure. This
program consists mainly of one statement (WRITELN) which does the actual work
here, as it displays whatever comes between the parentheses. The statement is
included inside a frame starting with the keyword BEGIN and ending with the keyword
END. This is called the program main body (or the program block) and usually
contains the main logic of data processing.
1. The background of Fluid Mechanics
2. Fields of Fluid mechanics
3. Introduction and Basic concepts
4. Properties of Fluids
5. Pressure and fluid statics
6. Hydrodynamics
Fluid mechanics (a letter to a friend) part 1 ...musadoto
1. The background of Fluid Mechanics
2. Fields of Fluid mechanics
3. Introduction and Basic concepts
4. Properties of Fluids
5. Pressure and fluid statics
6. Hydrodynamics
Fluids mechanics (a letter to a friend) part 1 ...musadoto
1. The background of Fluid Mechanics
2. Fields of Fluid mechanics
3. Introduction and Basic concepts
4. Properties of Fluids
5. Pressure and fluid statics
6. Hydrodynamics
Fresh concrete -building materials for engineersmusadoto
CONCRETE
is a building Material made from a mixture of gravel ,sand ,cement,water and air ,forming a stone like mass on hardenning.
FRESH CONCRETE
It is a concrete that has not reached the final setting time.
Course Contents:
Introduction; Linear measurements; Analysis and adjustment of measurements, Survey methods: coordinate systems, bearings, horizontal control, traversing, triangulation, detail surveying; Orientation and position; Areas and volumes; Setting out; Curve ranging; Global Positioning system (GPS); Photogrammetry.
Fresh concrete -building materials for engineersmusadoto
General introduction
CONCRETE
is a building Material made from a mixture of gravel ,sand ,cement,water and air ,forming a stone like mass on hardenning.
FRESH CONCRETE
It is a concrete that has not reached the final setting time.
DIESEL ENGINE POWER REPORT -AE 215 -SOURCES OF FARM POWERmusadoto
The diesel engine (also known as a compression-ignition or CI engine), named after Rudolf Diesel, is an internal combustion engine in which ignition of the fuel which is injected into the combustion chamber is caused by the elevated temperature of the air in the cylinder due to mechanical compression (adiabatic compression). Diesel engines work by compressing only the air. This increases the air temperature inside the cylinder to such a high degree that atomised diesel fuel that is injected into the combustion chamber ignites spontaneously. This contrasts with spark-ignition engines such as a petrol engine (gasoline engine) or gas engine (using a gaseous fuel as opposed to petrol), which use a spark plug to ignite an air-fuel mixture. In diesel engines, glow plugs (combustion chamber pre-warmers) may be used to aid starting in cold weather, or when the engine uses a lower compression-ratio, or both. The original diesel engine operates on the "constant pressure" cycle of gradual combustion and produces no audible knock.
A diesel engine built by MAN AG in 1906
Detroit Diesel timing
Fairbanks Morse model 32
The diesel engine has the highest thermal efficiency (engine efficiency) of any practical internal or external combustion engine due to its very high expansion ratio and inherent lean burn which enables heat dissipation by the excess air. A small efficiency loss is also avoided compared to two-stroke non-direct-injection gasoline engines since unburned fuel is not present at valve overlap and therefore no fuel goes directly from the intake/injection to the exhaust. Low-speed diesel engines (as used in ships and other applications where overall engine weight is relatively unimportant) can have a thermal efficiency that exceeds 50%.[1][2
Farm and human power REPORT - AE 215-SOURCES OF FARM POWER musadoto
Farm is an area of land and its building, used for growing crops a rearing of animals or an area of land
that is devoted primarily of agricultural process with the primary objective of producing food and other
commercial crops. Or an area of water that is devoted primarily to agricultural process in order to
produce and manage such commodities as fibers, grains, livestock or fuel.
The process of working the ground, planting seeds and growing of planting known as farming.it can
described s raising of animals for milk and meat as farming.
ENGINE POWER PETROL REPORT-AE 215-SOURCES OF FARM POWERmusadoto
What is an Engine?
Before knowing about how the Petrol Engine works, let's first understand what an engine is. This is common for both petrol and diesel engines alike. An engine is a power generating machine which converts potential energy of the fuel into heat energy and then into motion. It produces power and also runs on its own power.
The engine generates its power by burning the fuel in a self-regulated and controlled „Combustion‟ process. The combustion process involves many sub-processes which burn the fuel efficiently and results in the smooth running of the engine.
These processes include:
The suction of air (also known as breathing or aspiration).
Mixing of the fuel with air after breaking the liquid fuel into highly atomized / mist form.
Igniting the air-fuel mixture with a spark (petrol engine).
Burning of highly atomized fuel particles which results in releasing / ejection of heat energy.
How does an Engine work?
The engine converts Heat Energy into Kinetic Energy in the form of „Reciprocating Motion‟. The expansion of heated gases and their forces act on the engine pistons. The gases push the pistons downwards which results in reciprocating motion of pistons.
This motion of the piston enables the crank-shaft to rotate. Thus, it finally converts the reciprocating motion into the 'Rotary motion' and passes on to wheels.
A petrol engine (known as a gasoline engine in American English) is an internal combustion engine with spark-ignition, designed to run on petrol (gasoline) and similar volatile fuels.
In most petrol engines, the fuel and air are usually mixed after compression (although some modern petrol engines now use cylinder-direct petrol injection). The pre-mixing was formerly done in a carburetor, but now it is done by electronically controlled fuel injection, except in small engines where the cost/complication of electronics does not justify the added engine efficiency. The process differs from a diesel engine in the method of mixing the fuel and air, and in using spark plugs to initiate the combustion process. In a diesel engine, only air is compressed
TRACTOR POWER REPORT -AE 215 SOURCES OF FARM POWER 2018musadoto
A tractor is an engineering vehicle specifically designed to deliver a high tractive effort (or torque) at slow speeds, for the purposes of hauling a trailer or machinery used in agriculture or construction. Most commonly, the term is used to describe a farm vehicle that provides the power and traction to mechanize agricultural tasks, especially (and originally) tillage, but nowadays a great variety of tasks. Agricultural implements 0may be towed behind or mounted on the tractor, and the tractor may also provide a source of power if the implement is mechanised.
The word Tractor is derived prior to 1900, the Machine were known as traction motor (pulling-machine).After the year 1900 both the words are joined by taking ‘Tract’ from Traction and ‘Tor” from motor calling it a Tractor.
In our Country tractors were started manufacturing in real sense after independence and at present we are self-sufficient in meeting demand of country’s requirement for tractors. Our country is basically an agricultural country where 75% of our population is directly or indirectly connected with agriculture. This cannot be produced with our conventional bullock pulled agricultural implements. Tractor is one of the basic agricultural machines
used for speeding up agriculture production.
WIND ENERGY REPORT AE 215- 2018 SOURCES OF FARM POWERmusadoto
Wind is the flow of gases on large scale. On the surface of the earth, wind consists of the bulk movement of air. In outer space, solar wind is the movement of gases and charged particles from the sun though space, while planetary wind is the outgassing of light chemical from a planet’s atmosphere into space. Wind by their spatial scale, their speed, the type of force that cause them, the region in which they occur and their effect. The strongest observed winds on planet in solar system occur on Neptune and Saturn. Winds have various aspects, an important one being its velocity, density of the gas involved and energy content of the wind.
Wind is almost entirely caused by the effects of the sun which, each hour, delivers 175 million watts of energy to the earth. This energy heats the planet’s surface, most intensively at the equator, which causes air to rise. This rising air creates an area of low pressure at the surface into which cooler air is sucked, and it is this flow of air that we know as “wind”. In reality atmospheric circulation is much more complicated and, after rising at the equator air travels pole wards. As it travels the air cools and eventually descends to the earth’s surface at about 30° latitude (north and south), from where it returns once again to the equator (a closed loop known as a Hadley Cell). Similar cells exist between 30° and 60° latitude (the Ferrell Cells) and between 60° latitude and each of the poles (the Polar Cells). Within these cells, the flow of air is further impacted by the rotation of the earth or the "Coriolis Effect". This effect creates a sideways force which causes air to circulate anticlockwise around areas of low pressure in the northern hemisphere and clockwise in the southern hemisphere
In summary, the origin of winds may be traced basically to uneven heating of the earth’s surface due to sun. This may lead to circulation of widespread winds on a global basis, producing planetary winds or may have a limited influence in a smaller area to cause local winds.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptxEduSkills OECD
Iván Bornacelly, Policy Analyst at the OECD Centre for Skills, OECD, presents at the webinar 'Tackling job market gaps with a skills-first approach' on 12 June 2024
हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...Diana Rendina
Librarians are leading the way in creating future-ready citizens – now we need to update our spaces to match. In this session, attendees will get inspiration for transforming their library spaces. You’ll learn how to survey students and patrons, create a focus group, and use design thinking to brainstorm ideas for your space. We’ll discuss budget friendly ways to change your space as well as how to find funding. No matter where you’re at, you’ll find ideas for reimagining your space in this session.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
3. “If your experiment needs a statistician,
you need a better experiment”.
Ernest Rutherford
4. COURSE CONTENTS:
1. DESIGNING OF AN EXPERIMENT
1.1 Introduction
1.3 Basic Principles
1.2 Terminologies in Experimental designs
2. ANALYSIS OF VARIANCE (ANOVA)
2.1 Introduction
2.2 One way classifications
2.3 Two way classifications
1.4 Some basic designs
2.4 Three way classification
6. 5. DATA TRANSFORMATIONS
5.1 Introduction
5.2 Data transformation techniques/families
5.3 Practical problems
6. SIMPLE LINEAR REGRESSION
6.1 Tests of significance of regression parameters (Intercept and Slope)
6.2 ANOVA to test for significance of slope parameters
6.3 Confidence intervals for regression parameters
6.4 Using the model for prediction
6.5 Introduction to Multiple linear regression analysis
7. ANALYSIS OF FREQUECY DATA
7.1 Contingency tables
7. 1.1 INTRODUCTION TO DESIGN AND
ANALYSIS OF EXPERIMENTS
Questions:
What is the main purpose of running an experiment ?
What do one hope to be able to show?
Typically, an experiment may be run for one or more of the following reasons:
1. To determine the principal causes of variation in a measured
response
2. To find conditions that give rise to a maximum or minimum
response
3. To compare the response achieved at different settings of
controllable variables
4. To obtain a mathematical model in order to predict future
responses
8. Biometrics: is the application of statistics and
mathematics to problems with a
biological component, including the
problems in agricultural,
environmental, and biological sciences
as well as medical science.
Biometry: is a subject that is concerned with the
application of statistics and mathematics
to problems in the agricultural,
environmental, and biological sciences.
The Greek roots of biometry are bios (“life”) and metron (“measure”);
Hence biometry literally means “the measurement of life”.
1.2 Terminologies in Experimental designs
9. An Experiment involves the manipulation of one
or more experimental condition(s) by an
experimenter in order to determine the effects of
this manipulation to the response.
Much research departs from this pattern in that nature
rather than the experimenter manipulates the variables.
Such research is referred to as Observational studies
This course is concerned with COMPARATIVE
EXPERIMENTS.
These allows conclusions to be drawn about
cause
and effect (Causal relationships)
10. Experiment vs. Observational
OBSERVATIONAL STUDY
Researcher observes the response of interest under
natural conditions
EX: Surveys, weather patterns
DESIGNED EXPERIMENT
Researcher controls variables that have a potential
effect on the response of interest
Qn. Which one helps establish cause-and-effect
relationships better?
12. A treatment is something controlled and
administered by the researcher to an experimental
unit (EU)
– An experimental unit can also be thought of as the
physical entity assigned to receive a treatment from
which we measure the response
Essentially a design is the proposed allocation of
treatments to experimental units (or vice-versa)
13. Experimental Units (EUs)
We now introduce the term “Experimental Unit” (EU);
-EU is the “material” to which treatment factors
(treatments) are assigned
This is different from an “Observational Unit” (OU);
- OU is part of an EU that is measured
14. A source of variation is anything that could
cause an observation to be different from
another observation
Sources of Variation
Sources of Variation are of two types:
Those that can be controlled and are of interest are
called treatments or treatment factors
Those that are not of interest but are difficult to
control are nuisance factors
15. Dependent variable
The dependent variable (response) reflects
any effects associated with manipulation
of the independent variable
Independent Variables
The variable that is under the control of the
experimenter.
The terms independent variables, treatments,
experimental conditions, controllable variables
can be used interchangeably
16. PROCESS
Z1 Z2 ZP
X1 X2 XP
…….
…….
INPUTS
Uncontrollable factors
Controllable factors
OUTPUT (Response)
The primary goal of an experiment is to determine the amount of
variation caused by the treatment factors in the presence of other
sources of variation
Adapted fro m Mo ntgo mery (201 3)
17. Is a variable, which is believed to affect the
outcome of an experiment e.g. humidity,
pressure, time, concentration, fertilizer, grazing
period, sunlight, etc.
Factor
The various values or classifications of the
factors are known as the levels of the factor(s).
For example, suppose we wish to compare the
efficacy of three medications (M1, M2, and M3)
for lowering blood pressure among middle aged
women, thus, there are three levels of the factor
Medication.
Level
18. Is a measure of the variation among experimental
units that measures mainly inherent variation
among them.
Thus, experimental error is a technical term and
does not mean a mistake, but includes all types of
extraneous variation due to:
Experimental error
-Inherent variability in the experimental units
-Error associated with the measurements made
-Lack of representativeness of the sample to the population
under study
19. The objective of the experiment may include the following;
Determine which conditions are most influential on the response
Determine where to set the influential conditions so that the
response is always near the desired nominal value
Determine where to set the influential conditions so that variability
in the response is small
Determine where to set the influential conditions so that the effects
of the uncontrollable Variables are minimized
20. EXAMPLE;
Researchers were
interested to see the
food consumption of
albino rats when
exposed to microwave
radiation
“If albino rats are subjected to microwave radiation,
then their food consumption will decrease”
22. Design example:
Your child comes home from school and shows you what they
learned in class.
He/she asks for a film canister and an Alka-Seltzer tablet. They
fill the canister with a little water, put the tablet in the water,
close the canister and turn it upside down.
After a few seconds, the canister flies in the air! Your child
wants to know how to make the canister fly as high as possible
= BOOM
23. Design example :
Question: Does the amount of alka-seltzer affect flight
time? Which amount gives the best time?
The different amounts of alka-seltzer are:
– 1 1/2 tablets – 1 tablet
– 1/2 of a tablet
For now, we will reuse the same film canister
The response is the amount of time from liftoff to
landing in seconds
24. Design example :
What are some sources of variation?
– Amount of alka-seltzer (we control this)
– Amount of water
– Film canister seal
– Time Measurement
– Angle of liftoff
There may be more, let's choose the ones that we think
will be most significant and easiest to control
25. There have been four eras in the modern development
of statistical Experimental design
Agricultural era led by Ronald Fisher
Industrial era led by Box and Wilson
Quality improvement era led by Taguchi
Modern era
26. There are three fundamental concepts to any design:
– Replication of treatment
– Randomization of treatment assignment
– Local error control:
• Analysis of Covariance (ANCOVA)
• Blocking of EU's
Neglecting to acknowledge these will result in
unreliable results and immediate skepticism.
Fundamental Principles:
27. Treatments: Three different amounts of Alka-
Seltzer
EU's: Assume we have 9 nearly identical film
canisters.
How do we use the fundamental principles to
design this experiment?
Film Canister Experiment
The three basic principles were developed by Sir Ronald A. Fisher ,
during his time at Rothamsted Agricultural Experimentation Station.
28. Replicating a treatment means assigning that
treatment to multiple EU's.
Will reduce variance of estimates of that treatment's
effect.
If we have equal interest in all the treatments, we
want to try to equally replicate the number of
treatment assignments.
FC Example: There are three treatments (tablet
size) and say we use 9 canisters. So 9/3=3 reps
Replication
29. Independent repeat run of each factor combination
Replication
Number of Experimental Units to which a treatment
is assigned
Advantages
It allows the experimenter to obtain an estimate of the
experimental error
It permits the experimenter to obtain more precise estimates
30. Replication Extension to EU
Thus, a treatment is only replicated if it is
assigned to a new EU.
Taking multiple observations on one EU (i.e.
creating more OUs) does not count as
replication – this is known as subsampling.
31. Note that treating subsampling as
replicating increases the chance of
incorrect conclusions
(psuedoreplication)
Variability in multiple measurements is
measurement error, rather than
experimental error
32. Randomly assign which EU gets a treatment
How we randomize depends on the type of design.
Clearly we must randomize before measurements are
taken.
Reduces possibility of most types of bias caused by
unaccountable sources of variation
FC Example: Perhaps all film canisters have a chance of having a
small, indetectable hole. This will affect the pressure necessary to
launch the canister. Randomizing will give every treatment the same
chance of being affected by this.
Randomization
33. The allocation of experimental material and the order
in which the individual runs of the experiment are to
be performed are randomly determined.
Advantages
Allows the observations (or errors) to be independently distributed
random variables (It ensures random samples).
Proper randomization assist in “averaging out” the effects of
extraneous Factors that may be present.
Randomization cont.
It involves the assignment of treatments to the
experimental units, based on the chosen design, by
some chance mechanism or probabilistic procedures,
e.g. Random numbers
34. There may exist other factors affecting the response
that we can't control or measure until we perform
an experiment. These are called covariates.
We don't necessarily care about the covariate effect,
but by taking it into account we can better detect
treatment differences
Covariate accounts for unexplained experimental
error
FC example: Varying wind speeds during launch
Local Error Control: Analysis of
Covariance
35. A block is a set of experimental units sharing a
common characteristics thought to affect the
response, and to which a separate random
assignment is made
Blocking is used to reduce or eliminate the
variability transmitted from a controllable
nuisance factor
Local Error Control: Blocking
36. Use this when there are factors we are aware of prior
the experiment, but we cannot control them.
Group EU's so that each block contains EU's that
are more “homogeneous”.
Compare treatments within a block, which can
account for variance that would otherwise be
considered as “noise” or “error” (coming from
differences in block effects)
Local Error Control: Blocking
37. FC Example: Maybe we want to use three different
types of film canisters which we feel may be
significantly different from each other.
Local Error Control: Blocking
Each box
represents an EU
with the block
trait
Blocks
9 EU's in each
block, call this
“block size”
38. Covariates and block effects are
referred to as nuisance parameters
because they are “getting in
the way” of the estimation of
treatment effects
Detecting treatment differences is
the
goal! We mainly include blocks
and/or
covariates to reduce experimental
error.
39. 1.4 SOME STANDARD EXPERIMENTAL DESIGNS
The term experimental
design refers to a plan of
assigning experimental
conditions to subjects and
the statistical analysis
associated with the plan.
OR
An experimental design is a
rule that determines the
assignment of the
experimental units to the
treatments.
40. Some standard designs that are used frequently includes;
Completely Randomized design
A completely randomized design (CRD) refer to a design
in which the experimenter assigns the EU’s to the
treatments completely at random, subject only to the
number of observations to be taken on each treatment.
The model is of the form;
Response = constant + effect of a treatment + error
41. The simplest design assumes all the EU's to be
similar and the primary source of variation is
the different treatments.
A completely randomized design (CRD) will
randomize all treatment-EU assignments for the
specified number of treatment replications
Result: If equally interested in comparisons of all
treatments get as close as possible to equally
replicating the treatments
One Source of Variation: The CRD
42. CRD Example: FC Experiment
These are similar EUs
The design plan:
Before randomization
½ tablet 1 tablet 1 ½ tablet
44. Perhaps a single treatment is actually composed of a
combination of multiple factors with different levels.
Example: For the FC experiment we may also vary
water amount (low/medium/high). In this case one
“treatment” is actually a combination of tablet
and water amount.
The specific tablet and water amounts are referred
to as the levels of the tablet factor and water
factor, respectively.
CRD Extension: Factorial Experiments
45. Factorial Example: FC Experiment
½ tablet low water
1 ½ tablet high water
1 tablet medium
water
47. The valuable approach to dealing with
several factors is to conduct a
FACTORIAL EXPERIMENT
This is an experimental strategy in which
factors are varied together, instead of one
at a time
48. In a factorial design, in each complete trial
or replicate of the experiment, all possible
combination of the levels of the factors
are investigated.
e.g.
If there are a levels of factor A and b levels of factor B, each replicate
contains all ab treatment combinations
The model is of the form
Response = Constant + Effect of factor A + Effect of factor B
+ Interaction effect + Error term
49. Block designs
This is a design in which experimenter partitions the EU’s
in blocks, determines the allocation of treatments to
blocks, and assigns the EU’s within each block to the
treatments completely at random
The model is of the form
Response = Constant + effect of a block
+ effect of treatment + error
50. If the block size equals the number of treatments we
call this a randomized complete block design.
You can think of this as separate CRD's for each
block. By that I mean we know we want all the
treatments once in each block and we
RANDOMIZE TREATMENTS IN EACH BLOCK
Block Design: RCBD
51. RCBD Analysis: FC Example
1 1
1 2
1 3
2 1
2 2
2 3
3 1
3 2
3 3
1 1
1 2
1 3
2 1
2 2
2 3
3 1
3 2
3 3
1 1
1 2
1 3
2 1
2 2
2 3
3 1
3 2
3 3
Recall, the EU's in the
blocks are the time order
of reuses of same canister
1 1 means 1/2 tablet, low
water; 3 3 means 1 1/2
tablet, high water
Recall, we randomize
within each block (3 total
randomizations)
53. Designs with two blocking factors
These involves two major sources of variation that
have been designated as blocking factors.
The model is of the form
Response = Constant + effect of row block
+ effect of column block
+ effect of treatment + error
54. All Complex designs can be
constructed from and understood
in terms Of the three mentioned
basic designs
55.
56. Example( CRD)
A pharmaceutical manufacturer wants to investigate the
bioactivity of a new drug. A completely Randomized single
factor experiment was conducted With three dosage levels,
and the following results were obtained.
Dosage Observations
20 g
30 g
40 g
24 28 37 30
37 44 31 35
42 47 52 38
Is there evidence to indicate that dosage level affects
bioactivity? Use alpha of 0.05
57. Example( CRD)
A civil engineer is interested in determining whether four
different methods of estimating flood flow frequency produce
Equivalent estimates of peak discharge when applied to the same
Watershed. The resulting discharge data (in cubic feet per second)
Are shown below.
Estimation
Method
Observations
1
2
3
4
0.34 0.12 1.23 0.70 1.75 0.12
0.91 2.94 2.14 2.36 2.86 4.55
6.31 8.37 9.75 6.09 9.82 7.24
17.15 11.82 10.95 17.20 14.35 16.82
Is there a significant difference? use alpha = 0.05
58. Example( RCBD)
A medical device manufacturer produces vascular grafts (artificial veins). These
Artificial veins are produced using Resin. Frequently the grafts contains
defects known as flicks which is a main cause for rejection. The manufacturer
Suspects that extrusion pressure affects the occurrence of flicks and therefore
intends to conduct the experiment to investigate this hypothesis. However the
Resin is manufactured by an external supplier and the manufacturer and delivered
in batches. The manufacturer suspects that there will be batch to batch variation
and decided to Conduct a blocking design.
Extrusion
Pressure (PSI)
Batches of Resins
8500
8700
8900
9100
1 2 3 4 5 6
90.3
92.5
85.5
82.5
89.2
89.5
90.8
89.5
98.2
90.6
89.6
85.6
93.9
94.7
86.2
87.4
87.4
87
88
78.9
97.6
95.8
93.4
90.7
Is there evidence at 5%?
59. Example(LSD)
An experimenter is studying the effects of five different formulations of a
Chemical product on the burning rate. Each formulation is mixed from a batch
of raw materials that is Only Large enough for five formulations to be tested.
Furthermore the formulations are prepared by different operators and they
may be a substantial difference in Skill and experience. This tells us that
there are two nuisance factors.
Batches
Raw Materials
Operators
1
2
3
4
5
1 2 3 4 5
A=24 B=20 C=19 D=24 E=24
B=17 C=24 D=30 E=27 A=36
C=18 D=38 E=26 A=27 B=21
D=26 E=31 A=26 B=23 C=22
E=22 A=30 B=20 C=29 D=31
Is there a significant difference at 5% level of significance?
60. INTRODUCTION TO FACTORIAL DESIGNS
Experiments often involves several factors, and usually
the objective of the experimenter is to determine the
influence these factors have on the response.
Several approaches can be employed to deal when
faced with more than one treatments
Best – guess Approach
Experimenter select an arbitrary combinations of
treatments, test them and see what happens
61. One - Factor - at - a - time (OFAT)
Consists of selecting a starting point, or baseline set of
levels, for each factor, and then successively varying
each factor over its range with the other factors held
constant at the baseline level.
62. The valuable approach to dealing with
several factors is to conduct a
FACTORIAL EXPERIMENT
This is an experimental strategy in which
factors are varied together, instead of one
at a time
63. In a factorial design, in each complete trial
or replicate of the experiment, all possible
combination of the levels of the factors
are investigated.
e.g.
If there are a levels of factor A and b levels of factor B, each replicate
contains all ab treatment combinations
The model is of the form
Response = Constant + Effect of factor A + Effect of factor B
+ Interaction effect + Error term
64. B High
A High
B High
A Low
B Low
A Low
B Low
A High
Consider the following example (adapted from Montgomery, 2013)
of a two-factors (A and B) factorial
experiment with both design factors at two levels (High and Low)
5230
20 40
65. Main effect : Change in response produced by a
change in the level of a factor
Factor A
Main Effect = 40 + 52 _ 20 + 30
2 2
= 21
Factor B
Main Effect = ?
,Increasing factor A from low level to high lev
causes an average response increase of 21 un
67. At low level of factor B
The A effect = 50 – 20
= 30
At high level of factor B
The A effect = 12 - 40
= -28
The effect of A depends on the level chosen for factor B
68. “If the difference in response between the levels of one
factor is not the same at all levels of the other factors then
we say there is an interaction between the factors”
(Montgomery 2013)
The magnitude of the
interaction effect is the
average difference in
the two factor A effects
AB = (-28 – 30)
2
= -29
In this case, factor A has an effect, but it depends on the
level of factor B be chosen
A effect = 1
70. Factorial designs has
several advantages;
They are more efficient than One Factor at a Time
A factorial design is necessary when interactions
may be present to avoid misleading conclusions
Factorial designs allow the effect of a factor to be
estimated at a several levels of the other factors,
yielding conclusions that are valid over a range
of experimental conditions
71. he two factor Factorial Desig
The simplest types of factorial design involves
only two factors.
There are a levels of factor A and b levels of
factor B, and these are arranged in a factorial
design.
There are n replicates, and each replicate of the
experiment contains all the ab combination.
72. Example
An engineer is designing a battery for use in a device that will be
subjected to some extreme variations in temperature. The only design
parameter that he can select is the plate material for the battery.
For the purpose of testing temperature can be controlled in the product
development laboratory (Montgomery, 2013)
Life (in hours) Data
TemperatureMaterial
Type 15 70 125
130
74
150
159
138
168
1
2
3
155
180
188
126
110
160
34
80
136
106
174
150
40
75
122
115
120
139
20
82
25
58
96
82
70
58
70
45
104
60
73. The design has two factors each at three levels and is
then regarded as 32
factorial design.
The engineer wants to answer the following questions;
1. What effects do material type and temperature have on the life
of the battery?
2 .Is there a choice of material that would give uniformly long life
regardless of temperature?
Both factors are assumed to be fixed,
hence we have a fixed effect model
The design is a completely Randomized Design
74. Analysis of Variance for Battery life (in hours)
Source DF Seq SS Adj SS Adj MS F P-value
Material Type 2 10683.7 10683.7 5341.9 7.91 0.002
Temperature 2 39118.7 39118.7 19559.4 28.97 0.000
Material Type*Temperature 4 9613.8 9613.8 2403.4 3.56 0.019
Error 27 18230.7 18230.7 675.2
Total 35 77647.0
We have a significant interaction between temperature
and material type.
75. Interaction plot
Significant interaction is indicated by the lack of parallelism of the
lines, Longer life is attained at low temperature, regardless
Of material type
76. The General Factorial Design
The results for the two – factor factorial
design may be extended to the general
case where there are a levels of factor A,
b levels of factor B, c levels of factor C,
and so on, arranged in a factorial
experiment.
77. Sometimes, it is not feasible or practical
to completely randomize all of the runs
in a factorial.
The presence of a nuisance factor may
require that experiment be run in blocks.
The model is of the form
Response = Constant + Effect of factor A + Effect of factor B
+ interaction effect + Block Effect + Error term
78. The 2K
Factorial designs
This is a case of a factorial design with K factors, each
at only two levels.
These levels may be quantitative or qualitative.
A complete replicate of this design requires
2K
observation and is called 2K
factorial design.
Assumptions
1. The factors are fixed.
2. The designs are completely randomized.
3. The usual normality assumptions are satisfied.
79. The design with only two factors each at two levels is
called 22
factorial design
The levels of the factors may be arbitrarily called
“Low” and “High”
Factor
A B Treatment Combination
-
+
-
+
-
-
+
+
A Low, B Low
A High, B Low
A Low, B High
A High, B High
he order in which the runs are made is a completely
andomized experiment
(1)
a
b
ab
80. The four treatment combination in the design can be
represented by lower case letters
The high level factor in any treatment combination is
denoted by the corresponding lower case letter
The low level of a factor in a treatment combination is
represented by the absence of the corresponding letter
The average effect of a factor is the change in the
response produced by a change in the level of that
factor averaged over the levels of the other factor
81. The symbols (1), a, b, ab represents the total
of the observation at all n replicates
taken at a treatment combination
A main effect = 1/2n[ab + a – b – (1)]
B main effect = 1/2n[ab +b - a – (1)]
AB effect = 1/2n{[ab + (1) – a – b]
82. In experiments involving 2K
designs, it
is
always important to examine the
magnitude
and direction of the factor effect to
determine
which factors are likely to be importantEffect Magnitude and direction should always
be considered along with ANOVA, because the
ANOVA alone does not convey this information
83. Contrast A = ab + a – b – (1) = Total
effect of A
We can write the treatment combination in the order
(1), a, b, ab. Also called the standard order (or Yates order)
Treatment
Combination
Factorial Effect
I A B AB
(1)
a
b
ab
+
+
+
+
-
+
-
+
-
-
+
+
+
-
-
+
The above is also called the table of plus and minus signs
We define;
84. Suppose that three factors, A ,B and C, each at two levels
are of interest. The design is referred as 23
factorial design
Treatment
Combination
Factorial Effects
I A B AB C AC BC ABC
(1)
a
b
ab
c
ac
bc
abc
+
+
+
+
+
+
+
+
-
+
-
+
-
+
-
+
-
-
+
+
-
-
+
+
+
-
-
+
+
-
-
+
-
-
-
-
+
+
+
+
+
-
+
-
-
+
-
+
+
+
-
-
-
-
+
+
-
+
+
-
+
-
-
+
A contrast = [ab + a + ac + abc – (1) – b – c - bc
B contrast = ?
85. The design with K factors each at two levels is
called a 2K
factorial design
The treatment combination are written in
standard order using notation introduced
in a 22
and 23
designs
In General;