Unit ibp801 t l multiple correlation a24022022
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The multiple correlation coefficient denotes the correlation between one variable and multiple other variables. It is represented as R1.234...k, where 1 is the variable being correlated and 2, 3, 4, etc. are the other variables. As an example, R1.23 would represent correlating variable 1 with variables 2 and 3 simultaneously by creating a linear combination of 2 and 3. The document then discusses using multiple correlation to correlate academic achievement with a linear combination of anxiety and intelligence.
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DESIGN OF EXPERIMENTS (DOE)
DOE is invented by Sir Ronald Fisher in 1920’s and 1930’s.
The following designs of experiments will be usually followed:
Completely randomised design(CRD)
Randomised complete block design(RCBD)
Latin square design(LSD)
Factorial design or experiment
Confounding
Split and strip plot design
FACTORIAL DESIGN
When a several factors are investigated simultaneously in a single experiment such experiments are known as factorial experiments. Though it is not an experimental design, indeed any of the designs may be used for factorial experiments.
For example, the yield of a product depends on the particular type of synthetic substance used and also on the type of chemical used.
ADVANTAGES OF FACTORIAL DESIGN.
Factorial experiments are advantageous to study the combined effect of two or more factors simultaneously and analyze their interrelationships. Such factorial experiments are economic in nature and provide a lot of relevant information about the phenomenon under study. It also increases the efficiency of the experiment.
It is an advantageous because a wide range of factor combination are used. This will give us an idea to predict about what will happen when two or more factors are used in combination.
DISADVANTAGES
It is disadvantageous because the execution of the experiment and the statistical analysis becomes more complex when several treatments combinations or factors are involved simultaneously.
It is also disadvantageous in cases where may not be interested in certain treatment combinations but we are forced to include them in the experiment. This will lead to wastage of time and also the experimental material.
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A special set of factorial experiment consist of experiments in which all factors have 2 levels such experiments are referred to generally as 2n factorials.
If there are four factors each at two levels the experiment is known as 2x2x2x2 or 24 factorial experiment. On the other hand if there are 2 factors each with 3 levels the experiment is known as 3x3 or 32 factorial experiment. In general if there are n factors each with p levels then it is known as pn factorial experiment.
The calculation of the sum of squares is as follows:
Correction factor (CF) = (𝐺𝑇)2/𝑛
GT = grand total
n = total no of observations
Total sum of squares = ∑▒〖𝑥2−𝐶𝐹〗
Replication sum of squares (RSS) = ((𝑅1)2+(𝑅2)2+…+(𝑅𝑛)2)/𝑛 - CF
Or
1/𝑛 ∑▒𝑅2−𝐶𝐹
2(Cube) FACTORIAL DESIGN
In this type of design, one independent variable has 2 levels, and the other independent variable has 3 levels.
Estimating the effect:
In a factorial design the main effect of an independent variable is its overall effect averaged across all other independent variable.
Effect of a factor A is the average of the runs where A is at the high level minus the average of the runs
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factorial design.pptx
DESIGN OF EXPERIMENTS (DOE)
DOE is invented by Sir Ronald Fisher in 1920’s and 1930’s.
The following designs of experiments will be usually followed:
Completely randomised design(CRD)
Randomised complete block design(RCBD)
Latin square design(LSD)
Factorial design or experiment
Confounding
Split and strip plot design
FACTORIAL DESIGN
When a several factors are investigated simultaneously in a single experiment such experiments are known as factorial experiments. Though it is not an experimental design, indeed any of the designs may be used for factorial experiments.
For example, the yield of a product depends on the particular type of synthetic substance used and also on the type of chemical used.
ADVANTAGES OF FACTORIAL DESIGN.
Factorial experiments are advantageous to study the combined effect of two or more factors simultaneously and analyze their interrelationships. Such factorial experiments are economic in nature and provide a lot of relevant information about the phenomenon under study. It also increases the efficiency of the experiment.
It is an advantageous because a wide range of factor combination are used. This will give us an idea to predict about what will happen when two or more factors are used in combination.
DISADVANTAGES
It is disadvantageous because the execution of the experiment and the statistical analysis becomes more complex when several treatments combinations or factors are involved simultaneously.
It is also disadvantageous in cases where may not be interested in certain treatment combinations but we are forced to include them in the experiment. This will lead to wastage of time and also the experimental material.
2(square) FACTORIAL EXPERIMENT
A special set of factorial experiment consist of experiments in which all factors have 2 levels such experiments are referred to generally as 2n factorials.
If there are four factors each at two levels the experiment is known as 2x2x2x2 or 24 factorial experiment. On the other hand if there are 2 factors each with 3 levels the experiment is known as 3x3 or 32 factorial experiment. In general if there are n factors each with p levels then it is known as pn factorial experiment.
The calculation of the sum of squares is as follows:
Correction factor (CF) = (𝐺𝑇)2/𝑛
GT = grand total
n = total no of observations
Total sum of squares = ∑▒〖𝑥2−𝐶𝐹〗
Replication sum of squares (RSS) = ((𝑅1)2+(𝑅2)2+…+(𝑅𝑛)2)/𝑛 - CF
Or
1/𝑛 ∑▒𝑅2−𝐶𝐹
2(Cube) FACTORIAL DESIGN
In this type of design, one independent variable has 2 levels, and the other independent variable has 3 levels.
Estimating the effect:
In a factorial design the main effect of an independent variable is its overall effect averaged across all other independent variable.
Effect of a factor A is the average of the runs where A is at the high level minus the average of the runs
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Confounding is a confusing word in experimental design. I hope that one can easily understand the topic.
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This document provides information on general factor factorial designs. It defines factorial designs as experiments that study the effects of two or more factors by investigating all possible combinations of the factors' levels. Factorial designs are more efficient than one-factor-at-a-time experiments and allow for the estimation of factor effects at different levels of other factors. However, factorial designs become prohibitively large as the number of factors increases and can be difficult to interpret when interactions are present. The document also provides examples of designing two-factor factorial experiments using completely randomized and randomized complete block designs.
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This document summarizes a crossover design experiment testing the effects of two rations (A and B) on milk yield in cows. It describes that 8 cows were given either ration A or B in their better and poorer lactation periods, with the rations switched between periods. Milk yields were recorded for each cow and period. An ANOVA analysis found a significant difference between lactation periods but no significant differences between rations or cows. Crossover designs control for fluctuations due to time and can be used with small numbers of treatments. However, they require a longer time period and can be impacted by period, sequence, and carryover effects.
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Non parametric test
The document discusses parametric and non-parametric tests. It provides examples of commonly used non-parametric tests including the Mann-Whitney U test, Kruskal-Wallis test, and Wilcoxon signed-rank test. For each test, it gives the steps to perform the test and interpret the results. Non-parametric tests make fewer assumptions than parametric tests and can be used when the data is ordinal or does not meet the assumptions of parametric tests. They provide a distribution-free alternative for analyzing data.
Regression
Multiple regression analysis allows researchers to examine the relationship between one dependent or outcome variable and two or more independent or predictor variables. It extends simple linear regression to model more complex relationships. Stepwise regression is a technique that automates the process of building regression models by sequentially adding or removing variables based on statistical criteria. It begins with no variables in the model and adds variables one at a time based on their contribution to the model until none improve it significantly.
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Hi Dr. Kyzar and ClassWhen looking at the evidence, one notes .docx
Hi Dr. Kyzar and Class
When looking at the evidence, one notes that there is an independent variable and that a spearman’s ranked correlation is used in the analysis of the data. The spearman’s correlation can be referred to as the nonparametric version of the Pearson correlation. The correlation coefficient by Spearman’s measures the direction and the strength of the association between two variables which are ranked. For the use of this test, one requires two variables which are either ratio, interval, or ordinal. The spearman correlation is used when the assumptions of the Pearson correlation have been violated. The spearman’s correlation determines the direction and the strength of the monotonic relationship between these two variables as opposed to the strength and direction of the linear relationship (Schober et al., 2018). The person correlation is the one which looks at the linear relationship between the two variables. The monotonic relationship refers to the relationship when either as the value of one increases the other variable is increasing or as the value of one of the variable is increasing, the other variable is decreasing (Bakdash and Marusich, 2017). The spearman correlation is used in measuring the direction and strength of monotonic association between these two variables. The monotonicity is considered to be less restrictive compared to that of the linear relationship. When one normally picks the measure of association, it is after looking at the pattern of the data which is observed. When one looks at the scatterplot and it shows a relationship which looks monotonic, then one would use the spearman’s correlation (Akoglu, 2018). If there is a liner relationship, then one uses a person’s correlation as it shows the direction and strength of the linear relationship. The correct level of correlation analysis which should have been used in this case is Pearson’s correlation analysis. The data that has been presented has a normal distribution and has therefore met all assumptions of the Pearson’s correlation. There is manipulation of the independent variable and the Pearson’s is the better level.
Correlational analysis and association are sometimes used interchangeably but they have slightly different meanings when it comes to the technicality. Association refers to the presence of any relationship between two variables but the correlation is used to refer where there is existence of a linear relationship between the variables. The terms are often used interchangeably when it comes to various texts despite the differences. The correlation analysis explores the association which is there between two or more variables. The correlational analysis makes an inference about the strength of the relationship between the variables (Akoglu, 2018). There are several differences which can be shown when it comes to association. A scatter plot, for example, shows the association between two variables. The scatter plot matrix indicates t.
Correlation analysis
This document discusses correlation analysis and its various types. Correlation is the degree of relationship between two or more variables. There are three stages to solve correlation problems: determining the relationship, measuring significance, and establishing causation. Correlation can be positive, negative, simple, partial, or multiple depending on the direction and number of variables. It is used to understand relationships, reduce uncertainty in predictions, and present average relationships. Conditions like probable error and coefficient of determination help interpret correlation values.
raprap-opaw.pptx
There are three types of relationships between variables: null, covariant, and influential. Null relationships mean variables are independent, covariant relationships mean changes in one variable correlate with changes in the other, and influential relationships mean one variable causes changes in the other. Regression analysis is used to determine if covariant relationships exist by finding the line of best fit between two variables. Three characteristics describe relationships: statistical significance, linear pattern, and strength.
Learning Outcomes1. Describe correlations and regression a.docx
Learning Outcomes
1. Describe correlations and regression analyses.
2. Analyze the relationship between correlations and predictions.
Introduction
In contrast to Week Three where statistical tests focusing on differences were introduced, in Week Four, you will explore relationships in statistical tests. Correlations and linear regression techniques will be utilized and results will be evaluated and interpreted. The written assignments in Weeks One, Two, and Three prepared you for analyzing and evaluating research articles. In the written assignment this week, you will focus less on actual research and more on the report writing process.
If you work in a social/behavioral sciences field, you will likely be asked to conduct research (i.e., conduct an experiment or study) and create a report based on your findings. Generally speaking, people who investigate a scientific hypothesis have a responsibility to the scientific community to share those results. This is particularly true when that investigation adds to/or contradicts previous research. The research report outlines each step that was done during the research and summarizes the results and conclusions. The goal is to give the reader enough information so that the methods and results can be accurately evaluated, and the conclusions can be replicated if necessary. Although the research report this week will be based on hypothetical and/or fictitious data, the process of creating a correctly formatted research report with all the necessary components will provide you with important skills as you progress through your degree and as you continue into the world of the social/behavioral sciences.
Required Resources
Required Text
Read from the course text, Statistics for the Behavioral & Social Sciences:
· Chapter 8: Correlation
· Chapter 9: Linear Regression
Recommended Resources
Articles
1. Kirwan, J., Lounsbury, J., Gibson, L. (2010). Self-direction in learning and personality: The Big Five and narrow personality traits in relation to learner self-direction. International Journal of Self-Directed Learning, 7(2), 21-34. Retrieved from http://sdlglobal.com/IJSDL/IJSDL7.2-2010.pdf#page=25
· This is an article about personality, self-directed learning, and scale development and the major traits that may affect them. These include: agreeableness, conscientiousness, emotional stability, and openness. It incorporates correlation and regression procedures with tables that display the statistical results.
2. Stark, P.B. (2013). Chapter 9: Regression. Retrieved from http://www.stat.berkeley.edu/~stark/SticiGui/Text/regression.htm
· This website contains several video lectures and examples of how regression is used.
3. Trochim, W. M. (2006). Correlation. In Research Methods Knowledge Base. Retrieved from http://www.socialresearchmethods.net/kb/statcorr.php
· This website contains many tutorials and tools for statistical analyses and methods used in the social sciences. This pa ...
correlational research method
The document discusses correlational research methods, which examine relationships between two measured variables without manipulating variables. Correlational research can describe the direction (positive/negative), form (linear/nonlinear), and strength (magnitude) of relationships. Statistical analyses like Pearson correlation and regression can analyze correlational data. While correlational research allows observation of many variables, it cannot prove causation, as relationships may be due to other unmeasured variables.
Correlation and regression
Correlation and its importance
Types of correlation
Partial correlation
Mutiple correlation
Correlation coefficients
Regression
Multiple regression
Central tedancy & correlation project - 1
This document contains a final term project report submitted by three students to their professor. The report summarizes statistical techniques including correlation, regression, and measures of central tendency. For correlation, the document defines correlation, describes the correlation coefficient and different types of correlation. It also discusses the history and uses of correlation. For regression, it defines regression, describes the regression coefficient and line, and discusses the history and uses of regression. Finally, it defines different measures of central tendency including mean, median, mode, and discusses their advantages and disadvantages. The report is presented in a table of contents and contains examples, formulas and multiple choice questions.
Inferential Statistics - DAY 4 - B.Ed - AIOU
Inferential Statistics - Introduction to Inferential Statistics - Importance of Inferential Statistics in Research - Hypothesis Testing - T-Test
Correlation and regression
The document discusses correlation and regression analysis. It defines correlation as the statistical relationship between two variables, where a change in one variable corresponds to a change in the other. The key types of correlation are positive, negative, simple, partial and multiple, and linear and non-linear. Regression analysis establishes the average relationship between an independent and dependent variable in order to predict or estimate values of the dependent variable based on the independent variable. Methods for studying correlation include scatter diagrams and Karl Pearson's coefficient of correlation, while regression analysis uses equations to model the linear relationship between variables.
Unit i bp801 t k spearman coefficient of correlation24022022
The Spearman's rank correlation coefficient is a nonparametric measure of the monotonic relationship between two ranked variables. It assesses how well the relationship between two variables can be described using a monotonic function. Unlike Pearson's correlation, the Spearman's correlation does not assume a linear relationship between variables and can be used when assumptions of interval/ratio scaling and bivariate normality are not met. The Spearman's correlation measures statistical dependence between two variables using a monotonic function to represent their relationship.
Correlation and Regression Analysis.pptx
Correlation and Regression analysis is one of the important concepts of statistics which could be used to understand the relationship between the variables.
CORRELATION ANALYSIS NOTES.pdf
STATISTICS FOR DECISION MAKING - CORRELATION ANALYSIS, MEANING, TYPES, METHODS OF CALCULATION OF CORRELATION
Assessment 2 ContextIn many data analyses, it is desirable.docx
Assessment 2 Context
In many data analyses, it is desirable to compute a coefficient of association. Coefficients of association are quantitative measures of the amount of relationship between two variables. Ultimately, most techniques can be reduced to a coefficient of association and expressed as the amount of relationship between the variables in the analysis. There are many types of coefficients of association. They express the mathematical association in different ways, usually based on assumptions about the data. The most common coefficient of association you will encounter is the Pearson product-moment correlation coefficient (symbolized as the italicized r), and it is the only coefficient of association that can safely be referred to as simply the "correlation coefficient". It is common enough so that if no other information is provided, it is reasonable to assume that is what is meant.
Correlation coefficients are numbers that give information about the strength of relationship between two variables, such as two different test scores from a sample of participants. The coefficient ranges from -1 through +1. Coefficients between 0 and +1 indicate a positive relationship between the two scores, such as high scores on one test tending to come from people with high scores on the second. The other possible relationship, which is every bit as useful, is a negative correlation between -1 and 0. A negative correlation possesses no less predictive power between the two scores. The difference is that high scores on one measure are associated with low scores on the other.
An example of the kinds of measures that might correlate negatively is absences and grades. People with higher absences will be expected to have lower grades. When a correlation is said to be significant, it can be shown that the correlation is significantly different form zero in the population. A correlation of zero means no relationship between variables. A correlation other than zero means the variables are related. As the coefficient gets further from zero (toward +1 or -1), the relationship becomes stronger.Interpreting Correlation: Magnitude and Sign
Interpreting a Pearson's correlation coefficient (rXY) requires an understanding of two concepts:
· Magnitude.
· Sign (+/-).
The magnitude refers to the strength of the linear relationship between Variable X and Variable
The rXY ranges in values from -1.00 to +1.00. To determine magnitude, ignore the sign of the correlation, and the absolute value of rXY indicates the extent to which Variable X and Variable Y are linearly related. For correlations close to 0, there is no linear relationship. As the correlation approaches either -1.00 or +1.00, the magnitude of the correlation increases. Therefore, for example, the magnitude of r = -.65 is greater than the magnitude of r = +.25 (|.65| > |.25|).
In contrast to magnitude, the sign of a non-zero correlation is either negative or positive.
These labels are not interpreted ...
Assessment 2 ContextIn many data analyses, it is desirable.docx
Assessment 2 Context
In many data analyses, it is desirable to compute a coefficient of association. Coefficients of association are quantitative measures of the amount of relationship between two variables. Ultimately, most techniques can be reduced to a coefficient of association and expressed as the amount of relationship between the variables in the analysis. There are many types of coefficients of association. They express the mathematical association in different ways, usually based on assumptions about the data. The most common coefficient of association you will encounter is the Pearson product-moment correlation coefficient (symbolized as the italicized r), and it is the only coefficient of association that can safely be referred to as simply the "correlation coefficient". It is common enough so that if no other information is provided, it is reasonable to assume that is what is meant.
Correlation coefficients are numbers that give information about the strength of relationship between two variables, such as two different test scores from a sample of participants. The coefficient ranges from -1 through +1. Coefficients between 0 and +1 indicate a positive relationship between the two scores, such as high scores on one test tending to come from people with high scores on the second. The other possible relationship, which is every bit as useful, is a negative correlation between -1 and 0. A negative correlation possesses no less predictive power between the two scores. The difference is that high scores on one measure are associated with low scores on the other.
An example of the kinds of measures that might correlate negatively is absences and grades. People with higher absences will be expected to have lower grades. When a correlation is said to be significant, it can be shown that the correlation is significantly different form zero in the population. A correlation of zero means no relationship between variables. A correlation other than zero means the variables are related. As the coefficient gets further from zero (toward +1 or -1), the relationship becomes stronger.Interpreting Correlation: Magnitude and Sign
Interpreting a Pearson's correlation coefficient (rXY) requires an understanding of two concepts:
· Magnitude.
· Sign (+/-).
The magnitude refers to the strength of the linear relationship between Variable X and Variable
The rXY ranges in values from -1.00 to +1.00. To determine magnitude, ignore the sign of the correlation, and the absolute value of rXY indicates the extent to which Variable X and Variable Y are linearly related. For correlations close to 0, there is no linear relationship. As the correlation approaches either -1.00 or +1.00, the magnitude of the correlation increases. Therefore, for example, the magnitude of r = -.65 is greater than the magnitude of r = +.25 (|.65| > |.25|).
In contrast to magnitude, the sign of a non-zero correlation is either negative or positive.
These labels are not interpreted .
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Data Processing and Statistical Treatment: Spreads and Correlation
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Learning Outcomes1. Describe correlations and regression a.docx
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Unit i bp801 t k spearman coefficient of correlation24022022
Unit i bp801 t k spearman coefficient of correlation24022022
Assessment 2 ContextIn many data analyses, it is desirable.docx
Assessment 2 ContextIn many data analyses, it is desirable.docx
Assessment 2 ContextIn many data analyses, it is desirable.docx
Assessment 2 ContextIn many data analyses, it is desirable.docx
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This document provides an introduction to correlation. It defines correlation as quantifying the relationship between two quantitative variables. A positive correlation means high values of one variable are associated with high values of the other, while a negative correlation means high values of one variable are associated with low values of the other. The document uses a data set measuring socioeconomic status and bicycle helmet use across neighborhoods to illustrate these concepts. It shows the data follows a negative correlation, with higher socioeconomic status associated with lower helmet use. The correlation coefficient is introduced as a measure of the strength and direction of correlation.
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Unit ibp801 t l multiple correlation a24022022
- 1. Multiple correlation coefficient Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 1
- 2. 1. The multiple correlation coefficient denoting a correlation of one variable with multiple other variables. 2. The multiple correlation coefficient is denoted as R1.234...k which denotes that 1 is correlated with 2, 3, 4, up to k variables. For example, we want to compute multiple correlation between 1 with 2 and 3 then it is expressed as R1.23. In this case we create a linear combination of the 2 and 3 which is correlated with 1. Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 2
- 3. 3. We continue with the same example which we have discussed for partial and semipartial correlations. 4. This example has academic achievement, anxiety and intelligence as three variables. 5. The correlation between academic achievement with the linear combination of anxiety and intelligence is multiple correlation. Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 3
- 4. What does multiple correlation tell us? A multiple correlation coefficient (R) yields the maximum degree of liner relationship that can be obtained between two or more independent variables and a single dependent variable. Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 4
- 5. What is the difference between simple and multiple correlation? The distinction between simple, partial and multiple correlation is based upon the number of variables studied. When only two variables are studied it is a problem of simple correlation. In multiple correlation three or more variables are studied simultaneously. Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 5
- 6. How do you correlate multiple variables? One way to quantify the relationship between two variables is to use the Pearson correlation coefficient, which is a measure of the linear association between two variables. It always takes on a value between -1 and 1 where: -1 indicates a perfectly negative linear correlation between two variables Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 6
- 7. What are the uses of multiple correlation? A multiple correlation coefficient (R) yields the maximum degree of liner relationship that can be obtained between two or more independent variables and a single dependent variable. Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 7
- 8. Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 8