This document outlines objectives and concepts for a unit on statistical analysis in IB Diploma Biology. It discusses types of data, graphs, and statistics including mean, standard deviation, correlation, and significance testing. Key concepts covered are descriptive statistics like mean and standard deviation to summarize data, the importance of variability, and inferential statistics like hypothesis testing and p-values to draw conclusions about populations from samples. The goals are to calculate basic statistics, choose appropriate graphs, understand significance, and apply proper lab techniques and formats.
The document discusses objectives and concepts related to statistical analysis in biology, including:
- Types of data, graphs, and statistical analyses such as mean, standard deviation, and chi square analysis.
- Calculating and interpreting the mean and standard deviation of a data set to describe variability.
- Using standard deviation to compare the spread of data between samples and determine significance.
- Performing hypothesis testing using calculated t values, t tables, and p values to determine if differences between data sets are statistically significant.
1) The document discusses generating frequency tables and univariate charts in SPSS. It explains how to produce frequency tables, pie charts, bar charts, and histograms in SPSS.
2) It provides examples of frequency table components and properly formatted univariate charts.
3) The document concludes by summarizing religious, educational, and family background information learned about young adults in the 1980 GSS based on frequency tables.
This document provides an overview of descriptive statistics and graphing techniques used in survey research and psychology. It discusses getting to know data, levels of measurement, descriptive statistics for different data types, properties of the normal distribution, and non-normal distributions. Graphical techniques covered include bar graphs, histograms, pie charts, and box plots. The principles of graphing to maximize clarity and minimize clutter are also outlined.
This document provides an overview of key concepts related to data in biology including:
1. Qualitative and quantitative data types. Qualitative data relates to characteristics or descriptions while quantitative data uses numerical scales.
2. Methods for displaying and analyzing data including graphs, measures of central tendency (mean, median, mode), and standard deviation.
3. Statistical hypothesis testing using t-tests to compare two samples and determine if differences are statistically significant.
4. Correlation and scatter plots which show the relationship between two variables but do not prove causation.
This document provides an overview of how to use SPSS to conduct basic statistical analysis and present results. It outlines expectations for the workshop, including learning how to prepare an SPSS file, display and summarize data, and create graphical presentations. The document then covers key SPSS concepts like variables, data types, and examples. It also demonstrates how to perform descriptive statistics, frequency tables, crosstabs, measures of central tendency and dispersion. Finally, it discusses different methods of graphical presentation in SPSS like bar charts, histograms, box plots and more.
1) Statistics is the science of collecting, analyzing, and drawing conclusions from data. It is used to understand populations based on samples since directly measuring entire populations is often impossible.
2) There are two main types of data: qualitative data which relates to descriptive characteristics, and quantitative data which can be expressed numerically. Common statistical analyses include calculating the mean, standard deviation, and using t-tests, ANOVA, correlation, and chi-squared tests.
3) Statistical analyses allow researchers to determine uncertainties in measurements, compare groups, identify relationships between variables, and assess whether observed differences are likely due to chance or a factor being studied. Key concepts include null and alternative hypotheses, p-values, and effect size.
The document discusses objectives and concepts related to statistical analysis in biology, including:
- Types of data, graphs, and statistical analyses such as mean, standard deviation, and chi square analysis.
- Calculating and interpreting the mean and standard deviation of a data set to describe variability.
- Using standard deviation to compare the spread of data between samples and determine significance.
- Performing hypothesis testing using calculated t values, t tables, and p values to determine if differences between data sets are statistically significant.
1) The document discusses generating frequency tables and univariate charts in SPSS. It explains how to produce frequency tables, pie charts, bar charts, and histograms in SPSS.
2) It provides examples of frequency table components and properly formatted univariate charts.
3) The document concludes by summarizing religious, educational, and family background information learned about young adults in the 1980 GSS based on frequency tables.
This document provides an overview of descriptive statistics and graphing techniques used in survey research and psychology. It discusses getting to know data, levels of measurement, descriptive statistics for different data types, properties of the normal distribution, and non-normal distributions. Graphical techniques covered include bar graphs, histograms, pie charts, and box plots. The principles of graphing to maximize clarity and minimize clutter are also outlined.
This document provides an overview of key concepts related to data in biology including:
1. Qualitative and quantitative data types. Qualitative data relates to characteristics or descriptions while quantitative data uses numerical scales.
2. Methods for displaying and analyzing data including graphs, measures of central tendency (mean, median, mode), and standard deviation.
3. Statistical hypothesis testing using t-tests to compare two samples and determine if differences are statistically significant.
4. Correlation and scatter plots which show the relationship between two variables but do not prove causation.
This document provides an overview of how to use SPSS to conduct basic statistical analysis and present results. It outlines expectations for the workshop, including learning how to prepare an SPSS file, display and summarize data, and create graphical presentations. The document then covers key SPSS concepts like variables, data types, and examples. It also demonstrates how to perform descriptive statistics, frequency tables, crosstabs, measures of central tendency and dispersion. Finally, it discusses different methods of graphical presentation in SPSS like bar charts, histograms, box plots and more.
1) Statistics is the science of collecting, analyzing, and drawing conclusions from data. It is used to understand populations based on samples since directly measuring entire populations is often impossible.
2) There are two main types of data: qualitative data which relates to descriptive characteristics, and quantitative data which can be expressed numerically. Common statistical analyses include calculating the mean, standard deviation, and using t-tests, ANOVA, correlation, and chi-squared tests.
3) Statistical analyses allow researchers to determine uncertainties in measurements, compare groups, identify relationships between variables, and assess whether observed differences are likely due to chance or a factor being studied. Key concepts include null and alternative hypotheses, p-values, and effect size.
- Univariate analysis refers to analyzing one variable at a time using statistical measures like proportions, percentages, means, medians, and modes to describe data.
- These measures provide a "snapshot" of a variable through tools like frequency tables and charts to understand patterns and the distribution of cases.
- Measures of central tendency like the mean, median and mode indicate typical or average values, while measures of dispersion like the standard deviation and range indicate how spread out or varied the data are around central values.
SPSS is a widely used statistical software package for analyzing social science and medical data. It provides drop down menus and templates to make data analysis and presentation user-friendly compared to other statistical software. SPSS has tools for importing, cleaning, transforming, and analyzing data. Key functions include sorting cases, merging datasets, recoding variables, and checking for outliers and normal distribution of variables.
This document provides an overview of key concepts in statistics, machine learning, and data science. It discusses topics such as populations and samples, parameters and statistics, measures of central tendency and variation, hypothesis testing, linear and logistic regression, decision trees, overfitting and regularization, bagging and boosting, and random forests. The document also provides examples to illustrate statistical fundamentals like hypothesis testing, one sample t-tests, and type I and II errors.
The document discusses inferential statistics and its applications. It defines statistics as dealing with collecting, classifying, presenting, comparing, and interpreting numerical data to make inferences about a population. Inferential statistics help decision makers present information, draw conclusions from samples, seek relationships between variables, and make reliable forecasts. The document also distinguishes between descriptive statistics, parametric inferential statistics that assume normal distributions, and non-parametric inferential statistics that make no distribution assumptions.
Abstract: This PDSG workshop introduces basic concepts of statistics. Concepts covered are mean (average), median, mode, standard deviation discrete vs. continuous, normal distribution, sampling distribution, Z-scores and boxplots.
Level: Fundamental
Requirements: No prior programming or statistics knowledge required.
Error bars on graphs represent the variability or spread of data by showing the standard deviation or range. A normal distribution is a bell-shaped curve where the most frequent data points fall in the center. The standard deviation measures how spread out data points are from the mean and 68% of values fall within one standard deviation of the mean. A t-test statistically determines if two data sets are significantly different from each other. While a correlation means two variables vary together, it does not prove that one variable causes the other.
Application of Univariate, Bi-variate and Multivariate analysis Pooja k shettySundar B N
This document discusses different types of statistical analysis used to analyze data. Univariate analysis examines one variable at a time through methods like frequency distributions, histograms, and pie charts. Bivariate analysis considers the relationship between two variables, such as income and weight. Multivariate analysis studies three or more variables simultaneously, with applications in fields like social science, climatology, and medicine.
Basics of Educational Statistics (Inferential statistics)HennaAnsari
This document provides information about inferential statistics presented by Dr. Hina Jalal. It defines inferential statistics as using data from a sample to make inferences about the larger population from which the sample was taken. It discusses key areas of inferential statistics like estimating population parameters and testing hypotheses. It also explains the importance of inferential statistics in research for making conclusions from samples, comparing models, and enabling inferences about populations based on sample data. Flow charts are presented for selecting common statistical tests for comparisons, correlations, and regression.
Univariate analysis examines one variable at a time across a sample. There are three main tools used in univariate analysis: distribution of frequency, measures of central tendency (mean, median, mode), and measures of dispersion. Distribution examines individual values, range, and charts. Central tendency measures the average or middle value. Dispersion measures the spread around the central tendency, such as the standard deviation and range. Common univariate analysis procedures include frequencies, descriptives, and explore in SPSS.
Statistical analysis and its applications can be used in many fields including pharmaceutical research, clinical trials, public health, epidemiology, genetics, and demographics. Some key uses of statistics include evaluating drug effects, comparing drug treatments, exploring associations between diseases and risk factors, and analyzing clinical trial and genomics data. Measures of central tendency, dispersion, and other statistical methodologies help researchers draw conclusions from collected data.
This document outlines statistical analysis techniques that can be performed in SPSS, including loading and preparing data, descriptive statistics like frequencies and cross tabulations, inferential statistics like t-tests, ANOVA, correlation, and reliability analysis, and exporting results. Chi-square tests examine relationships between categorical variables while t-tests compare means and ANOVA examines differences in means between groups. Correlation analyzes relationships between interval variables.
A little summary on several types of computer intensive statistical methods developed from the fantastic book by Malcolm Haddon titled "Modeling and Quantitative Methods in Fisheries"
Authors: Daniele Baker and Stephanie Johnson
This document summarizes a discussion between Susan Athey and Guido Imbens on the relationship between machine learning and causal inference. It notes that while machine learning excels at prediction problems using large datasets, it has weaknesses when it comes to causal questions. Econometrics and statistics literature focuses more on formal theories of causality. The document proposes combining the strengths of both fields by developing machine learning methods that can estimate causal effects, accounting for issues like endogeneity and treatment effect heterogeneity. It outlines some open problems and directions for future research at the intersection of these fields.
The use of data and its modelling in science provides meaningful interpretation of real world problems. This presentation provides an easy to understand overview of data visualization and analytics , and snippets of data science applications using R - programming.
The document discusses descriptive statistics and inferential statistics. Descriptive statistics are used to describe basic features of data through simple summaries, while inferential statistics are used to make inferences beyond the sample data to general populations. Some common descriptive statistics are measures of central tendency, dispersion, frequency, and contingency tables. Inferential statistics allow for comparisons between groups and determining the probability of observed differences occurring by chance. Regression analysis is also discussed as a technique used to model relationships between dependent and independent variables and understand how changes in independent variables impact the dependent variable.
This document provides an overview of descriptive statistics and inferential statistics. Descriptive statistics are used to describe basic features of data through simple summaries, while inferential statistics are used to make generalizations beyond the sample data. Key concepts covered include measures of central tendency and dispersion, the general linear model, dummy variables, experimental and quasi-experimental designs, analysis of variance, analysis of covariance, and regression analysis.
This document provides an introduction to biostatistics. It outlines several key objectives of a biostatistics course including understanding descriptive statistics, statistical inference, common tests and their assumptions. It defines important statistical concepts like population, sample, parameters, statistics, variables, and types of statistical analysis. Descriptive statistics are used to summarize data, while inferential statistics allow generalizing from samples to populations. Examples of potential statistical abuses are also provided.
We review important concepts from Chapters 1-5 of the statistics textbook.
1) Descriptive statistics summarize sample data, while inferential statistics make predictions about populations from samples.
2) Variables can be categorical (nominal, ordinal) or quantitative (continuous, discrete), which affects analysis methods.
3) Random sampling and random assignment in experiments reduce bias to obtain reliable data.
4) Probability distributions, the normal distribution, and the Central Limit Theorem are important concepts for statistical inference.
Descriptive analysis and descriptive analytics involve examining and summarizing data using techniques like charts, graphs, and narratives to identify patterns. Common visualization tools include pie charts, bar charts, histograms, and more. Tableau, Excel, and Datawrapper are popular tools that allow users to import data and generate various visualizations. Queries allow users to sort, filter, and extract specific information from large datasets using clauses like ORDER BY and WHERE. Hypothesis testing uses the null and alternative hypotheses to determine if experimental results are statistically significant or due to chance. Analysis of variance (ANOVA) specifically tests hypotheses by comparing means across independent groups.
This document provides an overview and summary of key concepts from chapters 10 and 11 of the book "How to Design and Evaluate Research in Education". It discusses both descriptive and inferential statistics. For descriptive statistics, it defines common measures like mean, median, standard deviation, and explains how they are used to summarize sample data. For inferential statistics, it outlines statistical techniques like hypothesis testing, confidence intervals, and parametric and nonparametric tests that allow researchers to generalize from samples to populations. It provides examples of how these statistical concepts are applied in educational research.
- Univariate analysis refers to analyzing one variable at a time using statistical measures like proportions, percentages, means, medians, and modes to describe data.
- These measures provide a "snapshot" of a variable through tools like frequency tables and charts to understand patterns and the distribution of cases.
- Measures of central tendency like the mean, median and mode indicate typical or average values, while measures of dispersion like the standard deviation and range indicate how spread out or varied the data are around central values.
SPSS is a widely used statistical software package for analyzing social science and medical data. It provides drop down menus and templates to make data analysis and presentation user-friendly compared to other statistical software. SPSS has tools for importing, cleaning, transforming, and analyzing data. Key functions include sorting cases, merging datasets, recoding variables, and checking for outliers and normal distribution of variables.
This document provides an overview of key concepts in statistics, machine learning, and data science. It discusses topics such as populations and samples, parameters and statistics, measures of central tendency and variation, hypothesis testing, linear and logistic regression, decision trees, overfitting and regularization, bagging and boosting, and random forests. The document also provides examples to illustrate statistical fundamentals like hypothesis testing, one sample t-tests, and type I and II errors.
The document discusses inferential statistics and its applications. It defines statistics as dealing with collecting, classifying, presenting, comparing, and interpreting numerical data to make inferences about a population. Inferential statistics help decision makers present information, draw conclusions from samples, seek relationships between variables, and make reliable forecasts. The document also distinguishes between descriptive statistics, parametric inferential statistics that assume normal distributions, and non-parametric inferential statistics that make no distribution assumptions.
Abstract: This PDSG workshop introduces basic concepts of statistics. Concepts covered are mean (average), median, mode, standard deviation discrete vs. continuous, normal distribution, sampling distribution, Z-scores and boxplots.
Level: Fundamental
Requirements: No prior programming or statistics knowledge required.
Error bars on graphs represent the variability or spread of data by showing the standard deviation or range. A normal distribution is a bell-shaped curve where the most frequent data points fall in the center. The standard deviation measures how spread out data points are from the mean and 68% of values fall within one standard deviation of the mean. A t-test statistically determines if two data sets are significantly different from each other. While a correlation means two variables vary together, it does not prove that one variable causes the other.
Application of Univariate, Bi-variate and Multivariate analysis Pooja k shettySundar B N
This document discusses different types of statistical analysis used to analyze data. Univariate analysis examines one variable at a time through methods like frequency distributions, histograms, and pie charts. Bivariate analysis considers the relationship between two variables, such as income and weight. Multivariate analysis studies three or more variables simultaneously, with applications in fields like social science, climatology, and medicine.
Basics of Educational Statistics (Inferential statistics)HennaAnsari
This document provides information about inferential statistics presented by Dr. Hina Jalal. It defines inferential statistics as using data from a sample to make inferences about the larger population from which the sample was taken. It discusses key areas of inferential statistics like estimating population parameters and testing hypotheses. It also explains the importance of inferential statistics in research for making conclusions from samples, comparing models, and enabling inferences about populations based on sample data. Flow charts are presented for selecting common statistical tests for comparisons, correlations, and regression.
Univariate analysis examines one variable at a time across a sample. There are three main tools used in univariate analysis: distribution of frequency, measures of central tendency (mean, median, mode), and measures of dispersion. Distribution examines individual values, range, and charts. Central tendency measures the average or middle value. Dispersion measures the spread around the central tendency, such as the standard deviation and range. Common univariate analysis procedures include frequencies, descriptives, and explore in SPSS.
Statistical analysis and its applications can be used in many fields including pharmaceutical research, clinical trials, public health, epidemiology, genetics, and demographics. Some key uses of statistics include evaluating drug effects, comparing drug treatments, exploring associations between diseases and risk factors, and analyzing clinical trial and genomics data. Measures of central tendency, dispersion, and other statistical methodologies help researchers draw conclusions from collected data.
This document outlines statistical analysis techniques that can be performed in SPSS, including loading and preparing data, descriptive statistics like frequencies and cross tabulations, inferential statistics like t-tests, ANOVA, correlation, and reliability analysis, and exporting results. Chi-square tests examine relationships between categorical variables while t-tests compare means and ANOVA examines differences in means between groups. Correlation analyzes relationships between interval variables.
A little summary on several types of computer intensive statistical methods developed from the fantastic book by Malcolm Haddon titled "Modeling and Quantitative Methods in Fisheries"
Authors: Daniele Baker and Stephanie Johnson
This document summarizes a discussion between Susan Athey and Guido Imbens on the relationship between machine learning and causal inference. It notes that while machine learning excels at prediction problems using large datasets, it has weaknesses when it comes to causal questions. Econometrics and statistics literature focuses more on formal theories of causality. The document proposes combining the strengths of both fields by developing machine learning methods that can estimate causal effects, accounting for issues like endogeneity and treatment effect heterogeneity. It outlines some open problems and directions for future research at the intersection of these fields.
The use of data and its modelling in science provides meaningful interpretation of real world problems. This presentation provides an easy to understand overview of data visualization and analytics , and snippets of data science applications using R - programming.
The document discusses descriptive statistics and inferential statistics. Descriptive statistics are used to describe basic features of data through simple summaries, while inferential statistics are used to make inferences beyond the sample data to general populations. Some common descriptive statistics are measures of central tendency, dispersion, frequency, and contingency tables. Inferential statistics allow for comparisons between groups and determining the probability of observed differences occurring by chance. Regression analysis is also discussed as a technique used to model relationships between dependent and independent variables and understand how changes in independent variables impact the dependent variable.
This document provides an overview of descriptive statistics and inferential statistics. Descriptive statistics are used to describe basic features of data through simple summaries, while inferential statistics are used to make generalizations beyond the sample data. Key concepts covered include measures of central tendency and dispersion, the general linear model, dummy variables, experimental and quasi-experimental designs, analysis of variance, analysis of covariance, and regression analysis.
This document provides an introduction to biostatistics. It outlines several key objectives of a biostatistics course including understanding descriptive statistics, statistical inference, common tests and their assumptions. It defines important statistical concepts like population, sample, parameters, statistics, variables, and types of statistical analysis. Descriptive statistics are used to summarize data, while inferential statistics allow generalizing from samples to populations. Examples of potential statistical abuses are also provided.
We review important concepts from Chapters 1-5 of the statistics textbook.
1) Descriptive statistics summarize sample data, while inferential statistics make predictions about populations from samples.
2) Variables can be categorical (nominal, ordinal) or quantitative (continuous, discrete), which affects analysis methods.
3) Random sampling and random assignment in experiments reduce bias to obtain reliable data.
4) Probability distributions, the normal distribution, and the Central Limit Theorem are important concepts for statistical inference.
Descriptive analysis and descriptive analytics involve examining and summarizing data using techniques like charts, graphs, and narratives to identify patterns. Common visualization tools include pie charts, bar charts, histograms, and more. Tableau, Excel, and Datawrapper are popular tools that allow users to import data and generate various visualizations. Queries allow users to sort, filter, and extract specific information from large datasets using clauses like ORDER BY and WHERE. Hypothesis testing uses the null and alternative hypotheses to determine if experimental results are statistically significant or due to chance. Analysis of variance (ANOVA) specifically tests hypotheses by comparing means across independent groups.
This document provides an overview and summary of key concepts from chapters 10 and 11 of the book "How to Design and Evaluate Research in Education". It discusses both descriptive and inferential statistics. For descriptive statistics, it defines common measures like mean, median, standard deviation, and explains how they are used to summarize sample data. For inferential statistics, it outlines statistical techniques like hypothesis testing, confidence intervals, and parametric and nonparametric tests that allow researchers to generalize from samples to populations. It provides examples of how these statistical concepts are applied in educational research.
A teacher calculated the standard deviation of test scores to see how close students scored to the mean grade of 65%. She found the standard deviation was high, indicating outliers pulled the mean down. An employer also calculated standard deviation to analyze salary fairness, finding it slightly high due to long-time employees making more. Standard deviation measures dispersion from the mean, with low values showing close grouping and high values showing a wider spread. It is calculated using the variance formula of summing the squared differences from the mean divided by the number of values.
Basics in Epidemiology & Biostatistics 2 RSS6 2014RSS6
- The document discusses parametric and non-parametric data, describing key differences. Non-parametric data is for small samples and variables that are not normally distributed, requiring no assumptions. Descriptive statistics include range, rank, median, and interquartile range.
- It also covers topics like mean, standard deviation, standard error, confidence intervals, and the normal and t-distributions as they relate to parametric statistical analysis of sample and population data. The central limit theorem is also referenced.
This document provides an overview of quantitative data analysis methods for medical education research. It discusses summary measures, hypothesis testing, statistical methodologies, sample size determination, and additional resources for statistical support. Key points covered include choosing appropriate statistical tests based on study design, translating research questions into testable hypotheses, interpreting p-values and making conclusions, and factors that influence required sample size such as effect size and variability.
This document discusses various statistical concepts including outliers, transforming data, normalizing data, weighting data, robustness, and homoscedasticity and heteroscedasticity. Outliers are values far from other data points and should be carefully examined before removing. Data can be transformed using logarithms, square roots, or other functions to better fit a normal distribution or equalize variances between groups. Normalizing data puts variables on comparable scales. Weighting data adjusts for under- or over-representation in samples. Robust tests are resistant to violations of assumptions. Homoscedasticity refers to equal variances between groups while heteroscedasticity refers to unequal variances.
This document discusses processing and analyzing data. It defines processing as editing, coding, classifying, and tabulating raw data. Analysis is categorized as descriptive or inferential. Descriptive analysis studies distributions through measures like mean, median and correlation, while inferential analysis determines relationships through regression and hypothesis testing. Multivariate analysis simultaneously analyzes more than two variables using techniques like multiple regression, discriminant analysis, and ANOVA. Proper data analysis requires understanding concepts like sampling, standard error, and estimation to make valid statistical inferences.
This document summarizes quantitative data analysis techniques for summarizing data from samples and generalizing to populations. It discusses variables, simple and effect statistics, statistical models, and precision of estimates. Key points covered include describing data distribution through plots and statistics, common effect statistics for different variable types and models, ensuring model fit, and interpreting precision, significance, and probability to generalize from samples.
data analysis in Statistics-2023 guide 2023ayesha455941
- Statistics is the science of collecting, analyzing, interpreting, presenting, and organizing data. It is used across various fields including physics, business, social sciences, and healthcare.
- There are two main branches of statistical analysis: descriptive statistics, which summarizes and describes data, and inferential statistics, which draws conclusions about populations based on samples.
- Key concepts include populations, samples, parameters, statistics, and the differences between descriptive and inferential analysis. Measures of central tendency like the mean, median, and mode are used to describe data, while measures of variation like the range, variance, and standard deviation quantify how spread out the data is.
Introduction to Statistics53004300.pptTripthiDubey
This document provides an introduction to descriptive statistics and measures of central tendency. It discusses the difference between descriptive statistics of a population versus inferential statistics of samples. It then describes three common measures of central tendency: the mean, median, and mode. It explains how to calculate each measure and the advantages and disadvantages of each. The document concludes by discussing different types of graphs that can be used to organize and present descriptive statistics, including histograms, pie charts, line graphs, and scatter plots.
This document provides an overview of statistical methods used in research. It discusses descriptive statistics such as frequency distributions and measures of central tendency. It also covers inferential statistics including hypothesis testing, choice of statistical tests, and determining sample size. Various types of variables, measurement scales, charts, and distributions are defined. Inferential topics include correlation, regression, and multivariate techniques like multiple regression and factor analysis.
The document discusses various steps involved in analyzing and interpreting data, including developing an analysis plan, collecting and cleaning data, analyzing the data using appropriate techniques, interpreting the results by drawing conclusions and recommendations while also considering limitations. It provides examples of different analysis techniques like descriptive statistics, inferential statistics, and qualitative data analysis and emphasizes the importance of interpreting data in the context of the research questions.
I do not have enough information to determine what percentage of residents are asleep now versus at the beginning of this talk. As an AI assistant without direct observation of the audience, I do not have data on individual residents' states of alertness over time.
This document provides an overview of key concepts in quantitative data analysis, including:
1. It describes four scales of measurement (nominal, ordinal, interval, ratio) and warns against using statistics inappropriate for the scale of data.
2. It distinguishes between parametric and non-parametric statistics, descriptive and inferential statistics, and the types of variables and analyses.
3. It explains important statistical concepts like hypotheses, one-tailed and two-tailed tests, distributions, significance, and avoiding type I and II errors in hypothesis testing.
This document provides an introduction to inferential statistics. It defines key terms like probability, random variables, and probability distributions such as the normal distribution. It discusses how inferential statistics can be used to make generalizations about populations based on samples. Hypothesis testing is introduced as a core technique in inferential statistics for testing proposed relationships. Concepts discussed in more depth include the normal distribution, parameters like the mean and standard deviation, sampling error, confidence intervals, and significance levels.
This document provides an overview of descriptive statistics and inferential statistics. Descriptive statistics are used to describe basic features of data through simple summaries, while inferential statistics are used to make inferences about populations based on samples. Examples of descriptive statistics include measures of central tendency, dispersion, frequency distributions and contingency tables. Inferential statistics allow for comparisons between groups and populations through techniques like t-tests, analysis of variance, regression analysis, and other general linear models.
The document discusses the origin of the first cells on Earth. It states that cells can only be formed through the division of pre-existing cells, so the first cells must have arisen from non-living material through a process known as abiogenesis. Abiogenesis likely occurred in four stages: 1) the non-living synthesis of simple organic molecules, 2) the assembly of these molecules into complex polymers, 3) the development of polymers that could self-replicate, and 4) the encapsulation of these molecules within membranes. Early Earth had a reducing atmosphere containing gases like hydrogen, nitrogen, and methane that could have contributed to the non-living synthesis of organic compounds from which the first cells developed.
Membranes control the composition of cells through active and passive transport. Materials move across membranes via simple diffusion, facilitated diffusion, osmosis, and active transport. The sodium-potassium pump uses active transport to move ions against their gradients in axons. Vesicles transport materials within cells from the ER to the Golgi and plasma membrane by budding off and fusing. Endocytosis transports materials into cells while exocytosis releases them out of cells.
Membranes control the composition of cells through active and passive transport. Passive transport involves diffusion of substances down a concentration gradient and does not require energy. There are three main types of passive transport: simple diffusion of small molecules, osmosis of water molecules, and facilitated diffusion of larger molecules via membrane proteins. Active transport moves substances against a concentration gradient and requires energy. Membranes play a key role in cellular function by regulating what passes in and out of cells.
The structure of biological membranes allows them to be fluid and dynamic. Membranes are made of a phospholipid bilayer with proteins and cholesterol embedded within. Phospholipids form bilayers due to their amphipathic properties - their hydrophobic tails orient inward while hydrophilic heads remain on the outer surfaces. Membrane proteins perform diverse functions and can be integral or peripheral. Cholesterol increases membrane stability while reducing fluidity. Early models of membrane structure proposed protein layers sandwiching the bilayer, but evidence demonstrated proteins are mobile within the bilayer, leading to the current fluid mosaic model.
The document discusses membrane transport mechanisms, including passive transport processes like simple diffusion, facilitated diffusion, and osmosis as well as active transport. It provides examples of sodium-potassium pumps, potassium channels, and vesicles. The importance of osmotic control in medical procedures is highlighted. Summaries of laboratory techniques for estimating osmolarity in tissues are also included.
The structure of biological membranes allows them to be fluid and dynamic. Phospholipid molecules spontaneously arrange into a bilayer structure in water due to their amphipathic properties. This structure orients the hydrophobic tails of the phospholipids inward, shielded from water, while the hydrophilic heads remain in contact with water. Additional components such as membrane proteins and cholesterol are embedded within the phospholipid bilayer and influence membrane properties such as fluidity. Cholesterol increases the packing of phospholipids and regulates membrane fluidity and permeability.
Eukaryotic cells have a more complex structure than prokaryotic cells due to compartmentalization by membrane-bound organelles. An electron micrograph of pancreatic exocrine cells clearly shows organelles such as the nucleus, mitochondria, rough endoplasmic reticulum, Golgi apparatus, and vesicles. These organelles have specialized functions, for example the nucleus contains genetic material, mitochondria produce ATP through respiration, and the endoplasmic reticulum and Golgi apparatus are involved in protein transport and modification.
1. The cell theory states that all living things are composed of cells, cells are the basic unit of structure and function in living things, and new cells are produced from existing cells.
2. Unicellular organisms carry out all the functions of life within a single cell, including metabolism, reproduction, response to stimuli, homeostasis, excretion, nutrition, and growth. These functions can be observed in organisms like Paramecium and Chlorella through processes like contracting vacuoles and photosynthesis.
3. As cells increase in size, their surface area to volume ratio decreases, limiting their ability to exchange materials and wastes. This limitation on cell size is an important factor in the cell theory.
Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...indexPub
The recent surge in pro-Palestine student activism has prompted significant responses from universities, ranging from negotiations and divestment commitments to increased transparency about investments in companies supporting the war on Gaza. This activism has led to the cessation of student encampments but also highlighted the substantial sacrifices made by students, including academic disruptions and personal risks. The primary drivers of these protests are poor university administration, lack of transparency, and inadequate communication between officials and students. This study examines the profound emotional, psychological, and professional impacts on students engaged in pro-Palestine protests, focusing on Generation Z's (Gen-Z) activism dynamics. This paper explores the significant sacrifices made by these students and even the professors supporting the pro-Palestine movement, with a focus on recent global movements. Through an in-depth analysis of printed and electronic media, the study examines the impacts of these sacrifices on the academic and personal lives of those involved. The paper highlights examples from various universities, demonstrating student activism's long-term and short-term effects, including disciplinary actions, social backlash, and career implications. The researchers also explore the broader implications of student sacrifices. The findings reveal that these sacrifices are driven by a profound commitment to justice and human rights, and are influenced by the increasing availability of information, peer interactions, and personal convictions. The study also discusses the broader implications of this activism, comparing it to historical precedents and assessing its potential to influence policy and public opinion. The emotional and psychological toll on student activists is significant, but their sense of purpose and community support mitigates some of these challenges. However, the researchers call for acknowledging the broader Impact of these sacrifices on the future global movement of FreePalestine.
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2. Objectives of this Unit:
Types of Data, Types of Graphs, Applications and Statistics to match your data
o Bar Graphs, Line Graph, Scatter Plot, Histogram, Pie Chart
o Mean, S.D., Regression, Chi Square Analysis, Anova
State that error bars are a graphical representation of the variability of data
o Range and standard deviation show the variability/spread in the data
Calculate the mean and standard deviation of a set of values
Using Excel formulas
o Given a mean and S.D. state the range for different parameters
State the term standard deviation is used to summarize the spread of values around the mean
o 68% of all data +/- 1 standard deviation, 95% within 2 SD
Explain how S.D. is useful for comparing the means and spread of data between two or more
samples
o Greater S.D. shows greater variability of data
o This can be used to inter reliability in methods or results BUT in Biology we also expect
variability
Deduce the significance of the difference between two sets of data using calculated values for t and
tables
o Using t value and t table and critical values
o Directly calculating P values using excel in lab reports
o Difference between P and T
Explain that correlation does not establish that there is a causal relationship between two variables
Proper Lab Format
Designing Lab Process
3. What are statistics?
• Statistics are numbers used to:
Describe and draw conclusions about DATA
• These are called descriptive (or “univariate”) and
inferential (or “analytical”) statistics, respectively.
4. Variables
• A variable is anything we can measure/observe
• Three types:
– Continuous: values span an uninterrupted range (e.g. height)
– Discrete: only certain fixed values are possible (e.g. counts)
– Categorical: values are qualitatively assigned (e.g. low/med/hi)
• Dependence in variables:
“Dependent variables depend on independent ones”
– Independent variable – variable you are changing
– Dependent variable – variable you measure to see result
– Controlled variables – variables that can also impact the
dependent variable that you identify as needed to not vary
*** Experimental Control – NOT the same as controlled variables
5. Descriptive statistics
Numerical
– Mean
– Variance
• Standard deviation
• Standard error
– Median
– Mode
– Skew
– etc.
Graphical
– Histogram
– Boxplot
– Scatterplot
– etc.
Techniques to summarize data
7. What graph to use ?
Line Scatter Histogram Bar
Appropriat
e for data
when:
Important
Features
Include
Sample and
other notes
Outlier - An outlier is an observation that lies an abnormal distance from other values in
a random sample from a population. In a sense, this definition leaves it up to the analyst
(or a consensus process) to decide what will be considered abnormal. Before abnormal
observations can be singled out, it is necessary to characterize normal observations.
11. Additional central tendency measures
M = X(n+1)/2 (n is odd)
Median: the 50th percentile
(n is even)
Xn/2 + X(n/2)+1
2
M =
Mode: the most common value
1, 1, 2, 4, 6, 6, 6, 7, 7, 7, 7, 8, 8, 9, 9, 10, 12, 15
Which to use: mean, median or mode?
13. Variance:
Most important measure of “dispersion”
s2 = S
n - 1
Sample Variance
(Xi - X)2
From now on, we’ll ignore sample vs. population. But remember:
We are almost always interested in the population, but can measure only a sample.
15. The Friendly Histogram
• Histograms represent the distribution of data
• They allow you to visualize the mean, median,
mode, variance, and skew at once!
16. Constructing a Histogram is Easy
X (data)
7.4
7.6
8.4
8.9
10.0
10.3
11.5
11.5
12.0
12.3
Histogram of X
Value
6 8 10 12 14
0
1
2
3
Frequency
(count)
17. Interpreting Histograms
• Mean?
• Median?
• Mode?
• Standard
deviation?
• Variance?
• Skew?
(which way does the
“tail” point?)
• Shape?
Value
0 20 40 60
0
20
40
Frequency
18. Interpreting Histograms
• Mean?
= 9.2
• Median? = 6.5
• Mode?
= 3
• Standard
deviation? = 8.3
• Variance?
• Skew?
(which way does the
“tail” point?)
• Shape?
Value
0 20 40 60
0
20
40
Frequency
20. Boxplots also
summarize a lot
of information...
Within each sample:
6
5
4
3
2
1
SC Ba Se Es Da Is Fe
Island
Weight(kg)
Compared across samples:
25% percentile
75% percentile
Median
“Outliers”
22. The Normal Distribution
aka “Gaussian” distribution
• Occurs frequently in nature
• Especially for measures that
are based on sums, such as:
– sample means
– body weight
– “error”
• Many statistics are based on
the assumption of normality
– You must make sure your data
are normal, or try something
else!
Sample normal data:
Histogram + theoretical distribution
(i.e. sample vs. population)
23. Properties of the Normal Distribution
• Symmetric
Mean = Median = Mode
• Theoretical percentiles can be computed exactly
~68% of data are within 1 standard deviation of the mean
>99% within 3 s.d.
“skinny tails”
25. What if my data aren’t Normal?
• It’s OK!
• Although lots of data are Gaussian (because of the CLT),
many simply aren’t.
– Example: Fire return intervals
Time between fires (yr)
• Solutions:
– Transform data to make it
normal (e.g. take logs)
– Use a test that doesn’t
assume normal data
• Don’t worry, there are plenty
• Especially these days...
• Many stats work OK as long as data are “reasonably” normal
28. Inference: the process by which we draw
conclusions about an unknown based on
evidence or prior experience.
In statistics: make conclusions about a
population based on samples taken from
that population.
Important: Your sample must reflect the
population you’re interested in, otherwise
your conclusions will be misleading!
29. Statistical Hypotheses
• Should be related to a scientific hypothesis!
• Very often presented in pairs:
– Null Hypothesis (H0):
the “boring” hypothesis of “no difference”
– Alternative Hypothesis (HA)
the interesting hypothesis of “there is an effect”
• Statistical tests attempt to (mathematically)
reject the null hypothesis
30. Significance
• Your sample will never match H0 perfectly,
even when H0 is in fact true
• The question is whether your sample is
different enough from the expectation under
H0 to be considered significant
• If your test finds a significant difference, then
you reject H0.
31. p-Values Measure Significance
The p-value of a test is the probability of observing data
at least as extreme as your sample, assuming H0 is true
• If p is very small, it is unlikely that H0 is true
(in other words, if H0 were true, your observed sample would be unlikely)
• How small does p have to be?
– 0.05 is a common cutoff
• If p<0.05, then there is less than 5% chance that you would observe
your sample if the null hypothesis was true.
32. ‘Proof’ in statistics
• Failing to reject (i.e. “accepting”) H0 does not
prove that H0 is true!
• And accepting HA doesn’t prove that HA is true
either!
Why?
• Statistical inference tries to draw conclusions
about the population from a small sample
– By chance, the samples may be misleading
– Example: if you always accept H0 at p=0.05, then
1 in 20 times you will be wrong!
33. Play it Safe
Avoid using the term Prove in your labs
Instead say “the data accepts or supports” the
hypothesis
Watch out for reaching – classic student error,
stick to the scope of your lab data in your
conclusions, this is not your life work.
34.
35. “Why is this Biology?”
Variation in populations.
Variability in results.
affects
Confidence
in conclusions.
The key methodology in Biology is hypothesis
testing through experimentation.
Carefully-designed and controlled
experiments and surveys give us quantitative
(numeric) data that can be compared.
We can use the data collected to test our
hypothesis and form explanations of the
processes involved… but only if we can be
confident in our results.
We therefore need to be able to evaluate the
reliability of a set of data and the significance
of any differences we have found in the data.
Image: 'Transverse section of part of a stem of a Dead-nettle (Lamium sp.) showing+a+vascular+bundle+and+part+of+the+cortex'
http://www.flickr.com/photos/71183136@N08/6959590092 Found on flickrcc.net
36. “Which medicine should I prescribe?”
Image from: http://www.msf.org/international-activity-report-2010-sierra-leone
Donate to Medecins Sans Friontiers through Biology4Good: http://i-biology.net/about/biology4good/
37. “Which medicine should I prescribe?”
Image from: http://www.msf.org/international-activity-report-2010-sierra-leone
Donate to Medecins Sans Friontiers through Biology4Good: http://i-biology.net/about/biology4good/
Generic drugs are out-of-patent, and are
much cheaper than the proprietary
(brand-name) equivalents. Doctors need to
balance needs with available resources.
Which would you choose?
38. “Which medicine should I prescribe?”
Image from: http://www.msf.org/international-activity-report-2010-sierra-leone
Donate to Medecins Sans Friontiers through Biology4Good: http://i-biology.net/about/biology4good/
Means (averages) in Biology are almost
never good enough. Biological systems
(and our results) show variability.
Which would you choose now?
39. Hummingbirds are nectarivores (herbivores
that feed on the nectar of some species of
flower).
In return for food, they pollinate the flower.
This is an example of mutualism –
benefit for all.
As a result of natural selection,
hummingbird bills have evolved.
Birds with a bill best suited to
their preferred food source have
the greater chance of survival.
Photo: Archilochus colubris, from wikimedia commons, by Dick Daniels.
40. Researchers studying comparative anatomy collect
data on bill-length in two species of hummingbirds:
Archilochus colubris
(red-throated hummingbird) and
Cynanthus latirostris (broadbilled hummingbird).
To do this, they need to collect sufficient
relevant, reliable data so they can test
the Null hypothesis (H0) that:
“there is no significant difference
in bill length between the two species.”
Photo: Archilochus colubris (male), wikimedia commons, by Joe Schneid
41. The sample size must
be large enough to provide
sufficient reliable data and for us
to carry out relevant statistical
tests for significance.
We must also be mindful of
uncertainty in our measuring tools
and error in our results.
Photo: Broadbilled hummingbird (wikimedia commons).
42.
43. The mean is a measure of the central tendency
of a set of data.
Table 1: Raw measurements of bill length in
A. colubris and C. latirostris.
Bill length (±0.1mm)
n A. colubris C. latirostris
1 13.0 17.0
2 14.0 18.0
3 15.0 18.0
4 15.0 18.0
5 15.0 19.0
6 16.0 19.0
7 16.0 19.0
8 18.0 20.0
9 18.0 20.0
10 19.0 20.0
Mean
s
Calculate the mean using:
• Your calculator
(sum of values / n)
• Excel
=AVERAGE(highlight raw data)
n = sample size. The bigger the better.
In this case n=10 for each group.
All values should be centred in the cell, with
decimal places consistent with the measuring
tool uncertainty.
44. The mean is a measure of the central tendency
of a set of data.
Table 1: Raw measurements of bill length in
A. colubris and C. latirostris.
Bill length (±0.1mm)
n A. colubris C. latirostris
1 13.0 17.0
2 14.0 18.0
3 15.0 18.0
4 15.0 18.0
5 15.0 19.0
6 16.0 19.0
7 16.0 19.0
8 18.0 20.0
9 18.0 20.0
10 19.0 20.0
Mean 15.9 18.8
s
Raw data and the mean need to have
consistent decimal places (in line with
uncertainty of the measuring tool)
Uncertainties must be included.
Descriptive table title and number.
66. Standard deviation is a measure of the spread of
most of the data.
Table 1: Raw measurements of bill length in
A. colubris and C. latirostris.
Bill length (±0.1mm)
n A. colubris C. latirostris
1 13.0 17.0
2 14.0 18.0
3 15.0 18.0
4 15.0 18.0
5 15.0 19.0
6 16.0 19.0
7 16.0 19.0
8 18.0 20.0
9 18.0 20.0
10 19.0 20.0
Mean 15.9 18.8
s 1.91 1.03 Standard deviation can have one more
decimal place.=STDEV (highlight RAW data).
Which of the two sets of data has:
a. The longest mean bill length?
a. The greatest variability in the data?
67. Standard deviation is a measure of the spread of
most of the data.
Table 1: Raw measurements of bill length in
A. colubris and C. latirostris.
Bill length (±0.1mm)
n A. colubris C. latirostris
1 13.0 17.0
2 14.0 18.0
3 15.0 18.0
4 15.0 18.0
5 15.0 19.0
6 16.0 19.0
7 16.0 19.0
8 18.0 20.0
9 18.0 20.0
10 19.0 20.0
Mean 15.9 18.8
s 1.91 1.03 Standard deviation can have one more
decimal place.=STDEV (highlight RAW data).
Which of the two sets of data has:
a. The longest mean bill length?
a. The greatest variability in the data?
C. latirostris
A. colubris
68. Standard deviation is a measure of the spread of
most of the data. Error bars are a graphical
representation of the variability of data.
Which of the two sets of data has:
a. The highest mean?
a. The greatest variability in the data?
A
B
Error bars could represent standard deviation, range or confidence intervals.
69. Put the error bars for standard deviation on our graph.
70. Put the error bars for standard deviation on our graph.
71. Put the error bars for standard deviation on our graph.
Delete the horizontal error bars
72. A. colubris,
15.9mm
C. latirostris,
18.8mm
0.0
5.0
10.0
15.0
20.0
MeanBilllength(±0.1mm)
Species of hummingbird
Graph 1: Comparing mean bill lengths in two
hummingbird species, A. colubris and C. latirostris.
(error bars = standard deviation)
Title is adjusted to
show the source of the
error bars. This is very
important.
You can see the clear
difference in the size of
the error bars.
Variability has been
visualised.
The error bars overlap
somewhat.
What does this mean?
73. The overlap of a set of error bars gives a clue as to the
significance of the difference between two sets of data.
Large overlap No overlap
Lots of shared data points
within each data set.
Results are not likely to be
significantly different from
each other.
Any difference is most likely
due to chance.
No (or very few) shared data
points within each data set.
Results are more likely to be
significantly different from
each other.
The difference is more likely
to be ‘real’.
74.
75.
76.
77. A. colubris,
15.9mm
(n=10)
C. latirostris,
18.8mm
(n=10)
-3.0
2.0
7.0
12.0
17.0
22.0
MeanBilllength(±0.1mm)
Species of hummingbird
Graph 1: Comparing mean bill lengths in two
hummingbird species, A. colubris and C.
latirostris.(error bars = standard deviation)
Our results show a very small overlap
between the two sets of data.
So how do we know if the difference is
significant or not?
We need to use a statistical test.
The t-test is a statistical
test that helps us determine
the significance of the
difference between the
means of two sets of data.
78.
79. The Null Hypothesis (H0):
“There is no significant
difference.”
This is the ‘default’ hypothesis that we always test.
In our conclusion, we either accept the null hypothesis or reject it.
A t-test can be used to test whether the difference between two means is significant.
• If we accept H0, then the means are not significantly different.
• If we reject H0, then the means are significantly different.
Remember:
• We are never ‘trying’ to get a difference. We design carefully-controlled experiments and
then analyse the results using statistical analysis.
80. P value = 0.1 0.05 0.02 0.01
confidence 90% 95% 98% 99%
degreesoffreedom
1 6.31 12.71 31.82 63.66
2 2.92 4.30 6.96 9.92
3 2.35 3.18 4.54 5.84
4 2.13 2.78 3.75 4.60
5 2.02 2.57 3.37 4.03
6 1.94 2.45 3.14 3.71
7 1.89 2.36 3.00 3.50
8 1.86 2.31 2.90 3.36
9 1.83 2.26 2.82 3.25
10 1.81 2.23 2.76 3.17
We can calculate the value of ‘t’ for a given set of data and compare it
to critical values that depend on the size of our sample and the level of
confidence we need.
Example two-tailed t-table.
“Degrees of Freedom (df)” is
the total sample size minus
two.
What happens to the value of P
as the confidence in the results
increases?
What happens to the critical
value as the confidence level
increases?
“critical values”
81. P value = 0.1 0.05 0.02 0.01
confidence 90% 95% 98% 99%
degreesoffreedom
1 6.31 12.71 31.82 63.66
2 2.92 4.30 6.96 9.92
3 2.35 3.18 4.54 5.84
4 2.13 2.78 3.75 4.60
5 2.02 2.57 3.37 4.03
6 1.94 2.45 3.14 3.71
7 1.89 2.36 3.00 3.50
8 1.86 2.31 2.90 3.36
9 1.83 2.26 2.82 3.25
10 1.81 2.23 2.76 3.17
We can calculate the value of ‘t’ for a given set of data and compare it
to critical values that depend on the size of our sample and the level of
confidence we need.
Example two-tailed t-table.
“Degrees of Freedom (df)” is
the total sample size minus
two*.
We usually use P<0.05 (95%
confidence) in Biology, as our
data can be highly variable
*Simple explanation: we are working in
two directions – within each population
and across populations.
“critical values”
83. t was calculated as 2.15 (this is done for you)
t cv
2.15
If t < cv, accept H0 (there is no significant difference)
If t > cv, reject H0 (there is a significant difference)
2-tailed t-table source: http://www.medcalc.org/manual/t-distribution.php
84. 0.05
t was calculated as 2.15 (this is done for you)
t cv
2.15
If t < cv, accept H0 (there is no significant difference)
If t > cv, reject H0 (there is a significant difference)
2-tailed t-table source: http://www.medcalc.org/manual/t-distribution.php
85. 2.069
0.05
t was calculated as 2.15 (this is done for you)
t cv
2.15 > 2.069
If t < cv, accept H0 (there is no significant difference)
If t > cv, reject H0 (there is a significant difference)
2-tailed t-table source: http://www.medcalc.org/manual/t-distribution.php
86. 2.069
0.05
t was calculated as 2.15 (this is done for you)
t cv
2.15 > 2.069
If t < cv, accept H0 (there is no significant difference)
If t > cv, reject H0 (there is a significant difference)
Conclusion:
“There is a significant difference in the wing spans of
the two populations of birds.”
2-tailed t-table source: http://www.medcalc.org/manual/t-distribution.php
89. 2.0452.045
2-tailed t-table source: http://www.medcalc.org/manual/t-distribution.php
“There is no significant difference in the size of shells
between north-side and south-side snail populations.”
91. 2.086
2.086
2-tailed t-table source: http://www.medcalc.org/manual/t-distribution.php
“There is a significant difference in the resting heart
rates between the two groups of swimmers.”
92. Excel can jump straight to a value of P for our results.
One function (=ttest) compares both sets of data.
As it calculates P directly (the
probability that the difference is due
to chance), we can determine
significance directly.
In this case, P=0.00051
This is much smaller than 0.005, so
we are confident that we can:
reject H0.
The difference is unlikely to be due to
chance.
Conclusion:
There is a significant difference in bill
length between A. colubris and C.
latirostris.
93.
94. Two tails: we assume data are normally distributed, with two ‘tails’ moving away from mean.
Type 2 (unpaired): we are comparing one whole population with the other whole population.
(Type 1 pairs the results of each individual in set A with the same individual in set B).
95.
96. 95% Confidence Intervals can also be plotted as error bars.
These give a clearer indication of the significance of a result:
• Where there is overlap, there is not a significant difference
• Where there is no overlap, there is a significant difference.
• If the overlap (or difference) is small, a t-test should still be carried out.
no overlap
=CONFIDENCE.NORM(0.05,stdev,samplesize)
e.g =CONFIDENCE.NORM(0.05,C15,10)
97. Error bars can have very different purposes.
Standard deviation
• You really need to know this
• Look for relative size of bars
• Used to indicate spread of most
of the data around the mean
• Can imply reliability of data
95% Confidence Intervals
• Adds value to labs where we are
looking for differences.
• Look for overlap, not size
• Overlap no sig. diff.
• No overlap sig. dif.
98. Interesting Study: Do “Better” Lecturers Cause More Learning?
Find out more here: http://priceonomics.com/is-this-why-ted-talks-seem-so-convincing/
Students watched a one-minute video of a lecture. In one video, the lecturer was
fluent and engaging. In the other video, the lecturer was less fluent.
They predicted how much they would learn on the topic
(genetics) and this was compared to their actual score.
(Error bars = standard deviation).
n=21 n=21
99. Interesting Study: Do “Better” Lecturers Cause More Learning?
Find out more here: http://priceonomics.com/is-this-why-ted-talks-seem-so-convincing/
Students watched a one-minute video of a lecture. In one video, the lecturer was
fluent and engaging. In the other video, the lecturer was less fluent.
They predicted how much they would learn on the topic
(genetics) and this was compared to their actual score.
(Error bars = standard deviation).
Is there a significant difference in the actual learning?
n=21 n=21
100. Interesting Study: Do “Better” Lecturers Cause More Learning?
Find out more here: http://priceonomics.com/is-this-why-ted-talks-seem-so-convincing/
Evaluate the study:
1. What do the error bars (standard deviation) tell us about reliability?
2. How valid is the study in terms of sufficiency of data (population sizes (n))?
n=21 n=21
105. http://diabetes-obesity.findthedata.org/b/240/Correlations-between-diabetes-obesity-and-physical-activity
Interpreting Graphs: See – Think – Wonder
See: What is factual about the graph?
• What are the axes?
• What is being plotted
• What values are present?
Think: How is the graph interpreted?
• What relationship is present?
• Is cause implied?
• What explanations are possible and
what explanations are not possible?
Wonder: Questions about the graph.
• What do you need to
know more about?
See – Think - Wonder
Visible Thinking Routine
107. Correlation does not imply causality.
Pirates vs global warming, from http://en.wikipedia.org/wiki/Flying_Spaghetti_Monster#Pirates_and_global_warming
108. Cartoon from: http://www.xkcd.com/552/
Correlation does not imply causation, but it does waggle its eyebrows
suggestively and gesture furtively while mouthing "look over there."
Check out these funny “Correlations”
109. Correlation does not imply causality.
Pirates vs global warming, from http://en.wikipedia.org/wiki/Flying_Spaghetti_Monster#Pirates_and_global_warming
Where correlations exist, we must then design solid scientific experiments to determine the
cause of the relationship. Sometimes a correlation exist because of confounding variables –
conditions that the correlated variables have in common but that do not directly affect each
other.
To be able to determine causality through experimentation we need:
• One clearly identified independent variable
• Carefully measured dependent variable(s) that can be attributed to change in the
independent variable
• Strict control of all other variables that might have a measurable impact on the
dependent variable.
We need: sufficient relevant, repeatable and statistically significant data.
Some known causal relationships:
• Atmospheric CO2 concentrations and global warming
• Atmospheric CO2 concentrations and the rate of photosynthesis
• Temperature and enzyme activity