Statistics for the Behavioural Sciences: An Introduction

Part I: Introduction and Basic Concepts. Why is Statistics Useful in the Behavioural Sciences? Measurement Scales. Descriptive and Inferential Statistics. What is an Experiment? Part II: Descriptive Statistics. Organising Raw Data. Frequency Distributions and Histograms. Grouped Data. Stem-and-leaf Diagrams. Summarising Data. Measures of Central Tendency: Mode, Median and Mean. Advantages and Disadvantages of Mode, Median and Mean. A Useful Digression on the Sigma Notation. Measures of Dispersion (or Variability). Further on the Mean, Variance and Standard Deviation of Frequency Distributions. How to Calculate the Combined Mean and the Combined Variance of Several Samples. Properties of Estimators. Mean and Variance of Linearly Transformed Data. Part III: Introduction to Probability. Why Are Some Notions of Probability Useful? Some Preliminary Definitions and the Concept of Probability. Venn Diagrams and Probability. The Addition Rule and the Multiplication Rule of Probability. Probability Trees. Conditional Probability. Independence and Conditional Probability. Bayes's Theorem. Part IV: Probability Distributions and the Binomial Distribution. Introduction. Probability Distributions. Calculating the Mean (µ) of a Probability Distribution. Calculating the Variance (sigma-square) and the Standard Deviation (sigma) of a Probability Distribution. Orderings (or Permutations). Combinations. The Binomial Distribution. Mean and Variance of the Binomial Distribution. How to Use the Binomial Distribution in Testing Hypotheses. The Sign Test. Further on the Binomial Distribution and Its Use in Hypothesis Testing. Part V: Continuous Random Variables and the Normal Distribution. Introduction. Continuous Random Variables and Their Distribution. The Normal Distribution. The Standard Normal Distribution. Hypothesis Testing and the Normal Distribution. Type I and Type II Errors. One-tailed and Two-tailed Statistical Tests. Using the Normal Distribution as an Approximation of the Binomial Distribution. Part VI: The Chi-square Distribution and the Analysis of Categorical Data. Introduction. The Chi-square Distribution. The Pearson's Chi-square Test. The Pearson's Chi-square Goodness of Fit Test. Further on the Goodness of Fit Test. Assumptions Underlying the Use of Pearson's Chi-square Test. Pearson's Chi-square Test and the Analysis of 2 x 2 Contingency Tables. Further on the Degrees of Freedom and the Calculation of the Expected Frequencies for any Contingency Table. The Analysis of R x C Contingency Tables. One- and Two-tailed Tests. How to Measure the Strength of the Association between Variables in a Contingency Table. A Fundamental Conceptual Equation in Data Analysis: Magnitude of a Significance Test = Size of the Effect x Size of the Study. An Important Note on the Inclusion of Non-occurrences in Contingency Tables. Part VII: Statistical Tests on Proportions. Introduction. Statistical Tests on the Proportion of Successes in a Sample. Confidence Intervals for Population Proportions. Statistical Tests on the Difference between the Proportions of Successes from Two Independent Samples. Confidence Intervals for the Differences between Two Independent Population Proportions. Statistical Tests on the Differences between Non-independent Proportions of Successes (McNemar Test). Part VIII: Sampling Distribution of the Mean and Its Use in Hypothesis Testing. Introduction. The Sampling Distribution of the Mean and the Central Limit Theorem. Testing Hypotheses about Means When Sigma is Known. Testing Hypotheses about Means When Sigma is Unknown: The Student's t-distribution and the One-Sample t-test. Two-sided Confidence Intervals for a Population Mean.