Statistical Experiments and Significance Tests (ANOVA, Chi-square, Fisher’s Exact Test)

Statistical experiments and significance tests are essential components of data science that help students evaluate research hypotheses, compare groups, and identify statistically significant differences or associations in data. This topic introduces the principles of hypothesis testing, including the formulation of null and alternative hypotheses, selection of significance levels, interpretation of p-values, and understanding of Type I and Type II errors. Students will learn how to select appropriate statistical tests based on research objectives, variable types, study design, and underlying assumptions. Particular emphasis is placed on distinguishing analyses involving numerical outcomes from those involving categorical data and understanding how statistical evidence supports scientific conclusions.

The material focuses on three important statistical methods: Analysis of Variance (ANOVA), the chi-square test, and Fisher’s exact test. ANOVA is used to compare the means of three or more groups and determine whether there is evidence that at least one group mean differs from the others. Students will explore the concepts of between-group and within-group variability, the F-statistic, and the assumptions of independence, approximate normality of residuals, and homogeneity of variance. The chi-square test will be introduced for analyzing categorical data, including tests of independence and goodness-of-fit. Fisher’s exact test will be discussed as an alternative for examining associations between categorical variables, particularly when sample sizes are small or expected cell counts are limited. Students will learn the purposes, assumptions, and appropriate applications of each method through practical examples.

By the end of this topic, students are expected to select, conduct, and interpret ANOVA, chi-square tests, and Fisher’s exact tests using R and Python. Practical exercises will involve comparing group means, examining associations between categorical variables, calculating test statistics and p-values, and interpreting statistical outputs in the context of research questions. Students will also learn that a statistically significant result does not necessarily indicate a practically important effect and that further analyses, such as post-hoc comparisons following ANOVA, may be needed to identify specific group differences. These competencies will prepare students to conduct appropriate statistical experiments, evaluate evidence systematically, and make informed conclusions in data science applications.