Res112 LT 1

Pearson R

Measures linear correlation between two continuous variables.

Sensitive to outliers; assumes normality and linearity.

Spearman Rho

Measures rank correlation between two ordinal or continuous variables

Less powerful than Pearson R; assumes the variables increase or decrease at different rates. 

Independent Samples T-test

Compares means between two independent groups.

Assumes normality, equal variances, and independent samples.

Paired Samples T-test

Compares means between two related or paired groups.

Requires normal distribution of differences; applicable only to paired data.

Whole Sample T-test

Tests if a sample mean is significantly different from a known or hypothesized population mean.

Assumes normality; requires a single sample and known or hypothesized population mean.

Mann-Whitney U Test

Non-parametric test comparing medians of two independent groups. Ordinal.

assumes similar shape of distributions.

Wilcoxon Signed-Rank Test

Non-parametric test for comparing medians in paired samples. Ordinal.

Limited to paired data; sensitive to large sample sizes.

ANOVA

Compares means across three or more groups. (interval/ratio)

Assumes normality, homogeneity of variances, and independent samples.

Kruskal-Wallis

Non-parametric test for comparing medians across three or more independent groups. Ordinal.

Less powerful than ANOVA for small samples; assumes similar distribution shape across groups.

Example of Pearson R

Examining correlation between students’ study hours and test scores in a biology course.

Example of Spearman Rho

Analyzing the relationship between ranks in science and math subjects.

Chi-Square

Tests for association between categorical variables. (nominal/ordinal).

Requires sufficiently large sample sizes; expected frequencies in each cell should be ≥ 5.

Example of Chi-square Test

Examining the relationship between gender and choice of STEM-Med specialization.

Example of Kruskal-Wallis Test

Comparing median lab scores among students in different chemistry classes,

Example of ANOVA test

Analyzing the effectiveness of different teaching methods on physics exam scores across multiple sections.

Example of Wilcoxon Signed-rank test

Evaluating the effectiveness of a medical training session by comparing pre- and post-test ranks.

Example of Mann-Whitney U Test

Comparing median reaction times of two groups in a chemistry experiment.

Example of Whole Sample T-Test

Testing if students’ average score in microbiology differs significantly from a set national average.

Example of Paried T-Test

Comparing pre-test and post-test results after a physics tutoring session.

Example of Independent T-Test

Comparing average scores in anatomy between two different class sections.