Study Notes on Differences Between Two Groups

Differences Between Two Groups

  • Overview

    • Compare two conditions/groups using inferential statistics.

    • Conditions can involve:

    • Same group tested in different conditions (A and B)

    • Different groups in conditions A or B

  • Tests Used

    • Parametric Tests:

    1. Independent groups t-test

    2. Paired groups t-test

    • Non-parametric Equivalents:

    1. Mann–Whitney U test (independent groups)

    2. Wilcoxon signed rank test (repeated measures)

    • Other metrics include confidence intervals and effect sizes.

  • Parametric T-tests

    • Assumptions: normal distribution and similar variances.

    • Violations may not significantly affect results.

    • Adjustments available for t-test formulas when variances differ.

    • Bootstrapping method for skewed data.

  • Independent Samples T-test

    • Determines differences between group means.

    • Hypotheses:

    • H0: No difference in means

    • H1: Difference exists

    • Levene’s test checks variances:

    • Use results based on variance equality.

    • Interpret p-values to accept or reject H0.

  • Dependent Samples T-test (Paired)

    • Compares scores from the same participants across conditions.

    • Use when scores are correlated for higher sensitivity.

    • Evaluate with similar hypotheses as independent t-test.

  • Effect Sizes

    • Cohen’s d quantifies the difference magnitude; facilitates comparison across studies.

    • Z-score guidelines for effect strength:

    • 0.2: weak

    • 0.5: moderate

    • 0.8: strong

    • 1.5: very strong

  • Non-parametric Tests

    • Used with ranked data; resistant to outliers.

    • Mann–Whitney U test for independent groups; Wilcoxon for related samples.

  • Interpreting Results

    • Statistical significance determines if group means differ.

    • Confidence intervals assess the potential overlap of means.

    • Non-significant results imply no meaningful differences between conditions or groups.

  • Summary

    • T-tests are typical for comparing groups.

    • Descriptive stats: means and standard deviations.

    • Confidence intervals aid generalization to populations.

    • Non-parametric tests serve as alternatives for skewed data.