Summary of Independent Two Sample T-Test

INDEPENDENT TWO SAMPLE T-TEST OVERVIEW

  • Purpose: Used to compare means between two independent groups.

    • Examples: Immigrants vs. Non-Immigrants, Victims vs. Non-Victims.

HYPOTHESES

  • Null Hypothesis (H0): No difference between group means (μ1 = μ2).

  • Alternative Hypothesis (H1): There is a difference (μ1 ≠ μ2).

    • Directional (one-tailed) alternative hypotheses possible.

ASSUMPTIONS

  • Observations must be independent.

  • Groups should have similar variances.

  • Samples normally distributed.

STEPS FOR T-TEST

  1. Define hypotheses (null and research).

  2. Compare group means.

  3. Check assumptions (sample variance, distribution).

  4. Calculate t-statistic and effect size.

EXAMPLE CASE

  • Dependent Variable: Perceived Police Trustworthiness.

  • Independent Variable: Victimisation Status (0 = Not Victim, 1 = Victim).

DESCRIPTIVE STATISTICS

  • Victims Mean: 5.80, S.D.: 1.02, Variance: 1.03.

  • Non-Victims Mean: 6.45, S.D.: 1.39, Variance: 1.92.

T-TEST RESULTS

  • Observations: 34 for each group.

  • T-statistic: 2.185.

  • P(T<=t) two-tail: 0.032 (significant as p < 0.05).

  • Conclusion: Statistically significant difference in perceived trustworthiness.

EFFECT SIZE

  • According to Cohen's conventions, a

  • 0.2 is considered a small effect,

  • 0.5 a medium effect

  • 0.8 a large effect.

INTERPRETATION

  • Significant difference in perceived trustworthiness (Non-Victims vs. Victims).

  • Victims showed lower trustworthiness towards police.

  • Understanding significance and magnitude of difference is crucial for interpretation.