Paired-samples t-test Overview

  • Paired-samples t-test: A statistical method used to compare two means from the same participants.

  • General Assumptions for t-tests:

    • Dependent variable (DV) must be continuous (interval or ratio).
    • Independent variable (IV) must be categorical with two levels.
    • Population scores should ideally be normally distributed.
    • t-tests can tolerate some violations of normality.

  • Specifics for Paired-samples t-test:

    • Requires interval or ratio DV.
    • Two sets of scores from each participant (e.g., scores after different conditions).
    • Participant scores must be independent, meaning knowledge of one pair does not predict another.
    • Scores within pairs should be correlated, although it's not a strict requirement.

  • Testing Hypothesis:

    • The primary question is whether the difference between means is significantly different from zero.
    • Use the mean of difference scores from the two conditions for analysis.
    • Null hypothesis (H0): mean of difference scores = 0.

  • Formula for Paired-samples t-test:

    • t<em>D=DˉSE</em>Dt<em>D = \frac{\bar{D}}{SE</em>D} where SE_D = SD of differences divided by the square root of sample size (n).

  • Example Study:

    • Conducted by Garry and Franks (2000).
    • Investigated reaction time for bimanual movements based on which hand moved accurately.
    • Participants: Undergraduate students (N=10).
    • Conditions: BL (Left hand controls cursor), BR (Right hand controls cursor).

  • Paired Samples T-Test Results:

    • Sample Statistics:
    • BL Mean: 152.0 ms (SD = 43.6)
    • BR Mean: 140.2 ms (SD = 36.65)
    • t(9) = 3.05, p = 0.014; suggests a significant difference in reaction time by conditions.
    • Effect Size (Cohen's d): 0.964, indicating the strength of the effect.
    • Confidence Interval for mean difference: 95% CI [3.0, 20.6].

  • Reporting Results:

    • Clearly present means, SD, confidence intervals, t-values, p-values, and Cohen's d to support findings.
    • Highlight implications of results (e.g., sensitivity of initiation processes in bimanual tasks).