4. T-tests

Hypothesis testing

• Making inferences from sample means to population means

• Hypotheses about means

• Null: H0: µ1 = µ2

• Alternative: H1: µ1 ≠ µ2

After the statement of the hypothesis: (H0: µ1 = µ2; H1: µ1 ≠ µ2)

H0/HN

H1/HA

  • Can we reject the null?

  • • Calculate the sample statistic: t-value

    • Determine sig: use tcritical or calculate a p-value

    • One tail vs. two-tailed tests

    • 2 tailed can be 1 → P value divided by 2

      • Depends on the hypothesis

\One tailed vs two tailed

One-Tailed Test

• Interested in whether differences between groups/values occur in either one

direction or the other, but not both

Two-Tailed Test

• Interested in whether any differences between groups/values exist, regardless of direction

  • We could be inflating our power to see something that isnt there

    • False positive

  • One tailed is less common

Single samples t-test

  • comparing to something more or less set

    • final stats grade to upper year stats grade

• IV = 1 factor with 2 levels = 2 groups/conditions

• 1 group = sample mean

• 1 group = population mean

• DV = groups means for the measure/score/etc. (continuous)

Levene’s Test for Homogeneity of Variance

  • We dont want this to be significant

  • We’re testing for something innately different

• Not sig. = variances do not differ/approx. equal = assumption was met

• Sig. = variances differ = assumption violated

Effect Size

• Standardized measure of the magnitude of the effect

• Tells us how many SDs there are b/w the two group means

• Reported in addition to t and p

• Allows comparisons across studies

If its significant, how big is that difference?

Within subjects t-test

Paired Samples t-Tests

Test whether two dependent sample means are different between

conditions

• Comparing 2 conditions / groups with the same individuals in each group

• Samples are NOT independent (same ppl in both groups)

• e.g., matched/paired, longitudinal

• IV = 1 factor with 2 levels = 2 groups/conditions

• DV = groups means for the measure/score/etc. (continuous)