04. T-Tests

When is a T-Test used?

It is used when the IV is a category with two levels, and the DV is continuous

Origins of the T-Test - How was it created?

William Gosset created the test as an easy way to measure the quality of Guinness stout. He was banned from publishing findings, so used the name ‘student’ instead.

Independent T-Test: Design

• Between-subjects

• Comparing two different groups, can be naturally occurring or experimental

Independent T-Test: Assumptions

• Data must be continuous/scale

• Data should be approximately normally distributed

• Data must have homogeneity of variance

Homogeneity of Variance

Is the variance of group A similar to group B?

Levene’s Test

Tests the null hypothesis that the population variances are equal. If the test is significant (p < .05) the HoV is violated

APA Format of Independent T-Test

An Independent Samples T-test violated the assumption of homogeneity of variance and so equal variances were not assumed. Results shows that [DV] in the [IV1] condition were statistically significantly faster than in the [IV2] condition, t(xx) = x.xx, p=.xx, d=.xx [95% CI: x.xx, x.xx]

Cohen’s D effect size parameters

• 0.2 - small

• 0.5 - medium

• 0.8 - large

Welch Test

An alternative to the independent t-test that doesn’t assume homogeneity of variance

Paired Samples T-Test: Design

• Within-subjects

• Comparing one group at two different time points or conditions

Paired Samples T-Test: Assumptions

• Data must be continuous/scale

• Data must be normally distributed

APA Format of Paired Samples T-Test

A paired samples t-test showed that [DV] in the [IV1] condition were statistically significantly slower than in the [IV2] condition (mean difference = x.xx), t(xx) = x.xx, p = .xx, d = .xx [95% CI: x.xx, x.xx].