The t-test for two independent samples

1. The t-test for two independent samples Chapter 10

2. A new kind of t-test • With the one-sample t-test, you needed some kind of meaningful comparison value • What if you don’t have one? • What if, instead, you want to compare the means of two independent groups of people? •  independent samples t-test • Key = groups need to be independent • Between-subjects design

3. Goal of the independent samples t-test • Assess whether the means of the populations that two different samples came from are the same or different (or whether one is greater than the other, in a directional test)

4. Calculating this • Similar to one sample t-test • One sample t-test: compare the mean of the sample to what the mean of the population would be if the null were true, taking into account estimated standard error of the mean • Independent samples t-test: compare the difference in means of two samples to what the difference in means of the populations would be if the null were true, taking into account estimated standard error of the mean

5. Figuring out the pieces • Difference in means of two samples = M1-M2 • What the difference in means of the populations would be if the null were true = 0 • Estimated standard error of the mean = estimated average distance between difference between sample means and difference between population means

6. More on estimated standard error of the mean • With just one sample = square root of estimated variance of population divided by sample size • Two samples = two estimates of variance of population, two sample sizes • Plus, the more variability there is from sample to sample for each group, the more variability there will be in the size of the difference between means of those samples • First, pool the variance together: s2p = (SS1 + SS2)/(df1 + df2) • Then, use that pooled variance to calculate estimated standard error: square root of (pooled variance divided by sample size 1, plus pooled variance divided by sample size 2)

7. Summary of calculating independent samples t-test • Difference in means of samples, minus difference in what the means of populations would be if the null hypothesis was true, divided by estimate of standard error of the mean •  tells how many estimated standard errors of the mean separate the two groups

8. How big is big enough? • To look up critical t value, need df • df = df of group 1 plus df of group 2

9. Effect size with independent samples t-tests • Same options as with one-sample t-test: Cohen’s d and r2 • Cohen’s d captures number of standard deviations between the two groups • Difference between two sample means, divided by square root of pooled variance • r2 captures how much you know about someone’s value on a variable by knowing which group they belong to • t2/(t2+df)

10. Key aspects of independent samples t-test • Use when comparing two independent groups on a quantitative variable • Homogeneity of variance is assumed, especially in the calculating of pooled variance • This assumption can be tested

11. Be sure you know • What an independent samples t-test is • When to use it • How to calculate it • How to interpret it