Chapter 10: "t for 2" Most important concepts

1. Independent measures t is used to infer whether the µ's of *two* different *unknown*
populations are the same or different

2. With* two *population means to estimate, we need *two samples*, and we lose *two
degrees of freedom*, one for each sample mean.

3. This t test assumes that (a) both populations are **normally distributed** and (b) the
populations have **the same variance**

4. Violations of (a) are not serious if the sample size is large; violations of (b) are least serious if the samples are the same size. Homogeneity of variance (b) can be tested using Hartley's F-max test (p. 253)

5. Independent means uses a new null hypothesis trick: We hypothesize that the mean difference is 0.

Key skills from Chapter 10:

1. Compute the t-statistic. This has many steps!!! Especially tricky is the pooling of standard errors.

To find the *numerator*,

(1) Subtract one sample mean from the other

(2) Subtract this from the hypothesized difference between population means (0 for null hypothesis).

To get the *denominator,*

(3) Find the "pooled" variance

(4) add the estimated errors from both samples to get the estimated standard error

2. Compute the degrees of freedom for the t statistic (*n*-2, lose one df for each x-bar).

3. Conduct test on SPSS and interpret the output, summarizing results in English and in APA form (p.249)