Psy 232 - Stats/Methods I

The independent sample t-test

I. Independent Samples

Figure 10-3  (p. 314)
Two population distributions. The scores in population I vary from 50 to 70 (a 20-point spread)., and the scores in population II range from 20 to 30 (a 10-point spread). If you select one score from each of these two populations, the closest two values are X1 = 50 and X2 = 30. The two values that are farthest apart are X1 = 70 and X2 = 20.

 

A. Two Sources of Variability (error)

- each of the two samples will have some error as Xbar represents m

- would be nice to simply add and then average the "s Xbar" from each sample

- can't (unless samples are the same size)

 - Pooled Variance --allows the bigger sample to carry more weight in determining the final value

B. The formula

 where:

 

C. Degrees of Freedom

df = df1 + df2

= (n1 - 1) + (n2 - 1)

D. Assumptions

1. observations in each sample are independent

2. underlying populations are normal

                3. the two populations being compared have equal variances (homogeneity of variance)

 

 

II. Single Sample vs. Two Independent Samples

 

III. Variability and Effect Size