Chapter 8 Summary and Vocabulary 1
t test for independent means
For hypothesis-testing with scores from two entirely separate groups of people
Comparison distribution for t test for independent means
A distribution of differences between means of samples
Built up in two steps:
o Each population of individuals produces a distribution of means
o A new distribution is created of differences between pairs of means selected from these two
distributions of means
The distribution of differences between means has a mean of 0 and is a t distribution with the
total of the degrees of freedom from the two samples.
Steps for a t test for independent means:
1. Restate the question as a H 1nd H ab0ut the populations.
2. Determine the characteristics of the comparison distribution.
a. Its mean will be 0.
b. Figure the standard deviation
i. Figure the estimated population variances based on each sample.
ii. Figure the pooled estimate of the population variance.
( ) ( )
iii. Figure the variance of each distribution of means.
iv. Figure the variance of the distribution of differences between means.
v. Figure the standard deviation of the distribution of differences between means.
3. Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be
a. Determine the degrees of freedom ( ), desired significance level, and tails in the test (one
b. Look up the appropriate cutoff in a t table. If the exact df is not given, use the df below it.
4. Determine your sample’s score on the comparison distribution:
5. Decide whether to reject H b0 comparing the scores from Steps 3 and 4. If YOUR value is less than the
chosen significance level (i.e., p .05 or 5%), then you reject the null hypothesis and conclude that the
results are statistically significant. Chapter 8 Summary and Vocabulary 2
Assumptions of the t test for independent means include that the two populations are
normally distributed and have the same variance. However, the t test gives fairly accurate results when
the true situation is moderately different from the assumptions. Additionally, the scores must be entirely
independent from each other.
Effect size for a t test for independent means is the difference between the means divided by
the population standard deviation. Power for a t test for independent means can be determined using this
table, a calculator, or a software program
Number of Participants in Effect Size
Each Group Small (.20) Medium (.50) Large (.80)
10 .11 .29 .53
20 .15 .46 .80
30 .19 .61 .92