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Chapter 8

Chapter 8 Summary and Vocab

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Simon Fraser University
PSYC 210
Cathy Mc Farland

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 rejected. a. Determine the degrees of freedom ( ), desired significance level, and tails in the test (one or two). 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) One-tailed test 10 .11 .29 .53 20 .15 .46 .80 30 .19 .61 .92 40 .22
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