PSYC 2260 Lecture Notes - Lecture 8: Normal Distribution, Effect Size, Null Hypothesis
26 Jun 2018
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PSYC 2260 Introduction to Research Methods in Psychology Chapter 8
Chapter 8 The t-test for Independent Means
Used to compare 2 different groups that are independent of each other
- E.g. female vs. male
- E.g. control vs. experimental
Because we’re looking at differences between groups, the comparison distribution is the
distribution of differences between means
With independent, there are 2 samples, thus we need 2 comparison population
If we repeatedly sample from each population, subtracting one mean from the other
- We would build up a “Distribution of Differences”
Goal of independent t-test:
- To see if differences between sample means is more extreme than the cut-off differences on
the distribution of differences
The Null Hypothesis: µ1 = µ2
- Logic: if the 2 population have the same mean, then the 2 samples should also have the
same mean
Estimating the variance:
Because we have 2 population, we need 2 estimate of variance:
- We calculate the weighted average, called “pooled estimate of population variance”
- Estimating the variance of each distribution of means:
- Next, estimate the variance and SD (“error”) of the distribution of differences:
Formula for independent t-test
Determine total df: df total = df1 + df2
- If resulting is greater than critical cut-off (from table), at chosen alpha (“p-value”), the reject
null, conclude 2 samples have different means
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Document Summary
Used to compare 2 different groups that are independent of each other. Because we"re looking at differences between groups, the comparison distribution is the distribution of differences between means. With independent, there are 2 samples, thus we need 2 comparison population. If we repeatedly sample from each population, subtracting one mean from the other. We would build up a distribution of differences . To see if differences between sample means is more extreme than the cut-off differences on the distribution of differences. Logic: if the 2 population have the same mean, then the 2 samples should also have the same mean. Because we have 2 population, we need 2 estimate of variance: We calculate the weighted average, called pooled estimate of population variance . Estimating the variance of each distribution of means: Next, estimate the variance and sd ( error ) of the distribution of differences: Determine total df: df total = df1 + df2.
