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Chapter 10

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University of Guelph
PSYC 1010

Chapter 10- The Independent Samples t Test March 19 th Conducting an Independent-Samples t Test - Independent sample t test- used to compare two means for a between-groups design, a situation in which each participant is assigned to only one condition - Uses a distribution of differences between means - Biggest difference that this makes- it takes more work to estimate the standard error A Distribution of Differences Between Means - Looking at overall differences between two independent groups - We create a distribution of differences between means in order to establish that the distribution specifies the null hypothesis 6 Steps of an Independent-Samples t Test 1) Identify the populations, distribution, and assumptions 2) State the null and research hypothesis 3) Determine the characteristics of the comparison distribution  There are three degrees of freedom calculations  First- calculate the degrees of freedom for the first sample- subtract 1 from the # of participants in the sample: dfx=N-1  Then- calculate the degrees of freedom for the second sample- subtract 1 from the number of participants in that sample: df y=N-1  Finally- sum the degrees of freedom from the two samples to calculate the total degrees of freedom: dftota=df x+df y - Determine the mean and standard error - A) Calculate the variance - B) Pool the two estimates of variance - C) Calculate the variance versions of standard error for each sample - D) Combine the two variances  Sum the variance versions of standard error: + - E) Parallel the two calculations  Calculate the standard deviation of the distribution of differences between means: √ - Pooled Variance- weighted average of the two estimates of variance- one from each sample- that are calculated when conducting an independent-samples t test - We use all three degrees of freedom calculations (along with variance estimates) for each sample- in order to calculate pooled variance - Pooled Variance: ( ) +( ) - Then we calculate the variance version of standard error for each sample: and for the second sample: 4) Determine critical values, or cutoffs - Similar to the t tests but use total degrees of freedom: 5) Calculate the test statistic -
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