This example looks at the mean number of hours slept for male versus female students. We use the smaller of the two sample sizes, and then subtract one from this number. This may underestimate the number of degrees of freedom, but it is much easier to calculate than using Welchs formula. If the fourth assumption fails, then the more conservative unpooled estimated standard error is used (and the test is referred to as “Welch’s Test”). We can use the conservative approximation for our degrees of freedom. If the fourth assumption is met, then the pooled estimated standard error is used in the calculation of the test statistic. If the third assumption is not met, the alternative test is the Mann-Whitney U-Test, which can be run to see if there is a difference between two groups for a variable with any type of distribution. The population of each group is normally distributed.The estimated standard error is an aggregate measure of the amount of variation in both groups.ĭegrees of freedom: Varies by conditions, but the basic rule of thumb for hand calculations is the smaller of n 1 – 1 and n 2 – 1, where n is the sample size for each group. The test statistic for a two-sample independent t-test is calculated by taking the difference in the two sample means and dividing by either the pooled or unpooled estimated standard error. H a: The population mean of one group is greater than the population mean of the other group, or μ 1 > μ 2 Substituting in what we know, the degrees of freedom are calculated as: r ( s X 2 / n + s Y 2 / m) 2 ( s X 2 / n) 2 n 1 + ( s Y 2 / m) 2 m 1 ( ( 2.51) 2 / 10 + ( 1.90) 2 / 10) 2 ( ( 2.51) 2 / 10) 2 9 + ( ( 1.90) 2 / 10) 2 9 16. This test can also be conducted with a directional alternate hypothesis: H A: The population mean of one group does not equal the population mean of the other group, or μ 1 ≠ μ 2 H o: The population mean of one group equals the population mean of the other group, or μ 1 = μ 2 For example, we could see if the mean GPA differs between freshman and senior college students by collecting a sample of each group of students and recording their GPAs. A two-sample independent t-test can be run on sample data from a normally distributed numerical outcome variable to determine if its mean differs across two independent groups.
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