Welch's 2-Sample T-Test: Understanding Variance Equality
Welch's 2-sample t-test is a statistical method that allows the comparison of means between two groups when the assumption of equal variances is violated. This test is useful when dealing with unequal variances and sample sizes. It works by adjusting the degrees of freedom to accommodate the varying variances in the groups. In R, you can perform Welch's t-test by following specific steps, ensuring assumptions such as random sampling, independence, and normality are met. An example in R demonstrates how to set up data, calculate average sizes, estimate differences in mass, and interpret results to assess if apples and oranges differ significantly in size.
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Presentation Transcript
Welchs 2-sample t-test 1) What can it do? 2) How does it work? 3) How to perform Welch s t-test in R? Note: this video is intended to follow the video regarding a (standard) 2-sample t-test 1
Welchs 2-sample t-test Does the average mass of an apple differ significantly from the average mass of an orange? vs. Allows unequal variance 2 Orange by wuestenigel CC BY 2.0 Apple by idpams CC BY 2.0
Welchs 2-sample t-test How does it work? X1 X2 sp t = Difference between the means Measure of uncertainty Adjusts degrees of freedom (d.f.); d.f., may be a fraction 3
Assumptions of Welchs 2-sample t-test 1. Random sampling 2. Independence 3. Homogeneity of variances (no outliers) 4. Normality within each group (no outliers) Plot your data! 4
An example in R Set up data: 5
An example in R Set up data: 6
An example in R Set up data: What is the average size of apples? Oranges? What is the estimated difference in mass between apples and oranges? 7
An example in R Set up data: Do our data suggest that apples and oranges differ in size, on average? 8
An example in R Set up data: Our samples indicates that apples (mean mass +/- SE: 11.9g +/- 0.3) and oranges (15.1 +/- 0.7) differ in mass by (95% CI) 1.26 5.02 g, which differs significantly from zero (Welch s t-test; t = 4.24, df = 5.23, p = 0.0074). Plot data, too; state sample sizes 9
