2-Sample T-Tests: Application and Interpretation
Learn about the application, working, and performance of 2-sample t-tests in R for comparing averages between two groups. Explore how t-values measure uncertainty and differences, along with assumptions and examples in R.
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Presentation Transcript
2-sample t-tests 1) What can they do? 2) How do they work? 3) How to perform 2-sample t-test in R? 1
Comparing averages between two groups i) How big is the difference between these two groups? ( and how much uncertainty accompanies this estimate?) ii) Do we have evidence whether the difference differs from zero? 2
2-sample t-test vs. 3 Orange by wuestenigel CC BY 2.0 Apple by idpams CC BY 2.0
2-sample t-test How does it work? X1 X2 sp t = 4
2-sample t-test How does it work? X1 X2 sp t = Measure of uncertainty in difference between means t-value essentially estimates the difference between two means, corrected for uncertainty in this difference What makes t big vs. small? THINK Difference between the means 5
2-sample t-test How does it work? X1 X2 sp t = Measure of uncertainty in difference between means Difference between the means t-value essentially estimates the difference between two means, corrected for uncertainty in this difference Bigger t: bigger difference in means, or less uncertainty 6
Assumptions of 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! 7
An example in R Set up data: 8
An example in R Set up data: 9
An example in R Set up data: What was the average size of apples and oranges? What is the difference (with uncertainty) between apples and oranges? 10
An example in R Set up data: Do our data suggest that apples and oranges differ in size, on average? 11
An example in R Set up data: Our samples indicates that, on average, apples (mean mass +/- SE: 11.9g +/- 0.3) and oranges (15.1 +/- 0.7) differ in mass by (95% CI) 1.43 4.86 g, which differs significantly from zero (2-sample t-test; t = 4.24, df = 8, p = 0.0028). Plot data; indicate sample size. 12
