A Tale of Two, Two Sample T-tests

(say that 10 times fast!)

Background

Recognizing a one tailed test vs. a two tailed test is important. This unit will also require you to recognize a dependent samples t-test vs. independent samples t-test. We will use the class survey data to practice these skills. In this activity you will be completing 2 different types of 2 sample t-tests: one with dependent samples (or matched pairs), and one independent sample test.

Hopefully as you have begun to dig deeper into our class survey data you have developed some additional questions. Statistics comes alive when it is combined with the innate curiousity of those using who use them.

Your Task

Before getting started, decide which variables you will use from the Class Survey data to conduct these tests and what you hypothesize about the variables (challenge yourself by doing at least 1 one-tailed test). It is recommended that you run these ideas past your instructor so that they can confirm you have the correct set-up before you spend too much time on it.

Create a presentation to show your results.

• Slide 1: A title and, if applicable, the names of all group members

Independent Samples T-test

• Slide 2: Hypothesis
  1. State your null and alternative hypothesis in words
  2. State your null and alternative hypothesis in math symbols
  3. Pick a significance leve (alpha)
• Slide 3: Describe the Data
  1. Remove outliers/non-sense values
  2. Provide a side-by-side boxplot of the two samples
  3. Provide the sample size, mean and standard deviation of the two samples respectively
• Slide 4: Perform the test
  1. Report the test statistic (t) and degrees of freedom
  2. Report the p-value
  3. State your decision: reject or fail to reject the null hypothesis
  4. State your conclusion in a sentence without hypothesis testing jargon
• Slide 5: Confidence intervals
  1. Find the confidence interval for the true difference of means. Write a sentence to correctly interpret/report the confidence interval you found.
  2. Verify the requirements for the test/confidence interval have been met. Note: just assume the class survey data is a random, representative sample of BYU-Idaho students in general - even though it may not be.

Matched Pairs T-test (aka Dependent Samples Test)

• Slide 6: Hypotheses
  1. State your null and alternative hypothesis in words
  2. State your null and alternative hypothesis in math symbols
  3. Pick a significance leve (alpha)
• Slide 7: Describe the Data
  1. Remove outliers/non-sense values
  2. Provide a side-by-side boxplot of the two samples
  3. Provide the sample size, mean and standard deviation of the two sample respectively
  4. Provide the sample size, mean and standard deviation of the paired differences
• Slide 8: Perform the Test
  1. Report the test statistic (t) and degrees of freedom
  2. Report the p-value
  3. State your decision: reject or fail to reject the null hypothesis
  4. State your conclusion in a sentence without hypothesis testing jargon
  5. What type of error may you have committed in your conclusion: Type I or Type II? A. At the beginning of your study if you had wanted to reduce the risk of making this type of error what could you have done?
• Slide 9: Now find a confidence interval for the true mean difference. Write a sentence to correctly interpret/ report the confidence interval you found.