2.7: Comparing many samples

Supplementary Resource Materials

(ways to test hypotheses using your sample data if two populations are involved)

• t Tests: Comparing Two Measurements
  • Introduction to the t Distribution (non‑technical) (jbstatistics)
  • An Introduction to the Student t Distribution (mathematically speaking) (jbstatitics)
  • To z or to t, that is the question (Brandon Foltz)
  • Hypothesis Tests on One Mean: t‑Test or z‑Test? (jbstatistics)
  • Introduction to t‑Tests for One Mean (jbstatistics)
  • t‑Tests for One Mean: an example (jbstatistics)

• Hypothesis Tests for Two Populations Parameters

  • Inference for Two Proportions: an Introduction (jbstatistics)
  • Pooled or Unpooled Variance t Tests and Confidence Intervals (To Pool or Not to Pool? (jbstatistics)

  Interferences about the Difference between Two Population Means (Independent Samples: variances $\sigma _{1}^{2}$ and $\sigma _{2}^{2}$ not known but equal)

  • Introduction to Pooled‑variance t Tests and Confidence Intervals (jbstatistics)
  • Pooled‑variance t Tests and Confidence Intervals: an Example (jbstatistics)

  Interferences about the Difference between Two Population Means (Independent Samples: variances $\sigma _{1}^{2}$ and $\sigma _{2}^{2}$ not known and not equal)

  • Introduction to Welch (Unpooled‑variance) t Tests and Confidence Intervals (jbstatistics)
  • Welch (Unpooled‑variance) t Tests and Confidence Intervals: an Example (jbstatistics)
  • The Paired Difference t Procedure (jbstatistics)

  Interferences about the Difference between Two Population Proportions

  • An Introduction to Inference for Two Proportions (jbstatistics)
  • Inference for Two Proportions: an example of a Confidence Interval and a Hypothesis Test (jbstatistics)

Reference Materials

(Questions to consider when you are reading/writing a report containing the results of a two‑sample hypothesis test)

• Are only two groups being compared? If more than two groups are being compared two at a time, then a different type of analysis is preferable—namely the Analysis of Variance tests.
• Were the samples selected independently, or were the sample paired? If the samples were paired, was the analysis that was performed appropriate for paired samples?
• If a confidence interval is reported, is it correctly interpreted as an estimate of a difference in population/treatment means or proportions?
• What hypotheses are being tested? Is the test one‑ or two‑tailed?
• Does the validity of the test performed depend on any assumptions about the sampled populations (such as normality)? If so, do the assumptions appear to be reasonable?
• What is the $p$‑value associated with the test? Does the $p$‑value lead to rejection of the null hypothesis?
• Are the conclusions consistent with the results of the hypothesis test? In particular, if ${{H}_{0}}$ was rejected, does this indicate practical significance or only statistical significance? (From Introduction to Statistics & Data Analysis, by Peck, Olsen & Devore, Cengage Learning, 2014, pp. 605‑06)