Introduction to Biostatistics 03 – T-Tests and Multiple Comparison Procedures
Introduction to Biostatistics 03 – T-Tests and Multiple Comparison Procedures
This lecture focuses on the Student’s t-test, the most common statistical procedure for comparing the means of two independent groups. It highlights a frequent error in medical research: the misuse of multiple t-tests to compare more than two groups. The session introduces "Multiple Comparison Procedures" (such as Bonferroni, Holm, and SNK) as essential corrections to reduce the risk of false positives (Type I errors) when analyzing complex experimental designs.
Learning Objectives:
By the end of this lecture, students will be able to:
- Perform an unpaired t-test to compare the means of two independent, normally distributed groups.
- Explain why multiple t-tests lead to an "inflation of the alpha error" and why ANOVA must be used first for three or more groups.
- Calculate the pooled variance and the standard error of the difference between means for groups with equal or unequal sample sizes.
- Distinguish between one-tailed and two-tailed tests, understanding why the two-tailed approach is standard in most research.
- Compare and select appropriate multiple comparison procedures, such as the Bonferroni correction, Holm’s test, Student-Newman-Keuls (SNK), and Tukey’s test.
Topics covered in this lesson
- The logic of the t-test involves comparing the magnitude of differences between sample means against the inherent variability or standard error found within the samples.
- Increasing the sample size reduces statistical uncertainty and significantly increases the power of the t-statistic to detect real differences.
- Conducting multiple simultaneous tests creates a "coin-flip" problem in which the cumulative probability of a false positive approaches 50% after 10 tests.
- The Bonferroni correction is a conservative method that lowers the significance threshold by dividing it by the total number of tests conducted.
- Holm’s test provides a more powerful alternative to Bonferroni by using a step-down procedure to sequentially adjust the significance level.
- Ranking and range-based methods, such as the SNK and Tukey tests, allow for the safe comparison of all possible pairs of means across multiple groups.
- Specialized procedures like Dunnett's test are used when the primary goal is to compare multiple treatment groups against a single shared control group.
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