Introduction
When trying to accurately estimate the strength of association between an exposure and an outcome, there are several sources of error that must be considered:
- Random error (sampling error)
- Selection bias
- Information bias
- Confounding
Random errors are errors that arises from sampling. Just by chance the estimates from samples may not accurately reflect an association in the population from which the samples are drawn. In this module we will discuss how to evaluate random error when dealing with continuous outcomes. The statistical significance of these comparisons is often evaluated by computing a confidence interval or a p-value.
We will consider the relevance of p-values for population health science research, and we will also consider the limitations of using p-values to determine "statistical significance" when comparing groups. We will specifically address the common use of t-tests for evaluating associations between two continuous variables, for example, to determine whether people who are obese have a greater risk of having high blood pressure.
Essential Questions
- How can we test hypotheses regarding continuous outcomes?
- How can we tell if one group is more affected by a given disease than another group?
- What are the strengths and limitations of using p-values to guide our interpretations?
- What do we gain by using continuous data in comparison to categorical or dichotomous?
- What exposures and outcomes are well-suited for continuous measurement?
Learning Objectives
After successfully completing this section, the student will be able to:
- Conduct and interpret these statistical tests using tables and using R:
- one-sample t-test
- two-sample t-test for independent samples (unpaired)
- t-test for dependent samples (matched or paired samples)
- Explain results of t-tests in an understandable way to lay audiences
- Explain strengths and limitations of using p-values
- Select the correct statistical procedure for different questions
- Describe the difference between a 1-tailed and 2-tailed t-test
- Explain and differentiate between Type I and Type II errors
