• OneSampleOneVariable

Statistical Tests for Experiments with Single Samples

Sometimes, the research question is as simple as investigating whether the value of a certain property of a group differs from a hypothetical value (specified by the null hypothesis). Depending on what information is available, one can choose between the following types of tests:

• z-test

• single-sample t-test

In this section, we are going to review these two tests by working through a few toy problems.

Z-test

Single-sample t-test

The single-sample t-test is often more commonly used as we as experimenters rarely know the true standard deviation of the target population. The only available information has to come from the sample data collected in the experiment. For example, Smokin' Joe wants to know whether marijuana can increase appetite and conducted an experiment:

• The Problem

• Smokin’ Joe hypothesizes that marijuana can be used to mitigate some of the negative side effects of common AIDS drugs, such as loss of appetite. He wants to test the hypothesis that marijuana increases the appetites of AIDS patients who are taking common AIDS drugs. He measures the difference in calories eaten by patients the day after taking a THC pill and the day before taking the pill. Here are the measurements he obtains for 10 subjects – [101, 75, -82, 32, -50, 203, 165, 145, 303, 23]

In other words, Smokin' Joe wants to test whether the difference in calories eaten by AIDS patients (i.e. the property of a group) is different from 0 (i.e. a hypothetical value). If it is significantly different from 0, we can reject the null hypothesis that marijuana has no effect on appetite.