ABSTRACT
This lesson will introduce the first statistical test, that is, a way to test whether your sample (or samples in later lessons) agrees or not with a specific hypothesis. In a previous lesson, we characterized a population of ants by taking a large number of samples and computing the average length. If you recall, we conclude that this population had a length normally distributed with a mean of 7 millimetres. Let's suppose that you discover a nearby colony and you wonder whether these ants have the same distribution of lengths. We will follow the general experimental design described in Lesson 4 (as we will do for all other tests presented in the book). For a one-sample test, this is the procedure:
Set a hypothesis: We hypothesize that ants in the new colony follow the same length distribution as the ants from the already known colony (this is our null hypothesis).
Decide on the statistical test based on your hypothesis: we will perform a one-sample test for differences. 1
Collect data (samples): We decided to sample four ants from the new colony. The measured lengths in millimetres were 2, 4, 6 and 8.
Estimate population parameters: Following the instructions given in the previous lessons we estimate the population mean from the sample, assuming that the length in the original population follows a normal distribution. In our case, the estimated population mean is 5.
Test your hypothesis (using a statistical test): In this case, as we decided in step 2, we will find out our P value and support for our hypothesis by performing a one-sample test for differences. We will compare with our test the values of 5 (estimated) and 7 (our null hypothesis) via their associated variances.
