Inference for two independent samples (t-test)

An example

The data for this example come from a remarkable experiment carried out in the Department of Zoology at the University of Melbourne, over 22 years, by Wilfred Agar, Frank Drummond, Oscar Tiegs and Mary Gunson.

The experiment was a test of the theory of Lamarckian inheritance, which states that offspring can inherit characteristics that are acquired or learnt by their parents during the parents’ lifetime. They tested the idea out by testing 50 generations of rats; rats in one group were trained on a learning task over the generations, whereas the other group was not. The rats had to learn to escape from a tank of water from one of two exits. The correct exit was dimly lit, whereas the wrong exit was brightly lit. The bright exit was “wrong” because an electric shock was given at this exit. The intention was to induce a phobia of bright lights.

The data for each generation are published, but here we consider the number of errors made by the rats in the 14th generation; there were 37 control rats and 50 trained rats in this generation. There are results for two groups of different rats to compare, so the design involves two independent groups. As the number of errors is a quantitative variable, the methods of statistical inference that can be applied here are usually found under labels such as "2-sample t-test" or "independent samples t-test" in software menus or code.

An appropriate report of the analysis may include summary statistics, the estimated difference of means with a 95% confidence interval, and a P-value. The P-value is for a test of the null hypothesis of no difference in the true means of the two groups.

Here is a summary table that combines descriptive and inferential statistics. It uses the results from the analysis that does not assume equal variances.

This layout will allow you to add more rows with results from different outcomes, if you need. There are, of course, other ways of producing good summary tables for this analysis.