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Comparing two groups: Paired T-test
The t-test is a statistical test that compares the means of two groups of observations. The observations should be randomly assigned to the two groups, so that any difference in response is due to the treatment and not to other factors. For instance in a medical study patients with high blood pressure are randomly assigned to a placebo group and a treatment group. The patients in the placebo group receive an inactive pill and the patients in the treatment group receive a new drug that is expected to lower blood pressure. After treating the subjects, the t test is used to compare the average blood pressures level for the placebo group and the treatment group. The data below are from Darwin's study of cross- and self-fertilization. Pairs of seedlings of the same age, one produced by cross-fertilization and the other by self-fertilization, were grown together so that the members of each pair were reared under nearly identical conditions. The data are the final heights of each plant after a fixed period of time, in inches. Darwin consulted the famous 19th century statistician Francis Galton about the analysis of these data. pair crossfertilized selffertilized 1 23.5 17.4 2 12.0 20.4 3 21.0 20.0 4 22.0 20.0 5 19.1 18.4 6 21.5 18.6 7 22.1 18.6 8 20.4 15.3 9 18.3 16.5 10 21.6 18.0 11 23.3 16.3 12 21.0 18.0 13 22.1 12.8 14 23.0 15.5 15 12.0 18.0Assuming the heigths are normally distributed a t-test can be used. To test the null hypothesis of no difference between fertilization method we can use the paired t-test. We use the paired t-test to account for the correlation between the pairs because they shared the same environment. The results from the paired t-test are shown below
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