# SOFA Statistics

### Site Tools

help:paired_ttest

# Differences

This shows you the differences between two versions of the page.

 — help:paired_ttest [2012/08/12 18:17] (current) Line 1: Line 1: + [[http://​www.sofastatistics.com/​userguide.php | Contents]] + [[:​help:​stats_tests | Statistical Tests Available]] + + ====== Paired t-test ====== + + The paired t-test (see [[http://​en.wikipedia.org/​wiki/​Student'​s_t-test | Student'​s t-test]]) is useful for looking at differences in two variables. ​ The data must be paired e.g. looking at pre and post-diet weight. ​ The variables being averaged must also be numerical and adequately normal.  ​ + + If you are looking at independent/​unpaired data e.g. height between two countries, you need to use the [[:​help:​indep_ttest | independent t-test]]. + + If your data is not normally distributed,​ or there are outliers, you may be better using the [[:​help:​wilcoxon | Wilcoxon Signed Ranks Test]]. + + The p value tells you how likely the difference observed would occur if sampling from a population in which there is no actual difference. A small p value tells you that it would be rare to observe such a difference if there is no actual difference between the variables. From this we might reject the null hypothesis in favour of the alternative hypothesis - namely, that there is a difference. + + In the example below (based on false data for illustration only), the p value is very low. In which case we can reject the hypothesis that there is no difference in weight pre and post-diet. Of course, whether the difference is of practical significance is another matter entirely. + + {{:​help:​paired_ttest_example.gif|}} + + Be aware that there is a certain sensitivity about terminology around this area.  According to a widespread convention, we shouldn'​t conclude that there is a relationship,​ only that we reject the null hypothesis (see [[http://​www.stats.gla.ac.uk/​steps/​glossary/​hypothesis_testing.html#​h0 | Hypothesis testing]]). We might go so far as to reject the null hypothesis in favour of the alternative hypothesis. ​ See [[http://​en.wikipedia.org/​wiki/​Statistical_hypothesis_testing | Statistical hypothesis testing]]. + + [[https://​www.youtube.com/​watch?​v=DiAYu0aM9Zw |{{:​help:​play_button.gif|}}]] A video is available showing how to do paired t-tests using SOFA Statistics: ​ + [[https://​www.youtube.com/​watch?​v=DiAYu0aM9Zw]] + + [[http://​www.sofastatistics.com/​userguide.php | Contents]] + + [[:​help:​stats_tests | Statistical Tests Available]] + + [[:home | Wiki]] 