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====== Independent t-test ======

The independent t-test is of the most well-known statistical tests (see [[http://en.wikipedia.org/wiki/Student's_t-test | Student's t-test]]).  It is useful for looking at differences in the average between two groups when the variable being averaged is numerical and inadequately normal - for example, looking at the difference in height between countries.  If you are looking at paired data e.g. pre and post-diet weight, you need to use the [[:help:paired_ttest | paired t-test]].

If you want to look for differences between multiple groups, the [[:help:anova | ANOVA (Analysis of Variance)]] is required. If your data is not normally distributed, N is less than 20, or there are outliers, you should probably use the [[:help:mann_whitney | Mann-Whitney U]].

The p value tells you how likely the difference observed would occur if drawing from the same population (i.e. where the groups didn't really have a relationship with the value being averaged). A small p value tells you that it would be rare to observe such a difference if the group doesn't have a relationship with the value being averaged. From this we might reject the null hypothesis in favour of the alternative hypothesis - namely, that there is a difference according to the grouping variable.

In the example below (based on false data for illustration only), we shouldn't be surprised the p value is very low. It is possible to see a large difference in average age and N is reasonably large for each group. In this case we could reject the hypothesis that nation has no relationship with age. 

{{:help:indep_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=-mc_pLdd6Jg&list=UUFRr0ugWcqCfhLwJ5qBlzpQ |{{:help:play_button.gif|}}]] Another video is also available showing how to do an independent t-test using SOFA Statistics: [[https://www.youtube.com/watch?v=-mc_pLdd6Jg&list=UUFRr0ugWcqCfhLwJ5qBlzpQ]]

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