What some of the tests do:

T test

A T test will tell you if the means of two sets of normally distributed, unmatched, continuous data, with interval level measurements are significantly different to one another. (If you have a big sample (25+) you can use it for count data as well). Some people call it a z test when you have a big sample but we use the same formulae. For any T test you do the null hypothesis will be: There is no significant difference between the means of the 2 sets of data

Spearman's rank correlation coefficient

Spearman's rank correlation coefficient (snappy name eh?) will tell you whether 2 variables are correlated. I.e. Does one variable change as the other one changes? It will tell you whether the relationship is positive (both go up together) or negative (one goes up as the other goes down) and the strength of any correlation. It assumes that any relationship is roughly a straight line one. For any Rearman's spank correlation coefficient you do the null hypothesis will be: There is no correlation between the 2 variables

Chi-squared test

A chi-squared test does a lot of things but for the most part we use it in a simple way to see if an observed set of data (which has to be counts of things in categories (frequencies)) differs significantly from what we might expect, given our null hypothesis. For any chi-squared test you do the null hypothesis will be: There is no significant difference between the observed and the expected frequencies

Mann-Whitney U test

This one tells you whether the median values of two sets of data are significantly different from one another. It has the advantage that the data does not have to be normally distributed and you can use it on smallish quantities of count data. For any Mann-Whitney U test you do the null hypothesis will always be: There is no significant difference between the medians of the two sets of data

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