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==Comparing a quantitative variable between two groups==
==Comparing a quantitative variable between two groups==
===t-test===
===t-test===
The t-test (also known as the 'Student's t-test') is the most commonly used test for the comparison of two normally distributed variables, and can also be used to assess whether a single normally distributed variable differs from a particular value. As for many hypothesis tests, it involves the calculation of a test statistic which is assumed to follow a particular distribution (in this case, the t distribution). The general approach to the calculation of the test statistic is to divide the difference of interest (whether that is the difference between the mean of interest and a particular value, or the difference between two different means of interest) with the standard error of this difference. The methods of calculation of the standard error therefore differ depending upon the characteristics of the data in question:
* When comparing the mean of a group with a particular value, the difference between the mean and the value in question is divided by the product of the standard deviation of the group and the the reciprocal of the square root of the number of individuals in the sample.
* When comparing the means of two group, the approach used depends on other characteristics of the data:
** when both groups have approximately equal variances and there are equal numbers of individuals in each group, the difference in mean values between the two groups is divided by the product of the pooled standard deviation and the square root of two divided by the number of individuals in each group.
** when both groups have approximately equal variances but there are different numbers of individuals in each group, the difference in mean values between the two groups is divided by the product of the pooled standard deviation and the square root of the sum of the reciprocals of the group sizes.
** when the groups have different variances, the difference in mean values between the two groups is divided by the square root of the sum of the variances of each group divided by the group size
===Mann-Whitney U test===
===Mann-Whitney U test===
The Mann-Whitney U test (also known as the Wilcoxon Rank Sum test) is commonly used for the comparison of two groups where the variable of interest is continuous but not normally distributed for at least one group. The basic concept behind the test is that all observations within each group are combined and then ranked in order of magnitude. These are then reassigned to their original groups, and the sums of the ranks in each groups are calculated and compared (by counting, for each observation in either of the groups, the number of observations in the alternate group which have a lower rank, and summing these together). Alternative methods are available for those cases where this approach would not be feasible.
==Comparing a quantitative variable between more than two groups==
==Comparing a quantitative variable between more than two groups==
===ANOVA (analysis of variance)===
===F-test===
The F-test is used when comparing the means of two or more quantitative variables, as is the case when conducting an ANOVA (analysis of variance). The basic concept of an ANOVA is that the total variation in a population can be viewed as being comprised of the variation between the groups (i.e. 'explained variation') and variation within the groups (i.e. 'unexplained variation'). The F statistic is based upon the ratio of a measure of the variance between groups (the 'mean square of treatment', MSTR) to a measure of the variance within groups (the 'mean square error', MSE).
===Kruskal-Wallis test===
===Kruskal-Wallis test===