Maths and Stats Support

Use: Tests for differences in means of 3+ independent groups (subjects can only be in one group).

Dependent (Outcome): Continuous
Independent (predictor): One grouping variable with 3+ different categories

Example: Is there a difference in the % mean assessment score for a module using three different teaching methods

Summary statistics/graphs: Means/ standard deviations, boxplot or mean bar chart with error bars 

Ordinal variables: If your dependent variable is the mean of a set of related ordinal questions and the assumptions have been met, the parametric techniques such as ANOVA can be used. If you have one ordinal question, opinion is divided on whether ANOVA is suitable. 

Two-way ANOVA  is an extension of one-way ANOVA which has two categorical independent variables.  The two categorical variables are tested separately and an interaction/moderation term which tests whether the effect of one independent is different depending on the group of the second. Factorial ANOVA has more than two independent variables

Dependent (outcome) variable: Continuous                      Independent (predictor) variable: Two categorical grouping variables

Example (two-way): Does having maths A level or teaching group impact on grade?  Does the effect of teaching group differ depending on whether or not a student has maths A level?

Summary statistics/graphs: Use a mean bar chart with error bars or line chart to assess the impact of both variables together and look for an interaction  

ANCOVA  allows you to include a continuous independent variable as well as categorical in one or two way ANOVA

Dependent (outcome) variable: Continuous                      Independent (predictor) variable: At least on categorical (3+ groups) and one continuous

Example (ANCOVA): Is there a difference in the mean grade by teaching group after controlling for attendance?

Summary statistics/graphs: A scatterplot by group with different regression lines for each group helps assess whether there is an interaction between one continuous IV and one categorical IV on the DV. Use marginal means and mean bar chart from the ANCOVA for the groups  

MANOVA  allows you to test the impact of categorical variables for multiple related DEPENDANT variables

Dependent (outcome) variables: Multiple related continuous variables                      Independent (predictor) variable: At least one categorical (3+ groups)

Example (ANCOVA): Is there a difference in the mean grade for coursework, exam and group work scores by teaching group

Use: Comparing the distributions of three or more different groups of subjects (independent groups) when the assumptions of one-way ANOVA are not met or the dependent is one ordinal question. There are no non-parametric alternatives for two way or other types of ANOVA

Dependent (Outcome): Ordinal or skewed data       
Independent (predictor): Three categories

Example: If grade was recorded as 1st, 2.1, ..... Fail, these are ordered categories which are not evenly spaced so a non-parametric test should be used.  Or if students were asked one question such as 'How well do you think you performed in this module' where the options ranged from poorly to very well, then you would use a Kruskal-Wallis to compare three teaching methods.

Summary statistics/graphs: Use medians, Interquartile range and boxplot or for ordinal sometimes %'s and bar charts explain differences more clearly.

Note: If you have taken the mean or sum of several ordered questions (scale mean), use parametric tests such as t-tests. Some disciplines use parametric tests for individual ordinal questions but a wider range of responses (ideally 7+) is needed