In a past class exam paper you have to complete a 2x3 mixed design ANOVA table, after that it asks what further tests should be done which i am unsure of - could someone please help?

In another after completing a single factor ANOVA table it asks if this produces a signifcant result (which it does) what further steps are necessary to understand the pattern of the results? Again i'm not sure i was thinking perhaps a 1 way ANOva and/or a t-test?

I'd appreciate any help greatly :)

Sure! I can help you understand what further tests should be done in both scenarios.

1. Completing a 2x3 mixed design ANOVA table:
In a mixed design ANOVA, you have two independent variables: one between-subjects variable and one within-subjects variable. The between-subjects variable divides your participants into groups, while the within-subjects variable assesses changes within the same individuals. The purpose of this design is usually to examine the main effects and interactions of both variables.

After completing the ANOVA table, there are a few further tests you can consider, depending on the significance of the results. Here are the possibilities:

a) Post hoc pairwise comparisons: If you find a significant main effect or interaction, you can conduct post hoc tests to compare the means of specific groups or levels. Common post hoc tests include Tukey's HSD, Bonferroni correction, or Sidak correction. These tests allow you to determine which groups or levels significantly differ from each other.

b) Simple effects analysis: If you have a significant interaction, it is often useful to conduct simple effects analyses. Simple effects analysis examines the effect of one independent variable at each level of the other independent variable. It helps to understand the nature of the interaction and identify which specific conditions are driving the effect.

2. Single factor ANOVA with a significant result:
If you have conducted a single factor ANOVA and obtained a significant result, it indicates that there is a significant difference between at least two of the group means. In this case, there are a few additional tests you can consider to understand the pattern of the results:

a) Post hoc tests: Similar to the mixed design ANOVA, you can perform post hoc tests to compare the means of different groups and identify specific differences. Common post hoc tests include Tukey's HSD, Bonferroni correction, or Sidak correction.

b) Graphical analysis: Creating a plot, such as a bar graph or boxplot, can provide visual insight into the differences between groups. This can help you understand the overall pattern and any potential outliers or trends in your data.

c) Tukey's Honestly Significant Difference (HSD): Tukey's HSD test is commonly used to compare all possible pairs of means while controlling the overall Type I error rate. This test can be helpful when you have several groups and want to determine which pairs of means are significantly different from each other.

d) T-tests: If you have only two groups, you can perform independent samples t-tests or paired samples t-tests, based on the design of your study, to compare the means. T-tests help you assess whether the means are significantly different from each other.

Remember, the choice of further tests will depend on the specific research question, the design of your study, and the significance of your initial ANOVA results.