First off, based on your description this sounds like a three-way ANOVA rather than a two-way ANOVA since you listed three independent variables. Is that correct? If so, you should conduct a three-way ANOVA.

To clarify, you can conduct post hoc tests on any means you wish. Though, it really only makes sense to conduct post hoc tests for groups (i.e. means) that significantly differed in the ANOVA output. Moving forward, you have options. You could do follow-up t-tests on the significantly different means. A better idea is to conduct post-hoc analyses using the 'Post hoc' option in the Univariate dialogue box and specify which factor(s) you want to conduct post-hoc analyses for. The following article shows how to do this in SPSS (Refer to Step 8):

https://statistics.laerd.com/spss-tutorials/two-way-anova-using-spss-statistics.php

*You'll also want to make an adjustment to account for the multiple comparisons. Bonferroni is a good choice.

Hi Blaine,

First of all thank you for your quick reply.

What I said about Post Hoc tests is based on lines I found here: https://statistics.laerd.com/spss-tutorials/two-way-anova-using-spss-statistics-2.php

"When you have a statistically significant interaction, reporting the main effects can be misleading. Therefore, you will need to report the simple main effects."

"If you do not have a statistically significant interaction, you might interpret the Tukey post hoc test results ..."

Thank you for the clarification and for the suggestions. I did do a 3-way ANOVA, apologies for the typo.

Looking at the 3-way ANOVA guide (https://statistics.laerd.com/spss-tutorials/three-way-anova-using-spss-statistics.php) it mentions again the simple effect analysis (which I believe in SPSS can only be done with syntax).

My aim as I said is too break down an individual main effect (Variety) that was found to have a statistically significant effect on my dependent variable (SPAD) to it's components (Variety 1 (Desiree) and 2 (P.Dell)) and to see significance values for the individual components not just the main effect.

Going further, if I have an additional fixed factor (4 in total), is it possible to carry out a 4-way ANOVA using the same GLM univariate route? I am getting mixed findings about this. Or is it no problem.

Thank you in advance!

This looks like a 2x2x4 ANOVA (3 factors with 2 or 4 levels on each). I'll assume that the 3-way ANOVA was indeed run. It makes no sense to do pairwise tests on the factors with only two levels. This is already a test of the null hypothesis that the level means (in the population) are different. In this case the significant main effect of Variety indicates evidence that the mean SPAD is higher for one variety than the other (you see which one by looking at the means). The levels of Variety don't have individual significance levels because you are testing differences not individual levels (that's what ANOVA does). It is perhaps possible you are interested in whether the means for these levels differ from some hypothesised value. The easiest way to determine that is probably just to look at the CIs for individual means and see if they include that value.

The effect of Incoculum has 4 levels so you can do pairwise tests as follow-ups. However, it is important to use a post hoc test that doesn't require or assume a statistically significant F test for the main effect (if the effect of incoculum was NS). I think the majority of tests in SPSS don't do so - so you should be safe with something like Tukey's HSD or Games-Howell.

It makes little sense to look at simple main effects if you haven't hypothesised simple main effects in my view. There are quite a few contrasts that you could run - including interaction contrasts, polynomial contrasts for Incoculum etc. However, these are best done a priori - specifying the contrast pattern in advance of seeing the data. Doing so post hoc makes it hard to control family wise Type I error (because there are effectively an infinite number of possible contrasts in a complex design and one can typically find one that is statistically significant if you tried.). Correcting Type I error is hard in these cases because one rarely has a good sense of how many contrasts one might reasonably have considered.

Post hoc tests can be used to follow-up significant or non-significant effects but you need to be careful about what procedure you are using and how it controls Type I error (if at all).

Hi Thom,

Thank you for your reply!

It is very helpful.

If you have a significant interaction effect (A x B), I would emphasize and discuss this finding moreso than main effects (A). However, it is encouraged that all results of a statistical test be reported (including non-significant results) - at least in my field.

As Thom Baguley mentioned, if you have a factor with only two levels that yields a significant main effect, simply looking at the means of the two levels will tell you the direction of the difference. If you have more than two levels, pairwise comparisons can be conducted via Univariate analysis in SPSS. This enables you to systematically compare all levels within a factor, and also specific levels across factors.

Before conducting a four-way ANOVA, you need to consider statistical power. The more factors you include in a study the larger the sample size (i.e. number of observations per cell) you're going to need to achieve sufficient statistical power. You could conduct a power analysis to determine if your sample size (and estimated effect size) is adequate for such an ANOVA.

Hi Blaine,

Perfect. Thank you again!

I agree with Blaine Tomkins . Don't forget that what you do is first ,second,, third etc driven by your research question... Best wishes, D. Booth

Hi Daniel Anzelm Ganszky

Anyway, before running your model, check the ANOVA assumptions, especially homoscedasticity because SPAD measurements could have sampling difficulties due to the technique.