# Question on 2-way ANOVA stat use and interpretation

##### New Member
Hi everyone!

I am currently working on publishing an article from my Masters thesis. I had real trouble with the statistics section which was also pointed out by the markers. I was hoping to get some advice on how I could make this section clearer, concise, and overall of a better quality.

Briefly, the experiment involved each of the participants attending 5 exercise sessions. These exercise sessions were of 5 different durations that were performed on different days; these were 30mins, 20mins, 10mins, 6mins, and 2mins. Before and immediately after the exercise, and then after 30mins of rest after exercise, electrical stimulation was delivered to look at neuromuscular function.

With regards to analysis, the electrical activity recorded immediately after exercise and 30mins post exercise was normalised to the one recorded before exercise (the one recorded before exercise was therefore used as a reference), therefore we get data that shows the change relative to before exercise at the two testing points.

I am using SigmaStats 3.5 for statistics. I used two factor ANOVA with repeated measures. The two factors were ‘when electrical stimulation was applied’ and ‘exercise duration’. When a main effect or interaction was detected, significant differences were located using Tukey’s post hoc analysis. Basically we were looking to see how the different durations of exercise effects muscle activity after exercise.

My first question is whether the correct statistical measure has been used? Would it be better to use one way ANOVA? If two factor ANOVA is the correct statistical analysis to use I have a few questions about analysis and interpretation please. For one variable, it says that the mean values among the different levels of Condition is not great enough to exclude the possibility that the difference is just due to random sampling variability after allowing for the effects of differences in Time, and that There is a statistically significant difference between the different times, and that there is no interaction. So for this example does it mean that yes at the different exercise durations there is a sig difference but this can’t be determined for each of the two times stimulation was applied? So then how do you know at which point the difference exists, whether its straight after exercise or after 30min rest?

My next question is to do with interactions. When an interaction is detected, what does it mean? For example, if there is a significant difference for a variable measured 30 minutes post exercise compared to straight after exercise, for all exercise durations, what does it mean by saying there is an interaction between the two? Similarly, if significant differences occur between different exercise durations for each of the two conditions (the two points of neuromuscular function tests) what would that mean in terms of the interaction? Oh and also why isn’t the main effect analysed when there is an interaction, like would it not be useful to analyse the main effect for each factor even when there is an interaction?

As you can probably tell my stats knowledge is extremely limited. Any help or direction would be much appreciated. Thank you so much in advance for any help or advice that can be given

#### Disvengeance

##### New Member
It may be useful if you explicitly stated your hypothesis for this study.

Based on what you described, a two-way repeated measures ANOVA seems appropriate, assuming you checked the necessary assumptions. For your other questions regarding the two-way ANOVA, I think you need to clarify what type of sums of squares you are using. I'm also curious why you "normalized" the measures to the first measure instead of just including each measure in the model.

There are several possible types of interactions. Essentially, an interaction occurs when a variable in one group changes relative the other group. For example, you provide men and women with a treatment over time, and the treatment causes a variable to increase in men but not change in women. You can create an interaction plot to detect this visually and see if you should test for a significant interaction. Sometimes the main effect is analyzed in the presence of an interaction, depending on the interest of the researcher.

#### Lowpro

##### New Member
On the subject of interactions, when an interaction is detected you must present the stratified results. You cannot report the aggregate measure of association at that point as it is masked. This can lead to a few problems due to numbers (gender ratios etc) which can present "Simpson's Paradox" problems. Interactions have their own measures of significance (additive and multiplicative*) but the rule of thumb is that the interaction should be quite strong to be significant; more than just a significant P-value at that point

*I speak as an Epidemiologist more than a Biostatistician on this point; epidemiologists interpret interaction significance with a more heuristic rigor based on prior research. If a strong interaction is present when previous research never shows it for instance, it's often reported and commented on but not presented in conclusion. They're difficult to interpret.

##### New Member
Hi thank you for replying and the information you have given.

Firstly, the hypothesis was basically that the level of fatigue in the muscle would increase as the duration of exercise increased, and that the fatigue would still be present after the 30 minutes of rest for the longer exercise durations.

Yikes, i'm not to sure about the necessary assumptions, would the stats software I used not take care of that? And sorry, I am not to sure what you mean by what type of sums of squares I used? I just plugged everything into the software and let it analyse and do the rest. We had to normalise the data as the activity level measured at baseline would change subject to subject day to day, so by normalising the data we could account for day to day variations.

Oh right I see, so for my study we were looking at the interaction between fatigue immediately after exercise to that present after 30 minutes of rest over the different exercise durations. Yeah I did that, created graphs. We found significant interaction for many different variables, I think i am just confused on how to interpret them and if there is any point. So say fatigue is shown immediately after exercise with more fatigue with the longer exercise durations, while after 30 minutes of rest fatigue is only present at the longest exercise duration while all other exercise durations return to baseline, so there is significant interaction, statistically would it need anymore interpretation than that? And great, i think we would need to analyse main effect even in the presence of an interaction, I just wanted to make sure I wasn't breaking any statistical rules.

It may be useful if you explicitly stated your hypothesis for this study.

Based on what you described, a two-way repeated measures ANOVA seems appropriate, assuming you checked the necessary assumptions. For your other questions regarding the two-way ANOVA, I think you need to clarify what type of sums of squares you are using. I'm also curious why you "normalized" the measures to the first measure instead of just including each measure in the model.

There are several possible types of interactions. Essentially, an interaction occurs when a variable in one group changes relative the other group. For example, you provide men and women with a treatment over time, and the treatment causes a variable to increase in men but not change in women. You can create an interaction plot to detect this visually and see if you should test for a significant interaction. Sometimes the main effect is analyzed in the presence of an interaction, depending on the interest of the researcher.

##### New Member
On the subject of interactions, when an interaction is detected you must present the stratified results. You cannot report the aggregate measure of association at that point as it is masked. This can lead to a few problems due to numbers (gender ratios etc) which can present "Simpson's Paradox" problems. Interactions have their own measures of significance (additive and multiplicative*) but the rule of thumb is that the interaction should be quite strong to be significant; more than just a significant P-value at that point

*I speak as an Epidemiologist more than a Biostatistician on this point; epidemiologists interpret interaction significance with a more heuristic rigor based on prior research. If a strong interaction is present when previous research never shows it for instance, it's often reported and commented on but not presented in conclusion. They're difficult to interpret.