# 3-factor anova

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Elzbieta el 5 de Jul. de 2024
Respondida: William Rose el 19 de Jul. de 2024
Hello,
I would like to ask how to perform 3-factor anova (2-level noise, 3-level device, 9-level activity) on ECG signal data as well how to prepare related charts?
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### Respuestas (2)

Aditya el 5 de Jul. de 2024
Hi Elzbieta,
Please refer to the example mentioned in the anovan documentation, as the anovan function can calculate N-way ANOVA:
Example:
• Three-Way ANOVA
• Multiple Comparisons for Three-Way ANOVA
For plotting, you can explore the interactionplot and main_effects_plot functions in MATLAB. Here are the documentation links for these functions:
These resources will guide you through performing the analysis and visualizing the results.
I hope this helps!
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William Rose el 19 de Jul. de 2024
I interpret your original posting to mean that you are anayzing EKGs that are recorded with 2 levels of noise, 3 different devices, and nine "levels of activity". I don't know what "levels of activity" means. Does it refer to different exercise intensity levels, from no activity (level 1) to maximal activity (level 9)?
To do ANOVA on EKGs, you need to compute one number from each EKG signal. What is the one number which you will compute from each EKG? For example, you could compute a heart rate (HR) estimate from each EKG. Or you could estimate the HR variability from each EKG signal - and there are many measures of heart rate variability to choose from. Or you could compute some other quantity.
Consider the hypotheses you are testing with a 3-factor ANOVA. For purposes of illustration, I will assume that you are computing an estimate of HR from each EKG signal. For the 3-factor ANOVA, the first hypothesis tested is
H0 The mean HR is the same for all levels and combinations of of noise, device, and activity.
H1 The mean HR is not the same for all levels and combinations of noise, device, and activity.
The main effect hypotheses tested in the three factor ANOVA are
H0a The mean HR is the same for both levels of noise
H1a The mean HRs of the two noise levels are different.
H0b The mean HR is the same for all three deivces.
H1b The mean HR is not the same for all three devices.
H0c The mean HR is the same for all 9 activity levels.
H1c The mean HR is not the same for all 9 activity levels.
Three hypotheses about interactions between factors will also be tested. You must take considerable care to communicate the ANOVA results clearly and correctly to your audience. You may want to evluate you r overall research goals and consider carefully whether a three-way ANOVA is the best approach to meet your goals. See here for reasons to avoid three-way ANOVA.
I suspect that the third factor, activity, is naturally ordered, from low to high. If so, you may want to include regression analysis instead of ANOVA for the activity factor. ANOVA treats the 9 different activity levels like 9 different devices, or 9 different drugs, which have no intrinsic order to them, and by doing so, it fails to take into account something significant about the data.
ANOVA makes assumptions about the data. You should check that your data does not deviate a lot from these assumptions. The assumptions are 1. No outliers in the data. 2. Normally distributed data (i.e. the heart rates are normally distributed). 3. Homogeneity of variance (i.e. the variance is the same, or at least not hugely diffrerent, between the different levels of the different factors).
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