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I have a question on how to "prepare" data for an ANOVA. Imagine I have 20 subjects and each subject has to eat 10 waffles, 10 pancakes, 10 eggs, 10 sausages. This is repeated 3 times with different "eating techniques" (Each subject actually eats 3x40 objects then). This is just a weird example, just imagine they could eat infinitely without drawback.

I always measure the time it takes to eat a single object. I want to find out if the eating techniques have significant influence on the time to eat an object.

How would I "feed" this data to the ANOVA? Would I take all single values (time to eat an object) which would result in F(2,740) or the mean values (average time to eat all objects) for each subject F(2,17)?

Sorry if this is a rather dumb question, I am new to statistics and never had a university course about it.

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The answer depends on whether you want to distinguish among 3 eating techniques "in general", or whether you need to know whether eating techniques may have different consequences depending on type of food consumed (waffles, pancakes, eggs, sausages).

Begin by making a list of 'factors' that are important to you and (where possible) what interactions may be important. Make the design just intricate enough for your needs.

If you are going to make ad hoc comparisons for significant effects, then make sure you have enough replications to provide necessary power under the rules to avoid false discovery.

Note: I suppose times to eat food is a fictitious example to avoid public discussion of your actual project. If your actual project involves waiting times to do something, then you need to consider that real-world waiting times are often best modeled by an exponential distribution, which would pose a difficulty in a standard ANOVA that assumes normal data.

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    $\begingroup$ Thanks for your answer. It is a fictional example but I think it is very close to what I am doing. What I want to investigate is basically "which technique is faster" and are techniques significantly faster than others. So again, would you take the values for each eaten object or would you take the average time (from 40 objects) a person required to eat? The purpose for different objects is just that I want to be a bit more general as to the statement "eating waffles is fastest with technique A" but I want to say "eating is fastest with technique A". $\endgroup$ Dec 14, 2021 at 12:55
  • $\begingroup$ Then "[T]ake the average time (from 40 objects) a person required to eat...." If the main 'eating technique' effect is significant at the 5% level, then look at ad hoc comparisons of techniques to see if one of the 3 stands out as significantly best (no guarantee of this), perhaps using Tukey's HSD to avoid 'false discovery' in multiple tests on the same data. // Even if eating times are somewhat non-normal, the averages will tend to be more nearly normal. (But if eating times are exponential, averaging 40 may not be enough. Look to see if residuals from your ANOVA model are nearly normal.) $\endgroup$
    – BruceET
    Dec 14, 2021 at 14:03
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    $\begingroup$ Thank you Bruce. I will do that. $\endgroup$ Dec 14, 2021 at 23:30

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