Which ANOVA type to apply in experimental design with replication?

With the given experimental degisn below, I have to apply ANOVA test in order to test the significance of changing temperature and reaction time. The experiment included 2 temp. levels (50 60) and 4 time levels (20 30 50 68) - Test 1. After Test 1, the experiment is replicated with new samples to give Test 2.

I am confused how to apply ANOVA test with this experimental design as I have different levels for the factors and replication. I am also confused if I should apply One-way ANOVA or Two-way ANOVA.

Any information that would improve my understanding of ANOVA is appreciated.

In advance, thanks for all the support.

Answer 1

[Cris LaPierre]

It's best for you to make that call, but here are the relevant pages:

• 1-way Anova
• 2-way Anova

A quick observation is that only 2-way anova talks about replication.

Answer 2

[Ive J]

You have repeatedly measured the outcome, so this would be a two-way (two categorical independent variables) repated-measures ANOVA. see this example.

[Baris Kara]

As I know repetition and replication stand for different meaning in experiments. In this case, the experiment is replicated. Matlab provides two different command (anova2 - for two way anova & ranova - repeated measures anova). Does repeated measures anova can still be applicable in this case?

[Ive J]

Sorry for my sloppiness, my original answer is incorrect, your problem seems a mixed ANOVA with one within subject (time) and one between subject (temperature) factor. Note that, I'm not talking about replication here, but about time factor. In your case, time is not a between-subject factor (ergo you should not use a two-way ANOVA) because you are measuring the response/outcome of the same sample/subject over time; therefore, there is a correlation/relatedness among the subjects.

To better understand this, consider a case when you have several patients and you measure the effect of a treatment over time. Here, time is not a betwee-subject, but a within-subject factor, because the same individual is followed/observed over time.

[Baris Kara]

Thank you very much for this detailed description Ive J, I have better understanding of the situation now!