I am measuring the concentration of 8 different solutions (7 samples and 1 blanco (which should be 0)) with 3 different methods. Each solution is measured by 3 analysts (with all 3 methods).
I would like to know if the analyst and/or the method is of significant influence on the measured concentration.
I am currently looking at two-way ANOVA. In the example they are testing the concentration measured in 2 labs by 3 methods (and determing the influence of the lab, the method and the lab x method). But then the analyst is not a factor. How can I include this?
I added my dataset
Regress the measurement on solution, measurement, analyst, and relevant interactions (if any). Normally some of these things (at least analyst, maybe others) should be modeled as a random effect, but with only 3 analysts then it's probably fine to keep it as a fixed effect and thus just use a normal (OLS) regression rather than a mixed-effects regression.
Two-way ANOVA is applicable. You may use Microsoft Excel or any other statistical analysis software (such as SPSS) for your results.
Where do I send ResearchGate memes?
I love it.
The original poster says that a two-way anova isn't sufficient for what she wants to do, and then (after a useful answer,) there are three answers saying "Just use a two-way anova".
Haha :)
Two-way ANOVA might be the way to go, but then I don't know how.... So maybe some extra information can be given on that :) (how to do this in Excel)
Someone suggested me to use:
The repeated measures approach I suggested earlier can be one way to go. You might also use one-way repeated measures ANOVA (using 9 levels for the repeated measures factor) and then use one of the follow-up tests if necessary.
Repeated measures MANOVA is another possibility.
Stephen's answer was to use a three-way anova, with sample, method, and analyst as the main factors. I think this addresses your original question.
As your person --- and Stephen --- suggested, you could also construct somewhat more complicated models.
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I don't recommend using excel for doing statistics. You'd be much better off learning a capable statistics package, which allows you to conduct statistical tests, but also can make summarizing and plotting data easier.
Probably the best place to start is by seeing what packages your department colleagues use. Being at the university, you might have access to a variety of packages. But also, there are free options like R.
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You will also want to take a graduate level analysis of experiments course. Even with something as relatively simple as a two-way anova, there are considerations and assumptions that go in to the analysis. One shouldn't use it without a fair understanding of at least the practical aspects of the analysis.
I did take a look at your data.
Caveat: The anova approach may not be valid because there is heteroscedasticity in the data. That is, the samples with low concentrations are much less variable than some of the other samples. You can see this in the attached plot.... This can be corrected for in the model; I didn't do this, but it is worth doing for a final analysis...
The plot attached shows the mean for each combination of Sample and Method. Error bars represent standard error of the mean.
I also attached some R code for the three-way analysis of variance, and the results.
Upshot:
There was no significant effect of Analyst or any interaction with Analyst.
Sample, Method, and Sample x Method were all significant.
Take a look at the plot. For samples 5 and 6, Method 1 grossly over-estimated the values, and there wasn't that much variability among analysts. A real effect, or some kind of mix-up?
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