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I ran an experiment in a greenhouse investigating whether or not different plant species tend to grow taller when inoculated with symbiotic fungi. There were 8 trays which each had 18 pots; each of 4 species had one tray with the fungi and one without. The experiment took place over 8 weeks, and for 6 of those weeks I have a measurement of the height of the tallest plant in each pot. For 3 of the species, the inoculated tray usually had a greater average height than the non-inoculated one, but I want to run a P-value test to determine whether or not this is significant.

I have not done P-value tests before, and the information I have found online (through Khan Academy and elsewhere) seems to give contradictory advice. I would like to be able to include all of the data for each species instead of finding separate P-values for each week, and my current thought on how to do this is to use plant height divided by week number to get values that can be compared across the whole experiment.

However, I'm not sure how to calculate Z-scores, specifically because some sources seem to say to use the population standard deviation and others say to use the sample standard deviation, potentially divided by the square root of the number of samples. I am also unsure of how the terms "population" and "sample" apply to my experiment, since I have been thinking of it as comparing two different equally-sized groups.

So, my main questions are:

What do "population" and "sample" correspond to in this case?

How do I calculate a Z-score?

Any help with this would be greatly appreciated.

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Welcome! It seems like you have a fairly complex experimental design (4 species, 1 treatment, 8x18 pots, 6 time points) which could be analyzed in a variety of ways (*see note below). It also sounds like you are new to statistics. Based on your description, it sounds like you are trying to compute the p-value using a t-test or a two-way ANOVA. If you search for these terms in the documentation of whatever statistical software you have access to you will find descriptions of how to run them. Note that the p-value is not a test in of itself, but one of the results of many statistical tests.

*If it were me, I would run a mixed effect model with random intercepts for tray and pot, and a random slope for time. You have a fair amount of structure to your data, so running lots of t-tests or ANOVAs, and then correcting for multiple comparisons, is generally not advised. But, it's a decent first step for a new analyst.

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  • $\begingroup$ A potential issue: Independence of the height of a plant across adjacent weeks would seem fairly dubious for an assumption. $\endgroup$
    – Glen_b
    Feb 2, 2023 at 6:22
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    $\begingroup$ Exactly, hence my point about using a multi level model at the end. I just don't think OP is up to it, going by the language they used. $\endgroup$
    – David B
    Feb 2, 2023 at 11:18

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