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I would love some help with interpreting a non-parametric test. I have data on the # of seed heads produced by an invasive plant species (n=80 plants). I applied a grazing treatment in an attempt to reduce the number of seeds produced by this invasive plant (targeted grazing treatment). I harvested 40 plants post-targeted grazing, and 40 plants within a control, ungrazed enclosure.

Most plants within the targeted enclosure were grazed, and had values of 0. My data was not normal, so I used a Wilcoxon rank sum test with continuity correction. My null hypothesis is that there is no difference in # of seed heads between the grazing treatment and the control, ungrazed group.

Here is my code for that exact test:

wilcox.test(Seedheads~Treatment,mu=0,alt="two.sided",conf.int=T,conf.level=0.95,paired=F,exact=T,correct=T)

Please see below the output of this test:

W = 1384.5, p-value = 4.94e-09
alternative hypothesis: true location shift is not equal to 0
95 percent confidence interval:
  7.999998 30.000030
sample estimates:
difference in location 
              22.99994 

From my understanding, the p-value is much smaller than .05, so I reject the null hypothesis. There is a significant difference in the number of seedheads. Is my understanding of this correct? Could I state that my p-value is <0.05 when discussing my results?

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    $\begingroup$ Your understanding is correct. It is best to list the exact p-value. In your case, the result is highly significant because the p-value is much smaller than the significance level. $\endgroup$
    – stans
    Jan 26 '21 at 6:54
  • $\begingroup$ Your question is about interpretation of statistical results, which is fine. Using R is important for you but nothing to do with the question. $\endgroup$
    – Nick Cox
    Jan 26 '21 at 18:16
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You can see from the help of the function ?wilcox.test that your code performs a "Wilcoxon rank sum test (equivalent to the Mann-Whitney test: see the Note)".

Although this test is sometimes considered the non-parametric equivalent of t-test, this could be, or not, the case, depending on the distributions of the data you compare.

Your result could just mean that the populations you analyzed are different or that there is a difference in medians and means, depending on the shapes of your variables.

First of all, you should notice that the test compares ranks and not the actual values.

If the two variables have the same shape, then you can interpret the result as a rejection of the null hypothesis that there is no difference in the medians of the variables. If the two variables have the same shape, moreover, a change in median corresponds to a change in mean, so you can also consider the test as a rejection of the null hypothesis that there is no difference in means.

On the other hand, if the two variables have different shapes, you can interpret the result as the rejection of the null hypothesis that the two variables come from the same distribution, or that there is no differences between the ranks of the two variables.

You could watch this brief educational video that explains how the test works, which I found very useful to get a better understanding of the procedure behind the test.

Disclaimer: I am not a statistician so there could be much more appropriate explanations (you could also perform a search on the site to read other questions and answers on this test)

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