I have a dataset of the lengths of a species which has a 1-year lifespan, going back 20 years. I would like to test if the lengths recorded each year are significantly different from one another (for each sex, we already know that there is a difference between the sexes).

My length data does not have a normal distribution; therefore, I was thinking of using the Kruskal-Wallis test. However, I am not sure if that is the right way forward for the following reasons:

1) It requires an ordinal scale for the dependent variable, and I am unsure if this applies to length data

2) Is it okay that I am treating the years as a 'group' in this case? I would have ~20 groups.

3) Biologically speaking, I know that each year we are measuring different population, as this species spawns and dies (in a different location to where they are sampled) and the data is temporally independent. However, is there a way to prove this statistically? I attempted running the autocorrelation function in R but I am unsure if that is the way to go?

Many thanks!

  • $\begingroup$ How comes your lengths are not normally distributed? Because discrete ages? $\endgroup$ – KaPy3141 Oct 21 '19 at 14:00
  • $\begingroup$ @KaPy3141 Lengths will tend to be right skew. They certainly can't actually be normally distributed because lengths cannot be negative. $\endgroup$ – Glen_b Oct 21 '19 at 14:03
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    $\begingroup$ Lengths are ratio scale; Kruskal-Wallis should not have a problem (though personally I'd probably consider a generalized linear model). It's not clear that lengths are necessarily independent across years since the population in one year is descended from the population in the previous year. $\endgroup$ – Glen_b Oct 21 '19 at 14:04
  • $\begingroup$ @Glen_b: Thanks, I get it! $\endgroup$ – KaPy3141 Oct 21 '19 at 14:25
  • $\begingroup$ @Glen_b, thank you for the response, how would you suggest dealing with autocorrelation if I was to find that this is the case? Would a generalised least squares as described here - rpubs.com/markpayne/164550 applicable? $\endgroup$ – watermineporcupine Oct 21 '19 at 16:33

1): It doesn't need ordinal variables. Your R implementation automatically ranks your variables which makes them ordinal.

2): Yes, that's ok. Just be aware of additional biases than gender. (age distribution)

3) Yes, you can do a regression of your choice. For example linear regression to show that there is no linear time dependence.

(I am not a statistics expert myself, but I am quite confident this should be correct)

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    $\begingroup$ Could you explain how you're using linear regression to show there's no autocorrelation in "3)"? $\endgroup$ – Glen_b Oct 21 '19 at 14:07
  • $\begingroup$ I referred to the first part of the question: If there is a way to analyze temporal dependence. The answer is there are multiple ways. Just the result needs to be interpreted differently! (Linear for linear effect, auto-correlation for year-to-year effect) $\endgroup$ – KaPy3141 Oct 21 '19 at 14:18
  • $\begingroup$ @KaPy3141 Thanks for the info! $\endgroup$ – watermineporcupine Oct 21 '19 at 16:34

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