It depends if there are several groups that you want to compare if anova krustall wallis in case there are only two groups to compare seria u de mann withney

You have binomial data, so you should use a binomial (logistic) model.

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as suggested above by Jochen Wilhelm , logistic model is an option ; in case the binomial assumption is very strongly violated (hey ... i have no idea what the distribution of iguana hatching proportions may look like !), beta regression would be another option

(for binomial data, the link between the mean and the variance should be v = m(1-m) ; this should roughly hold when using the logistic model ; the beta model is much more flexible ; Jochen Wilhelm , please correct me if i'm wrong here ! )

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another simple computational option is bootstrap

• experimental results : N1 proportions in one group, N2 proportions in the second group, empirical mean proportions difference D
• null hypothesis ; both groups come from the same distribution
• cool, so lets believe the null hypothesis is true and put all the (N1+N2) proportions in one single bag
• then, lets draw (independently, with replacement) N1 proportions, put them in one bag, then N2 proportions and put them in another bag ; compute the mean proportion difference between bags, d

Lets repeat such drawing say 1000 times

We end up with 1000 values of what the difference of proportion means between two groups of sizes N1 and N2 may look like when the null hypothesis holds true

In fact, the 1000 values sample the distribution of such difference d under the null hypothesis (an approximation of this distribution, to be correct)

it just remains to compare the experimental value D to this distribution (compare D to the estimated quantiles, which can often be directly read from the 1000 ordered d values) and conclude about the possible rejection of the null hypothesis

(in words : if D falls in the middle of the 1000 d values, the null hypothesis cannot be rejected ; on the contrary, if D falls far in the tails of the distribution then the null hypothesis might be rejected, depending on the requested confidence level)

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This can be used for the difference in means but also for the difference in medians and in fact for many statistics you find relevant to characterize your hatching proportions (does not hold for any statistics, however : wouldn't work for the min or the max for instance)

Also, the value of 1000 is just an order of magnitude ; it should be fair enough for most purposes. For instance for a one (right) sided 95% confidence test, the 95th centile of the distribution should be nicely approximated by the 950th d value in ascending order.

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Last point : N1+N2 should at least be something like 30

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Fabrice Clerot wow thanks for the super clear explanation! So I should probably start with a logistic regression now. However, it’s still not clear to me why using a Unpaired Two-samples Wilcoxon test cannot be used like Cristian Ramos-Vera recommended. Perhaps you can help my to clearify that too ;)?