I want to compare proportion data (sex ratio) between two treatments. There are 19 populations for each treatment (i.e., 19 replicates).

The specifics of the data is that it is the proportion of male offspring (i.e., sex ratio) resulting from from two treatments a and b. The experiment was repeated 19 times, though the samples are independent (i.e., not paired). The null hypothesis is that the proportion of male offspring (sex ratio) is not different between the two treatments.

I therefore have a nominal response variable (i.e., proportion male) and a categorical explanatory variable (treatment a or b).

My data table is set up as:

Treatment / male offspring / female offspring
a / 17 / 54
a / 21 / 64
etc... (19 lines for a)
b / 34 / 56
b / 45 / 57
etc.. (19 lines for b)

I have got as far as thinking that I need to use either a Pearson's chi-squared or a Fisher's exact test. I am not sure if that is the correct approach? I am also not sure how to analyse the data where there are replicates. For example, do I need to combine all the figures from the replicates to put into a 2x2 contingency table (i.e., total male and total female offspring in treatment a and total male and total female offspring in treatment b?)

  • $\begingroup$ stats.stackexchange.com/help/on-topic explains what's on topic here. As you seem to be asking only for R help, this looks off-topic to me. If that is wrong, please re-write the question to bring out what's statistical. $\endgroup$ – Nick Cox Jan 22 '17 at 13:10
  • $\begingroup$ Thank you Nick. I have rewritten the question. My question is initially statistical. It is to determine an appropriate statistical test and how to deal with replicates. Once I have an answer to that I will decide how to approach this in R as the next step. $\endgroup$ – Sitobion Jan 22 '17 at 13:25
  • $\begingroup$ Is each "population" a mother? I can't tell if you simply have 19 binomial data points, or if there is more to this. $\endgroup$ – gung Jan 22 '17 at 14:35
  • 1
    $\begingroup$ This no longer seems to be about R code. I think this is on topic at present. $\endgroup$ – gung Jan 22 '17 at 14:35
  • $\begingroup$ Each population consists of the sons and daughters from a mother. Perhaps an easier way to think about this is I have 38 populations which were subject to a different treatment. 19 to treatment a and 19 to treatment b. I want to compare the % of sons in the populations of those subjected to treatment a to the % of sons in the populations subjected to treatment b, to see if these differ. It would appear that a t-test could do this. However, this is proportion data bound by 0 and 1. I am not sure how to approach this, but think of Chi-sq or Fishers test may be the answer. $\endgroup$ – Sitobion Jan 22 '17 at 14:58

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