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My goal is to know if significant differences exist between the different treatment concentrations as well as the two treatment timings (E5 and E6) in terms of survival rate.

The survival probabilities of each embryo are entirely independent from that of other embryos.

What statistical test can I use to analyze the data?

My data looks something like this.

trial treatment_day treatment replicate survived
1 E5 0 1 1
1 E5 0 2 1
1 E5 0 3 1
1 E5 10 1 1
1 E5 10 2 1
1 E5 10 3 1
1 E5 20 1 1
1 E5 20 2 1
1 E5 20 3 1
1 E5 50 1 1
1 E5 50 2 1
1 E5 50 3 1
1 E5 100 1 1
1 E5 100 2 1
1 E5 100 3 1
1 E6 0 1 1
1 E6 0 2 0
1 E6 10 1 1
1 E6 10 2 0
1 E6 20 1 0
1 E6 20 2 1
1 E6 50 1 0
1 E6 50 2 1
1 E6 100 1 1
1 E6 100 2 1

Treatment is in terms of mM of ethanol, with 0 as the control. There are 4 trials and 5 replicates (eggs) for each treatment (except for the initial trial, where there were only 3 for E5 and 2 for E6). Sample size is 105 eggs for E5 and 100 eggs for E6.

I tried running logistic regression using JASP and I'm getting these results, which don't seem right to me. enter image description here enter image description here

Does this just mean that treatment timing and concentration are not significant predictors of embryo survival? Can anyone help me out? My knowledge of statistics is not that good and we weren't taught logistic regression in our classes. Thanks in advance.

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    $\begingroup$ I would advise you to input the data as a table using markdown incase you want someone to be able to replicate your analysis or even use it to make their own analysis $\endgroup$
    – Derf
    Commented Nov 27, 2023 at 5:13
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    $\begingroup$ Thanks for the feedback. My data set is pretty large at n=205, but I'll add a table for a subset of the data. $\endgroup$ Commented Nov 27, 2023 at 5:44
  • $\begingroup$ (1) For E5, if there were 3 trials with 5 eggs for each of 6 treatments, & 1 trial (the initial one) with 3 eggs for each of 6 treatments, there'd be 108 eggs in total, not 105. For E6, with 2 eggs in the initial trial, there'd be 102 eggs in total, not 100. You're missing 5 eggs. (2) Presumably it's 1 embryo per egg: 'Egg'/'embryo'/'zygote'/ ... - best to stick to one term if readers won't need to make the distinction. (3) Presumably too, the egg number 1 that got 0 mM of ethyl alcohol on day E5 has got nothing to do with the egg number 1 that got 10 mM on day E5. $\endgroup$ Commented Nov 27, 2023 at 10:39
  • $\begingroup$ (4) If the presumptions in 2 & 3 are right, tabulating survivals & deaths for each combination of trial, treatment, & treatment time (96 counts in total) will suffice. (5) It would perhaps help an answerer if you explained what seemed wrong about the results. (6) You fitted an additive model with both predictors treated as categorical, but is that of particular interest, or just a software default? $\endgroup$ Commented Nov 27, 2023 at 12:10
  • $\begingroup$ Even with ~200 eggs you might not have enough data. For reliable fitting in logistic regression you typically need ~15 members of the minority outcome class per coefficient that you are trying to estimate. Your 6 coefficients (beyond the intercept) would then require ~90 members of the minority class, or pretty equivalent numbers of 0 and 1 values for survived. It looks like you have a lot more values of 1 than of 0, however. Also, I wonder if your model might be showing perfect separation. $\endgroup$
    – EdM
    Commented Nov 27, 2023 at 17:05

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