Hi,
I'm looking for the proper way to analyze some of my data.
I studied predation in fish, by looking at survival rates of different groups of larval fishes when facing predators.
In the first trial of the experiment, I put 10 larval fishes of the group A, 10 larval fishes of the group B, and 10 larval fishes of the group C, all together in a predation arena.
After 2 hours:
Group A had 10 survivors
Group B had 8 survivors
Group C had 6 survivors
In the second trial, same procedure.
Group A had 5 survivors
Group B had 4 survivors
Group C had 3 survivors
etc, multiple times.
The issue here is that predators are sometimes very hungry (see the second trial) and sometimes not that much (see thr first trial) so calculating a "survival mean" for each group, among all the trials, makes no sense to me (lot of variability).
So what I did is calculating the "overall survival rate" in each trial.
Overall survival in trial 1 : 0.8
Overall survival in trial 2 : 0.4
Then I substracted this "overall survival" to each group survival, in order to create some sort of an index that "normalizes" each survival rate according to the "overall predation" in each trial.
So this gives me the following:
In the 1st trial
Group A survival index = 1 - 0.8 = 0.2
Group B survival index = 0.8 - 0.8 = 0
Group C survival index = 0.6 - 0.8 = -0.2
In the second trial
Group A survival index = 0.5 - 0.4 = 0.1
Group B survival index = 0.4 - 0.4 = 0
Group C survival index = 0.3 - 0.4 = -0.1
So when I calculate the mean of these indexes for each fish groups among all the trials, I end up with something nice : group A survival index is always positive, group B around 0, and group C always negative, so low variability and nice means that suggest that group A survived more than group B, and group B survived more than group C.
But now I would like to test this statistically, and I can't find out how to compare multiple paired data of that type. I usually do my stats in R.
If anyone has suggestions I'll be more than happy.
Thank you very much for those who read me up to here, and thanks in advance for those who'll be able to help :)
Cheers
Marc
First, if your study is randomised and replicated correctly, you don't need to 'normalise' the data with an index (that's not true normalising btw). The design will take into account 'hunger'. Second, you need to analyse raw data, not percentages, otherwise you will have to transform them. Third, you can compare survival using paired t-tests or anova if the data is normally distributed or the Mann Whitney or Wilcoxon signed rank test or permanova if the data is non-parametric. BTW, are they atomic fish? lol
Hi Mark
I agree in large part with Andrew: Certainly use the raw data rather than converting to a percentage. Variability is expected; ANOVA accounts for that. I would add that you can simply test for normality to confirm that each of your three groups is normally distributed. If you learn that your data are not normally distributed then you can try some transformations to make them normal....that usually works; same transformation for each group. Then proceed with your ANOVA adding trial as a factor in the ANOVA thus accounting for fussy predators. If it's well replicated and the effect is real....you should be able to detect it.
Have fun!
Declan
Hi all and thank you for your answers! :)
Jos: I didn't understand your plot sorry :/. The yes are the survivors and the no the death because of predation. But I didn't get what corresponds to the circle size and color scale on your graph. Also why no circle for the B group ?
Andrew and Declan: I would like to perform Anova and Kruskal, this is what I've done so far and my results are cool, but I think this is not right.
Indeed, I think I really need a way to compare multiple means from "paired data".
During a trial, all the fish from all the groups are all together in the same predation arena (my goal is to study which group is more resistant/vulnerable to predation according to different environmental conditions). So the survival of a fish depends on the survival of the other fishes: if one dies, then others have more chance to survive (predators less hungry), so the number of survivors of one group clearly depends on the number of survivors of the other two groups, so i guess all my data are paired :/. So I have to find a way to compare that, and anova and kruskal are not applicable to paired data isn't it?
Also I have other data, not on survival, with paired samples, so a way to test and compare means from multiple groups with paired data would be really cool to me. No ideas for that?
Thank you again for your time and help!
The plot is for the "residuals" of Trial 1. The "residuals" are the differences from the Expected counts. Yes = survived, No = not-survived.
Observed counts for Trial 1:
A B C Yes 10 8 6 No 0 2 4
Expected counts for Trail1: A B C Yes 8 8 8 No 2 2 2 Residuals Trail1: A B C Yes 0.7071 0 -0.7071 No -1.4142 0 1.4142
For A there are more (-> blue) survivors than expected, for B the differences are zero (0), for C there are less (-> brown) survivors than expected. The darker the colors, the bigger the differences (from expected). If zero-> no color (shade = white).
See: https://cran.r-project.org/web/packages/corrplot/vignettes/corrplot-intro.html
I am not sure that the splitting of the problem into chi-squares is a good solution. The data crosses 3 categorical features : survival (yes/no), hunger (low/high) and group (A/B/C). Hence you have not a contingency _table_ but a contingency _cube_.
I add two files, one for copy of your data in a data frame format, the other is a pdf of a detailed treatment with the function glm() of R.
Hoping it may help and not being too verbous.
In attachment the R script for the GLM analysis proposed by Jean Maccario, in which I added the Mantel-Heanszel tests for Hunger and for Group.
R scripts can be run online (for free):
https://rdrr.io/snippets/
I ran a logistic regression on the same data with a SAS programme (see MS docx attachment).
SAS programmes can be run online (for free):
https://www.sas.com/en_us/software/on-demand-for-academics.html
Contingency tables are a device for log-linear models and can be any dimension 2 and more. And this looks like counts not continuous data. So log-linear model or multinomial.
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