Hi everyone,
I'm looking at how the number of neurons is reduced in mice with a certain genotype (two levels - one mutant mouse line, one control mouse line). I have looked at three time points (not in the same mice - between subjects design), and at the first time point there is no difference, but there is a clear difference in older ages.
My question is, how do I test this statistically, please?
I tried a two way ANOVA, which gave:
geno not sig. - 0.552
age sig. - 0.032
geno*age sig - 0.033.
The problem comes when I try to probe these interactions further -they are grouping genotype, or age together, so it's saying neither is significant. I don't want to run multiple one way ANOVAs or t-tests, so I was wondering if anyone knows how to bypass this issue?
(note - I'm not trying to force significance, I'm just noticing the results are not matching the very black and white data, and as I'm new to statistics I'm assuming it's something I've done wrong).
I would ignore the middle time point and analyze a 2x2 model. The interaction the directly tells you if the change in numbers between the time points (1->3) is different between the genotypes.
Another option is to code time numerically. This way, the interaction gives you the same as before, but "on average" over the time points (1->2->3). The problem might be that the time course is not very linear - but you may use a transformation of time to make that relationship linear.
Another thing: how large are the counts we are talking about? Do you recognize a relation between mean and variance in your data? Do you use a model for counts (Poisson or negative binomial?)
Is the output above the result of the first, second or third repetition of the analysis. I'm confuse about what the time variable is since it is not about the same mice over 3 periods.
Are the three period testing mice of different ages. Young, middle and old?
If the output is from one of the three times, then I would interpret it as age having a much greater effect on neuron numbers than genotype which has no effect at all at whatever age the output is from.
Are you saying that at older ages there is no difference?
If you could send the output from the various tests, including the ANOVA table with the coefficients (the slope) of the age effect, the genotype effect, and the interaction between the two variables as well as the sums of variance for each variable, I could more easily tell you what is happening. Either send it to me on Research Gate or to corneli@biology,utah.edu.
For the data above, I would say that the age*genotype means that the genotype is not expressed in young mice. But I don't know because I do not quite understand your experimental design.
Laura, if you tell us what software you are using, someone may be able to give more helpful advice about how to decompose the interaction. HTH.
A simpler approach would be to simply look at the values of the coefficients of each term (usually the first column of numbers) in the output ANOVA table. This provides more information about the effect of the interaction.
Do the ANOVA with and without an interaction term and compare the respective age and genotype coefficients under both models. It is possible that the value of the coefficients will be different with and without the interaction term. If so then regardless of whether age has a significant effect on its own, that the genotypes effect on age will be significant. Then age is a necessary component of the variance.
This could be because the genotype expression kicks in only at a certain age.
Did you try post-hocs (Fisher's LSD or Tukey's HSD if you want to be more conservative) for the interactions? These tests are usually included eith ANOVA in most packages and will tell you exactly which pairs of means are different from each other.
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