Apologies if this has been answered, I was not able to find anything similar to my question.
In 3 separate days, I have analysed cells from 10 WT and 10 KO animals by flow cytometry. Below I show some made up MFI values of a fluorophore to make my point. You can see that between each experiment the readings are shifted but in all 3 experiments, there is an approx 40% increase in the MFI values of the KO compared to the WTs. For this experiment, a 40% increase is biologically relevant but without any normalization, a T-test does not show a statistical significance.
If I was comparing two different treatments made on the same cells, I would run a paired T-test in the unnormalized data, but since here my KO and WT cells are not coming from the same animal, can I also do that?
Since I cannot repeat the experiments, my way of going around this is by dividing all values from each experiment by the average of the controls of that experiment (last 3 columns). The average of the control group will always be one but there is SD as well. The T-test ran with these normalized values now shows statistical significance, but is this correct?
If my understanding is correct, you had different baseline for each day of experiment. First, you can't use paired t test to compare KO and WT. These are two independent groups. Second, it's not clear to me whether or not you have same baseline reading for both KO and WT at each day. Regardless, you can use linear regression/ANOVA to compare group while control for each cell or experiment's baseline. Basically on the left side of equation you have the MFI value, right side you have group and baseline reading (covariate) as predictor. The regression coefficient of group tells you the difference of KO vs WT given baseline reading holds consistent.
Thanks very much for your reply. I have probably misused the word baseline in my question (now corrected). What I meant was that both the absolute values of WT and KO change between experiments but the relative differences are maintained. That I am aware, flow cytometry does not provide any baseline value per se that can be used to correct for the variability between experiments like you suggested
In order to make the distribution of differences more symmetric the standard approach is to use log(MFI_WT)-log(MFI_KO).
To control for the heterogeneity caused by the day of the experiment, perhaps, you should introduce a dummy variable.
But the major problem is that 10 cases is not sufficient to conduct a reliable analysis.
When relative performances or relative indicators are being compared we presented a special technique in this chapter (Davydenko and Fildes, 2016, see p. 24 of the author version available on RG or p. 246 of the original chapter published by Springer):
Chapter Measuring Forecasting Accuracy: Problems and Recommendations...
So, as suggested by (Davydenko and Fildes, p. 246) you need to use the Wilcox test applied to log(WT)-log(KO). If this test shows high evidence for the median being different from 0, then you can confirm your finding. T-test can also be applied, but you cannot be sure your distribution is normal. Given that you cannot repeat the experiments, I would report the t-test and Wilcox test results for reference, but at least the same number of observations is needed to make the analysis more reliable.
Andrey, thanks for your detailed reply.
As I tried to explain in my question, WT and KO are not paired groups as these samples are coming from different animals.
As a result, in the calculations to make the distribution of differences more symmetric, I don't know which log(MFIs) to subtract. Would it make sense to average the MFI WT and KO used in each separate day and run a paired T-test? If there is evidence the groups are different, can I then do the analysis I propose in the last paragraph of my question?
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