I am carrying our an experiment to characterize the biological effect of three mutant proteins compared to the wild-type control. I carry out triplicate experiment each time for the four proteins (to reduce random errors), and repeat this three times in different days (to be sure there is no systematic error due to equipments, etc.). So in total I have 3 x 3 data points for each protein. My ultimate question to answer is, is the biological effect of mutants statistically significant compared to the wild-type?
I am thinking to: (1) take mean for the triplicates (now I have 4 groups of data, each has 3 values); (2) carry out t-test to compare each mutant group to the wild-type group.
Is this approach appropriate?
" is the biological effect of mutants statistically significant compared to the wild-type? " - this question is ill posed. Statistical significance is about your sample data in relation to some assumed effect in some assumed model. I suppose this is what you meant to ask, but formulating the question the way you did can easily confuse readers, as they may think that hypothesis tests may be about biological effect (actually, I think many do just believe this, erroneousely).
The first thing you should think about is an error model. You need some understanding of the data-generating process or experience with "such kind of data". If these are counts, for instance, a Poisson or negative binomial error model would likely be a good choice, if these are concentrations, a log-normal or gamma model could be appropriate, and so on.
The other part is the functional model, what is realted to your experimental design. You have the experimental factor "genotype" (or sequence, or call it whatever you want) what is categorical with 4 different values/categories: wt, mut1, mut2 and mut3. For each category you have 3 replicate measurements per day, and this is replicated over several days (so you have "within-day-replicates" and "between-day-replicates"). You thus have a hierarchy of replication, what is called a hierarchical design. The variation in each hierarchy level may be different.
If you want to make a statistical statement about expected differences (of the response) between the levels of your experimental factor, these expectations should relate to what one should expect when one would replicate the experiment. The key point here is that any replicate experiment will neccesarily be on a different day (the highest level of replication in your design). Therefore, it is the variriation between days that is of interest when expressing the uncertainty of your conclusions (p-values, confidecne intervals, whatever).
Hierarchical designs can be analyzed with hierarchical models (that allow a hierarchical formulation of the error-structure). They give you estimated of the within-day variance and of the between-day variance. However, your interest is only in the between-day variance. You can thus simplify the analysis by averaging all within-day measurements, so that you have a single (average) value per day and use a simple (non-hierarchical) model that only estimates one variance (i.e. the between-day variance). Within this model you can get the p-values and confidence intervals you want.
If you have many proteins, you may even think of sharing information (about the variance) between proteins to get more robust conclusions.
T-Test is in case you have a multivariated normal data, which requires to do more tests, try instead studying each effect among days, becouse the experiments with any effect should be not dependent each other if not tests can get more complex.
Hello
1. Your question is not very clear, and what is your problem?
2. The analysis should be based on your research questions and hypothesis.
3. What is the relation between the random variables, i.e. related or not.
4. The sample sizes of the random variables have to be given.
5. Several statistical tests could be developed in your research(parametric and non-parametrics measures, testing of hypothesis of the differences, ANOVA, estimating some parameters, components analysis, correlation coefficients, modelling regression equations, multiple comparisons, …).
Regards,
Zuhair
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