What are the 5 steps of hypothesis testing ?
Decide the effect and design a suitable experiment
Set up null hypothesis ( assumed to be true )
Decide rejection region
Do experiment and collect data
Make a decision
Whats the p-value ?
Propability value
Propability of obtaining test results at least as extreme assuming the null hypothesis is correct
Whats a Type I error ?
Rejecting the Null hypothesis even though it is true
Whats a type II error ?
Propability to fail to reject the null hypothesis given that its false.
Whats the t-test ?
A test to compare if 2 means are statistically significantly different
Null distribution is the t distribution
m1 / m2 mean values
s scale ( sum of variances of both groups normalized by sample sizes)
c scale for different group sizes
What are problems with the t-test ?
It assumes equal variance in both sample
=> Welch-test can be used instead
With small samples the t-test is only valid if Xj is normally distributed
Variance estimator is highly variable with small sample sizes
What are t-test alternatives ?
Fold-changes
Modified t-tests
Permutation procedures
no distributional assumptinos, compute intensive, not adequate for small samples
Wilcoxon-test (distribution free, does not require normal dist)
only take rank into account
not adequate for small samples
What are caveats of one-at-a-time testing ?
By doing many many different univariate tests some null hypothesis will be rejected by chance
Which test should be used for which omics data?
binary Y; transcriptomic X => t-test
binary Y; SNP data => X2-test, Fishers exact test
censored Y; transcripomic data => Wald test
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