I have a dataset with 300 rows/genes and 900 columns/samples. The data were collected in 10 different batches, and study design was balanced in all of the batches. However, there is a huge difference in variances of each gene across multiple batches (1-5 units). I assume because of this, I am not getting statistically significant results because higher variance batches reduce the t-statistics.
One approach, I was taking is removing those high variance batches and do t-tests on small variance batches. However, is there any method that I can use which can account for different batch variances?
a <- rnorm(20, mean = 15, sd = 2)
b <- rnorm(20, mean = 13, sd = 2)
data: a and b
t = 2.8167, df = 36.319, p-value = 0.007799
Now I add another batch with same means but higher standard deviation-
A <- c(a,rnorm(20, mean = 15, sd = 5))
B <- c(b,rnorm(20, mean = 13, sd = 5))
data: A and B
t = 0.69185, df = 77.973, p-value = 0.4911
As I add another batch with higher standard deviation, I lose significance.