Using t-test to compare bias of means between uniform distributions

chi squaredhypothesis testingstatisticsuniform distribution

I am trying to figure out how to use t-test (or chi-squared test) to compare the bias between uniformly distributed data points I get from two sources.

For example, from

  1. S1 I have 400 data points (between 0 and 1) that average out to 0.520
  2. S2 I have 100 data points (between 0 and 1) that average out to 0.515.

Now both these samples are not purely uniform (which is okay). For now, I just was to know if the bias between 0.520 and 0.515 is significant enough.

I am confused about using a t-test because it requires the variance of the two samples (for standard error) and I don't know if it makes sense to use uniform dist variances.

For chi-squared test, I would want to compare if the uniform distribution of S1 and S2 match. I would create two intervals (0.0 to 0.5 and 0.5 to 1.0) and compare the frequencies for S1 and S2. Would these sample sizes (400 vs 100) be enough for me to do that or is there a better alternative test?

Best Answer

It makes sense to calculate the variance because it's not about the variance of the data points as much as it is about the variance of the averages. The probability distribution of the averages converge to a normal distribution as N grows (that's called the Central Limit Theorem).

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