Comparison of 2 groups

Question 1

t-test

Answer 1

Test difference in mean of two samples
Assumptions:
1) Two samples drawn from normal distribution
2) Observations within each sample independent of one another
3) Sample sizes of two samples, n1 & n2, are large (>30 each)
4) Population standard deviation, sd1 & sd2, are equal
Robust to small outliers, but doesn’t work if skewed

Question 2

Satterthwaite’s approximation

Answer 2

If sample standard deviations not equal, apply this approximation.

Question 3

Nonparametric tests

Answer 3

Do not typically assume a distribution of data or for test statistics.

Question 4

Wilcoxon rank sum test

Answer 4

Assigns ranks from 1 to N to each observation. If tires present, takes average of rank each would receive.
If the null hypothesis is true, then the sums of ranks only depends on sample sizes & not on shape of distributions.
If sums of ranks larger than theoretical expectation, evidence that distributions shifted by some difference, delta.
Very similar to Mann-Whitney U test.
Assumptions:
1) 2 samples of size n1 & n2
2) Observations independent of one another
3) Distributions of samples are the sample, except for a shifting factor (delta)