I am having a hard time to understanding when to use which of these tests. Fisher's test is useful for small sample sizes to compare categorical variables. Ok. Take a simple example, you have data such that in R code:
sampledata = data.frame("male" = sample(0:1, r = T, size = 1000), "obese" = sample(0:1, r = T, size = 1000), "heightShort" = sample(0:1, r = T, size = 1000), heightTall = sample(0:1, r = T, size = 1000))
And if you wished to do comparisons to see if the proportion of obese, heightShort and heightTall is different for male and female what is the appropriate test? Since this is binary and I want to compare proportion I think also Welch's T test statistic may be appropriate also but I do not know if there is a right or wrong or best choice to do. Again I wish to compare proportions.