I wanted to test if there is a difference between group levels so I created a contingency table that looks like
Respondents could fall into one of 4 levels of group B and they can pass or fail the test. I wanted to test if there is a difference between 4 levels in success/failure ratio.
Chi2 statistic suggested that I should reject null hypothesis and accept alternative hypothesis, i.e. it suggested that there is a difference between levels.
Since I wanted to know between which levels there is a difference, I used one sample t-test. It showed me that there is a difference between levels II&III and III&IV (I am not interested into differences between levels I&III, I&IV and II&IV).
Is this a proper way to do check for differences or there is some quicker, more proper and more elegant way to to that?