Now, to determine if any of these findings actually have any statistical significance and we are sure that these differences are not due to 'luck' or 'chance', we have to do some (not so interesting, but very important) statistical analysis. If you are not interested in this, just skip straight ...
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If you're still reading however, let's get into it. We will be performing a series of one-sided hypothesis tests with a z/t-test statistic and a significance level of 0.05. We assume normality because our sample ..
First, let's look at the general results. In part 1, we got:
A sample of 192 with an average of 0.73 before and 1.27 after. The differences over these 192 cases had a st. dev. of 0.6499. In this case, we actually use a t-test, and get a t-statistic of approx.
In part 2, we got:
A sample of 167 with an average of 0.94 before and 1.27 after. The differences over these 167 cases had a st. dev. of .6298, which gives us a t-statistic of approx. 6.77, which again is very strong evidence ...
Then, for the individual categories, we perform z-tests with the variance of the population (managers that stayed) to the sample (new hires). I will not bore you with all the variances and such. But in PART 1, we got z-scores of:
0.5-0.99: 1.900
1-1.49: 1.592
PART 2:
0.0-0.49: <0
0.5-0.99: 2.08
1-1.49: 3.06
For 0.05 significance level, we get z-score of 1.645. In this case, in part 1 we fail to reject the first and third category (but barely for the third) and reject the second category, and in part 2 ...
Now that all the statistical mumbo-jumbo is out of the way, let's get to the conclusion.