I am a beginner trying to learn statistics. I have a questions related to randomising simulations to accept or reject null hypotheses.

A random experiment was conducted with 48 bank managers to determine if there is a gender discrimination at the work place.

There were 48 IDENTICAL RESUMES, 24 of them belonged to male applicants, 24 belonged to female applicants.

24 managers received 24 RESUMES belonging to MALES, the distribution of the resumes to the managers was assigned at RANDOM.


24 managers received 24 RESUMES belonging to FEMALES, the distribution of the resumes to the managers was assigned at RANDOM.

Out of 24 males, 21 were promoted.

Out of 24 females, only 15 were promoted.

Meaning that the difference between the male promotion rate and female promotion rate was roughly 29%

NULL HYPOTHESIS: There was no discrimination. In other words, the 29% was due to chance.

ALTERNATIVE HYPOTHESIS: There was discrimination.

The same experiment was simulated 100 times and a dot plot was drawn.

X AXIS - Promotion percentage difference between male and female observed from -100% to +100%. Centre being 0%, left extreme being -100% and right extreme being 100%.

Y AXIS - DOT COUNT from each simulation.

I hope you can visualise it. The video explained that, since from the 100 randomised simulations, since there were approximately only 2 or 3 data (represented by the DOTS) that had the difference of 29% just like the data we observed and LOTS of data (represented by the DOTS) which had -3% to 3% (negative 3% meaning, that females were favoured) we can reject the null hypothesis.

My questions is, if in these 100 randomised simulations, the dot plot showed that there were in fact MAJORITY (largest no. of DOTS) at the 29% mark, then we must ACCEPT the null hypotheses? That the discrimination occurred due the chance since even after randomising (making it appear the everything is due to chance) we still obtained the same data that the FIRST record of 29% difference showed?

  • 1
    $\begingroup$ Welcome to CV. Since you’re new here, you may want to take our tour, which has information for new users. "The video explained that", which video are you referring to? Also, please edit the question to fix the formatting. As a side note, it might be better to use "failure to reject the null hypothesis", instead of saying "accepting the null hypothesis." To get a better idea about the interpretation of the null hypothesis check here. $\endgroup$ – T.E.G. Apr 30 '17 at 5:38

The image is not being shown [1], but I'll try to answer based on what you wrote:

Your reasoning is correct. Roughly speaking, hypothesis tests are built upon a process that is fed using a sample of the data. In the most common form the result of this process is called a 'test statistic', which you compare to 'critical values' to decide whether or not to reject the null hypothesis.

In your example the statistics​ produced is the number of dots surrounding the 29% mark. Usually the troublesome part is coming up with critical values, which is often done through simulations.

The author in this case suggests that observing 2 or 3 dots leads to not rejecting the null hypothesis, so it makes sense to believe that a higher amount [2] would yield evidence for rejecting it. We could consider, as an example, that the critical value here is the number 10, so anything below it would lead to rejection of the null hypothesis.

[1] - new members can't post images, you have to upload them and then a link is embedded in your post. Try checking​ what went wrong in this process.

[2] - by higher we mean an amount obtained through a rigorous method that associates such a number (or an interval) with the event described by the null hypothesis.

p.s.: as suggested in the comment in your question, try referencing any relevant third-party material you mention and fixing spelling and format issues in your question - it helps people help you better.

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