2022 Introduction to Statistics in Research Mitchell 2nd ed

I N T R O T O R E S E A R C H : D A T A V I S U A L I Z A T I O N & C O M M O N S T A T T E S T S

So, when we run the statistics, we get the following results (this is in JMP) where zero (0) means dead and one (1) means alive.

Reject the Null Hypothesis

A p -value less than 0.05 is statistically significant. As you can see here, the Prob>ChiSq is 0.0466 which is under .05. This gives us strong evidence against the null hypothesis. Essentially, there is less than a 5% probability that the null is correct. Therefore, we reject the null hypothesis and accept the alternative hypothesis. But be careful - our alternative hypothesis does not mean quite what you think! When I did this in JMP, I changed the colors in the mosaic plot to match the uniform color. As you can see in the plot, most crewmen are associated with red uniforms (55%), whereas blue is 32% and gold is 13%. So, if we reject the null hypothesis, aren’t we saying that red uniforms have earned this reputation? We can conclude there is a relationship between shirt color and deaths! But there are a few more things to check out. One of the neat things about chi-square is that you can determine the contribution to the chi- square statistic. So, let’s take a look at it graphically.

Table 73: Chi Square of Star Trek Red Shirt dilemma

It's the blue and gold uniforms that contribute the most to the significance!

Included: the Cell Chi-Square (blue arrow in the contingency table above) which tells you how much each uniform color contributes to the Chi-square statistic.

Table 74: Chart representing contribution to the Chi-square statistic

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