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Let me ask you this. Is the size of this effect .05? Pause the video and write down what you think the answer is.
No. .05 is our level of doubt or our chance of making a Type One error
or false positive, or being wrong. When we reject the null. Is the size of the effect
5.82? And the answer here is no. Just because we compute a Chi Square of 5.82, that does
not mean it is an effect size of anything like 5.82. So the takeaway here is that we
still need to do another test to figure out what the effect size is. And we have not yet
done it. So now that we have, this is like an overall omnibus significant Chi Square.
Now we can assess the effect size and figure out if it is small, medium or big.
And I will show you how to do that now. We are going to compute "phi" coefficient. Like
"fe, fi, fo, fum" and the notation for it is like that. And to figure how big the effect
is you take your Chi Square statistic divide it by "n" where "n" is the total number of
people in the whole study. Then you are going to take the square root of it. Why? Well,
because think about what we computed with squared stuff all out of proportion. We are
now un-squaring by doing the square root and also the more people that are in your study
the more your expected frequencies and everything would be. So, in the example that we did today
what was Chi Squared? Just do the formula and then plug everything in to calculate "phi"
or the effect size. This is a measure of the size of the effect once you have a significant
Chi Squared. What was Chi Square again? 5.82, right? And what was the total number of people
in our study? Look back at you notes from video number one in this series. We have 136
people in the study. So now pause this video and take 5.82 divided by 136. See if you get
it right. 5.82 I should say divided by 136 and you are going to get, if you did it right,
.043. Now, take the square route of .043 and make sure you have your calculator and you
know how to use it to do this. Pause the video and see if you get it right. The square route
of .043 is about .2. Now this number, "phi" is always going to be between zero and one,
so this is in the right range. We probably might think that we did this right. And is
it big, medium or small? Well you can look it up in your book what makes a big, medium
and small "phi" or effect size. This is not quite medium. It is not very big. OK, so this
is the final step after a significant Chi Square. If you have an effect and you can
quantify the size of it.