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This is not very clear. In the guidance it says, " if there were no association between the leader and influence questions, we would expect 2087 people to answer no to both… The more that the expected and observed tables differ, the more sure we can be that the variables are associated. In this example, we see some pretty big differences (eg., 3015 in the observed table compared to 2087 in the expected table). This provides additional evidence that these variables are associated.
In our observed and expected tables,
observed contingency table:
authority no yes
special
no 4069 1905
yes 2229 2894
[[3390. 2584.]
[2908. 2215.]]
Well 4069 is bigger than 3390? Likewise 2894 and 2215. But it’s printed “expected contingency table (no association):”)
The expected is a hypothetical number that shows the frequencies of responses that you would get if the two categorical values are not correlated in any way.
Looking at the values we actually got (the first part of exercise, ie the responses of a real survey), we notice they are different, (it does not matter if they are bigger or smaller) it just means that its likely that our categorical values have a correlation… be it positive or negative, that is for us to work out if we wanted to…
I think you did the order wrong on your statement. The output should look like:
observed contingency table:
authority no yes
special
no 4069 1905
yes 2229 2894
expected contingency table (no association):
[[3390. 2584.]
[2908. 2215.]]
The top specifies what we got and the bottom (expected) output is the values we would have expected if there was no association. It is not stating that there is no association.
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