There is one more important detail that you need to know about all forms of chi-square tests from one way to
large cross tabulations,
and it has to do with the size of the expected frequencies that you use.
I want to warn you about the nuisance of small expected frequencies.
In the one-way Chi-square goodness-of-fit tests that we learned on, the
expected frequencies were all larger than 5, but
small values for expected frequencies in a cell will increase the chance of a Type I error.
To address this problem at least 80% of the cells should have expected frequencies greater than or equal to 5.
In fact you will notice that
SPSS gives you a notification about the percentage of cells that have expected frequencies less than 5.
Violations of this assumption increase the chance of making a Type I error
You will find outcomes that appear to be statistically significant
but are not. So what can you do if your expected frequencies are too small?
Well you have options.
When you have two small expected frequencies the best option is to collect more data.
Fundamentally you have too small of a sample size, and you need more data.
Now ideally you don't wait until you have this problem before you address it
Plan your data collection for this contingency to make sure that you will have enough participants
Now another option is to collapse categories with expected values less than 5
Now this only works that the categories are conceptually related. If you're using categories, let's say, from a high school
with freshmen, sophomores, juniors, and seniors
But the cell for seniors had an expected value less than 5
You could combine the juniors and seniors into a category called
"upperclassmen" because those class standing categories are conceptually related
By contrast if the categories were racial groups such as Black, White, Hispanic, Asian,
Pacific Islanders, and Native Americans
But you had small numbers of Pacific Islanders and Native Americans,
you could not reasonably combine those two racial categories because Pacific Islanders and Native Americans are not conceptually the same.
These are folks from two very different parts of the world.
You could, however,
combine to create categories such as "White" versus "Non-White" because those do make sense conceptually.
Now if the categories cannot be combined
then you could remove categories with expected values less than 5.
Now this, of course, will reduce your sample size which may reduce the power of your test.
On the other hand, if the people in the categories were underrepresented, and you had plenty of people in the remaining categories
then you probably have enough people anyway, so this might not be a problem.
Finally, you can use something called Yates' Correction for Continuity.
Yates' Correction for Continuity changes the difference between O - E.
It adds a 0.5 if O is greater than E and subtracts a 0.5
if O is less than E by adding a negative.
If you want to use Yates' correction, there are two things you should know:
First, it can only be used if you have a 2x2 design, not a one-way chi-square or a large cross tabulation
Second, Yates' Correction tends to over-correct leading to more Type II errors,
and because of this the use of Yates' correction is generally considered unnecessary.
I'd recommend against using it. Now, on the other hand,
I have seen researchers use it, so I wanted to let you know what it is, and when its use would be appropriate.