How do you find your expected numbers for the Chi-Square analysis table?

Answer 1

As the first person who answered this question said, the answer to the question depends on what distribution you have in mind.

However, in practice, the most common application of the chi square test is to test if a crosstabs table has any rows or columns related to each other.

The definition of chi square statistic is sum of [ the square of (observed - expected) / expected ]

In a crosstab table,

the expected value in a cell at the intersection of a particular row and column is

the row total times the column total divided by the grand total.

This expected value could also be described as

grand total
* ( row total / grand total )
* (column total / grand total)


which some folks find easier to understand because
it's the same as

grand total
* proportion the row is of the total
* proportion the column is of the total.

Answer 2

Chi square is a 'goodness of fit' test. You decide what distribution you think fits the data and the Chi square test tells you how good the fit is.

So, what distribution do you propose the data comes from?

kermit is right.

What you're testing in that case is independence. In the case of independence of rows and columns, the cell values are given by the product of the marginal distributions. Once you get row sums and column sums, then you get expected cell values. Then use the chi square to test how closely observed values come to expected values.