# Chi Square Analysis Percentages

I've used chi-square analysis in school, but was absent for the lesson, and I never quite got the hang of it. I've been successful with it in the past, but now I'm trying to use percentage values, and I'm not getting the answers I'm expecting. I'm doing a survey and comparing my findings with national averages, but when I use percentages (such as the percent of participants between the ages of 21 and 29) I get understandably tiny numbers (2.3% is 0.023). If I'm using percentages for the expected value, should it matter?

Ex: Chi² for 21–29 age group is $(.084 - 0.1642)^2 / 0.1642 = .039187$

The total chi-square value is 0.1368, which is much smaller than the 0.5% chi squared table value for 8 degrees of freedom, 17.535, but the numbers seem way off. Do I have to find the whole numbers?

• Chi-squared calculations in the usual form is for counts. If you scale all the counts down to percentages, you scale the chi-square down as well. (It's possible to work with percentages if you know the totals by which every value was scaled, but it's easier to do it with the counts.) ... there are many elementary tutorials on the various forms of chi-square test (goodness of fit, homogeneity / independence, and a number of others) that might be used on such data. Jun 22, 2014 at 23:25

Chi-squared calculations in the usual form is for counts. If you scale all the counts down to percentages, you scale the chi-square down as well.

Example

            Agegroup1   Other
Obs count     40         920
Exp %         3.1%      96.9%
Exp count     29.76      930.24

Chi-square = (40-29.76)^2/29.76 + (920-930.24)^2/930.24 = 3.636

Agegroup1     Other
Obs %         4.17%      95.83%
Exp %         3.1%       96.9%

Not actually chi-square: (.0417-.031)^2/0.031 + (.9583-.969)^2/0.969 = 0.00381


If the calculations are done exactly, the second calculation gives 1/960$^\text{th}$ of the correct values, for this example ($960=40+920$). In this case, rounding error in the second calculation means we got a little over that.

It's possible to adjust to make it work with percentages if you know the totals by which the values were scaled, but it's easy to just scale back to counts and do it with the counts anyway.

There are many elementary tutorials on the various forms of chi-square test (goodness of fit, homogeneity / independence, and a number of others) that might be used on such data.