How Do You Determine the Expected Number in a Chi-Square Test?

[vipertongn]

Ok, I am confused as to how we determine the expected number in the chi square equation: sum of (observed-expected)^2/expected. Can someone explain to me the concept of this. How do you find the expected number? Give examples too please,

My guess is that like the expected is like the the total progeny, and the ratio they are closest too, like for example if the ratio they are most similar to is 1:1:1:1. You add 1+1+1+1=4 so it's 1/4 and you multiply that by the total number to get the expected number.

Or for example if the ratio looks to be close to 9:3:3:1. you multiply the highest ratio number by the total (which is 16) so 9/16.

 

[Redbelly98]

It's easier to see with specific examples. Usually the expected number is what you'd get if there were no difference between the various groups or classes in the study.

 

[mg0stisha]

Also, with a chi-square test you are normally given groups of objects, and then a percentage of the odds of something happening to each group are.

For example: say you have groups 1, 2, 3, and 4. Each group has 10 people in it, making your n = 40. Now, the odds for a group to do something is as follows; 1 - 25%, 2- 12%, 3 - 50%, 4 - 13%.

To get the expected value, you take n times the percentage the occurrence will happen to each group (as a decimal). So in this case, the expected value for Group 1 would be (40 x .25). Group 2 - (40 x .12), Group 3 - (40 x .50), and Group 4 - (40 x .13).

Sorry if this was kind of confusing, but i hope it helps!