Chi-squared, and the associated Probability Density Table, is used to quantify the match between a hypothesis and observed data. Chi-Squared is used a heck of a lot in all sorts of statistical sciences but has become a pain in my life recently because of genetics. So let’s use our TI-83 calculator to crunch the numbers for us.
To make things easy we’ll need three different programs. Let us start with the most basic:
Chi
hit the ‘program’ button (here on callled prgm), then arrow over to the ‘New’ menu and choose ‘Create New’.
name it ‘Chi’ – Enter the following code
Disp "Input Observerd"
Input O
Disp "Input Expected"
Input E
((O-E)^2/E -> C
We now have our Chi-Squared function so now lets make the Probability Density program. Again, create a new program, called ‘ChiTable’ here – and enter the following code:
N-1 -> D
(T^((D/2)-1)*e^(-T/2))/(2^(D/2)*(((N-1)!)*(D/2)))->P
Alright almost done – let’s tie it all together with our main program. Again new program, called here ‘ChiSQR’ – enter the following code:
0->R&8800
0->T
0->N
0->C
0->P
Disp "Number of Sets"
Input N
While R ≠ N
R+1 ->R
prgmCHI
C+T->T
Disp T
End
PrgmCHITABLE
Disp "Probability"
Disp P
Alright – so let’s test it to make sure it works – Hit PRGM, EXEC Tab, Then CHISQR and input the following information:
| Type | Observed | Expected |
| 1 | 62 | 50 |
| 2 | 38 | 50 |
The program should output 2.88 for the first set, then 5.76 for the second and the probability should be .03307……something.
If you don’t get that double check your work.
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