252chisqx2 10/27/06
Computations for the First Chi-squared example.
————— 10/27/2006 5:10:10 PM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > PRINT C11-C14
Data Display
Row O1 O2 O3 O4This is the original O table. Top line is labels.
1 10 15 15 10This is the same data as you were given for
2 5 10 15 10the first problem that I did in class.
3 15 15 10 20
MTB > chisq c11-c14
Chi-Square Test: O1, O2, O3, O4
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
O1 O2 O3 O4 TotalThese are the column labels.
1 10 15 15 10 50This is the first line of the O
10.00 13.33 13.33 13.33This is the first line of the E
0.000 0.208 0.208 0.833This is (E – O) squared, divided by E.
2 5 10 15 10 40
8.00 10.67 10.67 10.67
1.125 0.042 1.760 0.042
3 15 15 10 20 60
12.00 16.00 16.00 16.00
0.750 0.063 2.250 1.000
Total 30 40 40 40 150
Chi-Sq = 8.281, DF = 6, P-Value = 0.218All that you have here is the value of chi- squared that we computed in class, the degrees of freedom that we computed in class and a p-value which is too high for us to reject the null hypothesis of independence or homogeneity.
MTB > let c15 = c11+c12+c13+c14I am now setting up the problem as we did it
MTB > let c16 = c15/sum(c15)in class. The original data stays in columns
MTB > let c17 = c16*sum(O1)11-13. C14 is the sum of the rows. C15 is
MTB > let c18 = c16*sum(O2)the proportion in each row. By multiplying
MTB > let c19 = c16*sum(O3)the column totals by the row proportions
MTB > let c20 = c16*sum(O4)I got E.
MTB > print c11-c20
Data Display
Row O1 O2 O3 O4 sumO pr E1 E2 E3 E4
1 10 15 15 10 50 0.333333 10 13.3333 13.3333 13.3333
2 5 10 15 10 40 0.266667 8 10.6667 10.6667 10.6667
3 15 15 10 20 60 0.400000 12 16.0000 16.0000 16.0000
MTB > Stack c11-c14 c1.To do the chi-squared computations I
MTB > stack c17-c20 c2stacked the O columns in C1 and the E
MTB > let ‘O-E’ = C1 – C2'columns in C2. O – E was computed.
MTB > let chisq1 = 'O-E' * 'O-E'The last column was computed by squaring
MTB > let chisq1 = chisq1/E(O – E) and then dividing by E.
MTB > sum chisq1
Sum of chisq1 This is the value of chi-squared we got.
Sum of chisq1 = 8.28125
MTB > print c1-c4This is the table we had in class.
Data Display
Row O E O-E chisq1
1 10 10.0000 0.00000 0.00000
2 5 8.0000 -3.00000 1.12500
3 15 12.0000 3.00000 0.75000
4 15 13.3333 1.66667 0.20833
5 10 10.6667 -0.66667 0.04167
6 15 16.0000 -1.00000 0.06250
7 15 13.3333 1.66667 0.20833
8 15 10.6667 4.33333 1.76042
9 10 16.0000 -6.00000 2.25000
10 10 13.3333 -3.33333 0.83333
11 10 10.6667 -0.66667 0.04167
12 20 16.0000 4.00000 1.00000
MTB > let c7 = c11/sum(c11)To demonstrate the computations in
MTB > let c8 = c12/sum(c12)Chisqnote I made C7 – C11 into proportions
MTB > let c9 = c13/sum(c13)of their column sum. These were stacked in MTB > let c10 = c14/sum(c14) C6. This is O in proportions.
MTB > stack c7 c8 c9 c10 c6
MTB > print c7 - c10
Data Display
Row C7 C8 C9 C10
1 0.333333 0.375 0.375 0.25
2 0.166667 0.250 0.375 0.25
3 0.500000 0.375 0.250 0.50
MTB > stack c16 c16 c16 c16 c7To get E as proportions I stacked the row
MTB > print c6 c7proportions in C7.
Data Display
Row C6 C7
1 0.333333 0.333333
2 0.166667 0.266667
3 0.500000 0.400000
4 0.375000 0.333333
5 0.250000 0.266667
6 0.375000 0.400000
7 0.375000 0.333333
8 0.375000 0.266667
9 0.250000 0.400000
10 0.250000 0.333333
11 0.250000 0.266667
12 0.500000 0.400000
MTB > let c8 = c6To protect my work, I copied it into C8 and C9.
MTB > let c9 = c7
MTB > print c8 c9 c10
Data Display
Row pbars p0s csums
1 0.333333 0.333333 30
2 0.166667 0.266667 30
3 0.500000 0.400000 30
4 0.375000 0.333333 40
5 0.250000 0.266667 40
6 0.375000 0.400000 40
7 0.375000 0.333333 40
8 0.375000 0.266667 40
9 0.250000 0.400000 40
10 0.250000 0.333333 40
11 0.250000 0.266667 40
12 0.500000 0.400000 40
MTB > let c5 = c8 - c9I am now computing. This is the method described in chisquarednote.
MTB > print c5 c8 c9
Data Display C5 is the difference between expected and observed.
Row C5 pbars p0s
1 0.000000 0.333333 0.333333
2 -0.100000 0.166667 0.266667
3 0.100000 0.500000 0.400000
4 0.041667 0.375000 0.333333
5 -0.016667 0.250000 0.266667
6 -0.025000 0.375000 0.400000
7 0.041667 0.375000 0.333333
8 0.108333 0.375000 0.266667
9 -0.150000 0.250000 0.400000
10 -0.083333 0.250000 0.333333
11 -0.016667 0.250000 0.266667
12 0.100000 0.500000 0.400000
MTB > let c5 = c5*c5To get chi-squared, square C5. Multiply result by co
MTB > let c5 = c5*c10column sums.
MTB > let c5 = c5/c9
MTB > sum c4
Sum of chisq1
Sum of chisq1 = 8.28125
MTB > sum c5
Sum of chisq2
Sum of chisq2 = 8.53125
MTB > print c4 c5 c8 c9 c10
Data Display
Row chisq1 chisq2 pbars p0s csums
1 0.00000 0.00000 0.333333 0.333333 30
2 1.12500 1.12500 0.166667 0.266667 30
3 0.75000 1.00000 0.500000 0.400000 40
4 0.20833 0.20833 0.375000 0.333333 40
5 0.04167 0.04167 0.250000 0.266667 40
6 0.06250 0.06250 0.375000 0.400000 40
7 0.20833 0.20833 0.375000 0.333333 40
8 1.76042 1.76042 0.375000 0.266667 40
9 2.25000 2.25000 0.250000 0.400000 40
10 0.83333 0.83333 0.250000 0.333333 40
11 0.04167 0.04167 0.250000 0.266667 40
12 1.00000 1.00000 0.500000 0.400000 40
Results for: ChiEx1a.MTW
MTB > WSave "C:\Documents and Settings\RBOVE\My Documents\Minitab\ChiEx1a.MTW";
SUBC> Replace.
Saving file as: 'C:\Documents and Settings\RBOVE\My
Documents\Minitab\ChiEx1a.MTW'
MTB >