1. Chi-square test ( or χ2 test)

2. The value of the test-statistic is
X2 = ∑ (O-E)2
E
O= Observed Frequency
E = Expected frequency
d.f. = (n- 1)

3. ILLUSTRATION 1

4. Illustration 5 (page no 240)
Genetic theory states that children having one parent
of blood type A and the other of blood type B will
always be one of three types A,AB, B and the
proportion of three types will on an average 1:2:1.
To collect data 300 children ( having one A parent
and B parent)have been observed and on the basis
of observation a report has been made. The report
states that out of 300 children , 30% found to be type
A, 45% found to be type AB, and remainder found to
be type B. Test the hypothesis that genetic theory is
correct by ‫א‬2 test at 5% level of significance.

5. Use of ‫א‬2 for testing the null hypothesis that two
criterion are independent
The table given below shows the data obtained during
outbreak of smallpox:
Test the effectiveness of vaccination in preventing the attack
for preventing the attack from the smallpox by using ‫א‬2 at
5% level of significance.
Attacked Not Attacked Total
Vaccinated 31 469 500
Not Vaccinated 185 1315 1500
Total 216 1784 2000

6. Formula for expected frequency:
E( AB) = (Row total for the row A)x ( column total for the coloumn B)
Grand Total
degree of freedom in this case is (r-1) (c-1) where r = total no. of rows
and c= total no. of coloumns in the table.
Attacked: B Not Attacked: b Total
Vaccinated: A 31 469 500
Not Vaccinated: a 185 1315 1500
Total 216 1784 2000=N(grand
Total)