1. Chi square test

2. Uses and Applications
 Used when you have frequency
distribution of qualitative type of variables.
 Applications:
 To test goodness of fit.
 In the 2X2 table, it is used to test whether
there is an association between the row
and the column variables; ie whether the
distribution of individuals among the
categories of one variable is
independent of their distribution among
the categories of the other.

3. Example, Influenza vaccination trial
Influenza No Total
influenza
Vaccine 20 220 240
(8.3%)
Placebo 80 140 220
(36.4%)
Total 100 360 460
(21.7%)

4. The question is:
 Is the difference (in the percentages of
influenza) due to vaccination or occurred
by chance?
 To answer, a Chi square test is done
which compares the observed numbers in
each of the four categories in the
contingency table with the numbers to be
expected if there was no difference in the
effectiveness between the vaccine and
placebo.

5. The expected frequencies:
Influenza No Total
influenza
Vaccine 52.2 187.8 240
Placebo 47.8 172.2 220
Total 100 360 460

6. Solution, continued
 Ho: The proportion of influenza among the vaccine
group = The proportion of influenza among the
placebo group.
 Level of significance (alpha) = 0.05
 D.f. = (No. of rows-1) (No. of columns-1).
 Test statistics: Chi square test.
∑ (O − E ) 2
χ =
2
E

7. Solution, continued
(20 − 52.2) 2 (80 − 47.8) 2 (220 − 187.8) 2 (140 − 172.2) 2
χ2 = + + + = 53.09
52.2 47.8 187.8 172.2
The tabulated value for X2 for 1 d.f. is 3.841
The calculated value (53.09) > tabulated value
Therefore reject Ho and conclude that there is statistically
significant difference between the 2 proportions. This
difference is unlikely to be due to chance.
Therefore the vaccine is effective.
P < 0.05