This document discusses how to perform and interpret a chi-square test. It provides the steps to conduct a chi-square test: 1) make a hypothesis, 2) determine expected frequencies, 3) create a table with observed and expected frequencies and chi-square values, 4) find degrees of freedom, 5) find the chi-square statistic, and 6) determine whether to reject or fail to reject the null hypothesis based on whether the chi-square statistic is greater than the calculated value. An example is provided showing a chi-square test performed on package color preferences to test the hypothesis of equal preference, finding the null hypothesis should be rejected.

1. By
Akhil sankar

2.  The chi-square test is useful measure of
comparing experimentally obtained results
with those expected theoretically and based
one the hypothesis .
 In general chi-square best is applied to those
problems with which a given event has
occurred is significantly different from the
one as expected theoretically.

3.  1 or more categories
 Independent observations
 A sample size of at least 10
 Random sampling
 All observations must be used
 For the test to be accurate, the expected
frequency should be at least 5

4. 1) Make a hypothesis based on your basic
biological question
2) Determine the expected frequencies
3) Create a table with observed frequencies,
expected frequencies, and chi-square values
using the formula:
Χ2=(O-E)2
E
4) Find the degrees of freedom: (c-1)(r-1)
5) Find the chi-square statistic in the Chi-Square
Distribution table
6) If chi-square statistic > your calculated chi-square
value, you do not reject your null
hypothesis and vice versa.

5.  There is no significant difference between
the observed and expected frequencies.
 Chi-Square formula:
χ2 =  (O-E)2
E

6. Package Color
preference by
Consumers
Red 70
Blue 106
Green 80
Pink 70
Orange 74
Total 400
Random sample :400

7. Package
Color
Observed
Frequencie
s (O)
Expected
Frequencie
s (E)
(O-E)²
χ2 =  (O-E)2
E
Red 70 80 100 1.250
Blue 106 80 676 8.450
Green 80 80 0 0.000
Pink 70 80 100 1.250
Orange 74 80 36 0.450
Total 400 400 11.400
value of chi-square ( X²) = 11.400
Degree of freedom = (c-1)(r-1)
(2-1)(5-1)
=4

8.  null hypothesis: equal preference for all
colors being true, the expected frequencies
for all the colors will be equal to 80.
 The critical value of X2 at 5% level of
significance for 4 degrees of freedom is
9.488.
 So, the null hypothesis is rejected.

9.  Tossing of coin 100 times.
 Observation 68 H and 32 T.
No. O E (O-E) (O-E)2
1 68 50 18 324
2 32 50 -18 324
-------- ----------
100 64 8
Degree of freedom = (c-1)(r-1)
(2-1)(2-1)=1
Level of significance = 5%

10. χ2 = 648/100
= 6.48
Critical value is 3.841
Reject the null hypothesis

11. THANK U