# The Chi-square Test of Independence

Document Sample

```					                 The Chi-square Test of Independence

Assumptions:
1.      The sample of N observations is a random sample
2.      Each observation may be classified into exactly one of r different
categories according to one criterion and into exactly one of c different
categories according to a second criterion.

Hypotheses:
Ho: Rows and columns are independent
Ha: Rows (dependent variable) are dependent on columns (independent variable.)

Decision Rule:
Reject Ho if T exceeds the 1-α quantile of a chi-square random variable with
(r-1)(c-1) df. (A one-sided test, because it is squared, so it has to be positive.)

EXAMPLE:

Q: Is response to “life exciting or dull” dependent on gender?

Ho: View of life is not dependent on gender
Ha: View of life is dependent on gender
(knowing gender helps you to predict view of life)

Procedure:
SEX
COUNT           Male            Female           ROW TOT.
EXP VAL
LIFE                                      1               2
Excited            1                   300              384               684
279.0            405.0             46.8%
Not excited        2                   296              481               777
317.0            460.0             53.2%
COLUMN              596              865               1461
TOTAL              40.8%            59.2%             100%

Chi-square DF               Significance         Cells with EF<5
4.76884                 1           0.0290                   None

1
What percent of total group were excited with life?   eg. 46.8%
What percent of total group were not excited?         eg. 53.2%

Expected values (if independent):
Excited      46.8% x 596 men = 279 men
Not          53.2% x 596 men = 317 men

Excited     46.8% x 865 women = 405 women
Not         53.2% x 865 women = 460 women

Observed values:
Number of men who actually marked “exciting” and “not
exciting.”
Number of women who actually marked “exciting” and “not
exciting.”

Computation:
for each cell-
1.    Find the difference between the observed and expected
frequency.
2.    Square this difference
3.    Divide the squared difference by the expected frequency.
then-
4.    Add them up. This is the Chi-square statistic

2

```
DOCUMENT INFO
Shared By:
Categories:
Stats:
 views: 45 posted: 12/23/2009 language: English pages: 2