CHI SQUARE AS A TEST OF INDEPENDENCE

CHI SQUARE AS A TEST OF INDEPENDENCE

Chi square: 

Test of independence comes under the non-parametric test. It explains whether two or more variables are associated or not.

Final Formula

O ---> Observed Value

E ---> Expected Value

Steps:

• We will proceed with the NULL Hypothesis
• Find the expected frequency from the observed frequency table., by using the formula

• Obtain the differences between the observed and expected frequency and square it.
• Divide the above value by the corresponding expected value
• Now, sum up all the values., It is the calculated value.
• Calculating Table value(Critical Value): 
• To do this, first find the Dof (Degrees of Freedom)., 
• "Dof=(r-1)(c-1)"                   r---> No. of rows; c---> No. of columns
• Now, go to chi square table and find the value with appropriate Dof and level of significance. 
• It is the critical value.,
• Comparing
• The calculated value should be compared with the critical value
• If, the calculated value is less than the critical value, we accept the NULL Hypothesis and Reject Alternative hypothesis.
• If the calculated value is greater than the critical value, we reject NULL Hypothesis and accept Alternative hypothesis.

Example:

H0: No difference among the customers on the basis of age

H1: Difference among the customers on the basis of age

Observed

Frequency

	Users	Non-users	Total
18-25	67	6	73
26-35	30	1	31
35-45	18	5	23
45-rest	19	14	33
Total	134	26	160

The above table is the observed frequency which we have with us. Now, we need to calculate the expected frequency table.

Expected Frequency

	Users	Non-users	Total
18-25	61.1375	11.8625	73
26-35	25.9625	5.0375	31
35-45	19.2625	3.7375	23
45-rest	27.6375	5.3625	33
Total	134	26	160

Interpretations

(73*134)/160 = 61.1375

(31*134)/160 = 26.9625

(23*134)/160 = 19.2625

(33*134)/160 = 27.6375

(73*26)/160   = 11.8625

(31*26)/160   =   5.0375

(23*26)/160   =   3.7375

(33*26)/160   =   5.3625

Calculation

Observed – Expected	(O-E)2	(O-E)2/E
5.8625	34.36890625	0.562158
4.0375	16.30140625	0.627883
-1.2625	1.59390625	0.082747
-8.6375	74.60640625	2.699463
-5.8625	34.36890625	2.897273
-4.0375	16.30140625	3.236011
1.2625	1.59390625	0.426463
8.6375	74.60640625	13.91262
Total		24.44461

Degree of Freedom

(R-1)(C-1) = (2-1) (4-1) = 3

Critical Value @ 5% significance level and Dof = 3 is 7.82

Since, the critical value is less than calculated value., we reject NULL Hypothesis. There is difference among the customers of age.

Chi square-table:

http://home.comcast.net/~sharov/PopEcol/tables/chisq.html