Test Using Contingency Tables

 Test for homogeneity of proportions

       -is used to determine whether the proportions for variable are equal when several samples are selected from different populations.

Example:
      A researcher selected a sample of 180 senior citizens from different Brgy. and asked each senior citizen, " Do you avail the discount fee for being a senior citizen?" The data are shown in the table. At a=0.05, test the claim that the proportion of senior citizen who avail the discount fee is the same at all Brgy.

	Brgy.1	Brgy.2	Brgy.3	Total
Yes	20(14.44)	10(14.44)	22(14.44)	52
No	30(27.22)	40(27.22)	28(27.22)	98
	50	50	50	180

State the Hypothesis
*Ho: p1=p2=p3(claim)
  Hi: at least one proportion is different from others

Find the Critical Value
*d.f=(r-1)(c-1)
   d.f=(2-1)(3-1), C.V=5.991

Compute the Test Value.
*Summation of (Observed value-expected value)2 /expected value
   =13.77
Note:(In order to solve the Expected value,you must multiply the total in row with the total in the column and divide it with the grand total.For example,E1,1=(50 x  52)/180. the steps will be repeated until it reaches the Expected value of the last column and last row)

Make the decision:
*Reject the null hypothesis since 13.77>5.991

Summarize the results
*There is enough evidence to reject the claim



by: Dustin Joshua Esquia III-Gold