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Chi square test ( x2 )

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  • 1. CHI-SQUARE TEST ( X2 )
  • 2.  It is the most popular test of significance in social science research  It is used to make comparison between two or more nominal variables  It is used to make comparison between frequencies rather than between the mean  This test evaluated whether the difference between the observed frequencies and the expected frequencies under the null hypothesis
  • 3. A chi square value is obtained by the formula: X2=∑(f0-fe)2/fe  fo= the observed frequency  fe=the expected frequency in terms of the null hypothesis
  • 4.  Suppose we want to examine the relationship between education and income. What will be,  The Null hypothesis ?  Alternative / Research hypothesis? Income Education Low High Total Low 30 12 42 High 10 28 40 Total 40 40 80
  • 5.  H0= there is a no relation between educational and income level  Ha=there is a relation between educational and income level
  • 6. Procedure, X2=∑(f0-fe)2/fe  We can compute the expected frequencies (fe) with the observed once. (f0)  To compute the (fe) for any cell, the following formula is used: fe= (row total * column total)/n  n= total number  To compute X2 , the expected frequency of each cell is subtracted from the observed one, squared, divided by the expected frequency of the cell and then all quotients are added up.
  • 7.  The expected frequencies computed are shown in brackets. Income Education Low High Total Low 30 (21) 12 (21) 42 High 10 (19 ) 28 (19) 40 Total 40 40 80
  • 8.  21= (42*40)/ 80  19=(38*40)/ 80
  • 9. X2= X2=∑(f0-fe)2/fe = ((30-21) 2/ 21) + ((12-21)2/ 21) + ((10-19)2/19 ) +((28-19)2/19) = 3.86 + 3.86 + 4.26 + 4.26 X2 =16.24
  • 10. To reject or accept the null hypothesis, we need to compare X2 value to the critical value of sampling distribution of X2 The sampling distribution of X2 is determined by 1. The level of significance 2. The number of degree of freedom
  • 11. 1. Level of significance = 0.01 or 0.05 2. The number of degrees of freedom of the X2 distribution is set by the number of cells for which the expected frequencies can be selected freely. The formula used is: df= (r-1)*(c-1) r= the number of rows C=the number of columns Thus in a 2*2 table df=(2-1)*(2-1)=1 In a 3*3 table df=(3-1)*(3-1)=4 and so on.
  • 12.  In our example with 1 degree of freedom and 0.01 level of significance the table value of X2 is 6.64.  Our obtained X2 value 16.24 is much larger than the table value  Hence the null hypothesis is rejected and research hypothesis is supported  i.e. we may conclude that there is significant relationship between education and income.
  • 13.  In a survey of a brand preference of high school students for the soft drink, the following result was obtained:  Find out is there any relationship between brand preference and the gender of the consumer? Use chi square test at the 0.05 level of significance Gender Brand A B Boys 25 30 Girls 46 22 Total 71 52