Kendall coefficient of concordance

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  Kendall coefficient of concordance W
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  • 1. Three Judges rated eight essays with the following results. Calculate the coefficient of Concordance for these data.
  • 2. ESSAY A B C D E F G H Judge 1 Judge 2 Judge 3 8 7 8 6 5 6 4 6 5 1 2 1 3 3 2 2 1 3 5 4 4 7 8 7 R 23 17 15 4 8 6 13 22 108 D 9.5 3.5 1.5 9.5 5.5 7.5 0.5 8.5 D2 90.25 12.25 2.25 90.25 30.25 56.25 0.25 72.25 S =354
  • 3. FORMULA for Kendall’s W Coefficient: =Sum of squares of the R- from the Ā =Number of judges or respondents ranking the objects or attributes. =Number of attributes or objects that is evaluated by judges or respondents.
  • 4. Kendall‟s W only gives the degree of association or agreement among the ranks assigned by different judges or respondents on different objects or attributes. However, the significance of this W should be tested through either critical X2 or F values.
  • 5. Five consumers of similar profile rated the eight different colors of packages for biscuit to find out the most preferred one. Calculate the coefficient of concordance for these data.
  • 6. The null hypothesis there is no significant agreement among the judges (or respondents) in the ranking of different color packages. The alternative hypothesis there is a significant agreement among the judges (or respondents) in the ranking of different color packages. Formulate a null hypothesis and an alternate hypothesis:
  • 7. COLOR CONSUMERS R D D2 1 2 3 4 5 red 1 2 1 1 2 7 15.5 240.25 orange 2 1 2 3 4 12 10.5 110.25 Yellow 3 4 3 2 6 18 4.5 20.25 green 4 3 6 6 7 26 3.5 12.25 blue 5 6 4 4 3 22 0.5 0.24 pink 6 5 8 7 8 34 11.5 132.25 violet 7 8 7 5 5 32 9.5 90.25 black 8 7 5 8 1 29 6.5 42.25 ∑=180 S=648 Ā=180/8=22.5
  • 8. The size of this coefficient of concordance indicates that there is a moderate agreement among these five judges in ranking the eight package colors.
  • 9. We can find out the critical value by referring to the table 1, which gives values of “S” for W‟s significance of 0.05 and 0.01 levels. Please note that this table is applicable only when „m‟ ranges from 3 to 20 and „n‟ ranges from 3 to 7. In case of large samples, that is, when the number of objects or attributes to be ranked are evaluated is greater than 7, we have the option of finding out the critical value either through computation of X2 distribution values or F-distribution values.
  • 10. X2=5(8-1)0.62 X2=21.7
  • 11. Locate the critical chi value at 0.05 level: Get the degrees of freedom: N-1 -> 8-1= V=14.07
  • 12. Compare the calculated value and critical value: X2=21.7 V=14.07 Therefore, the null hypothesis that there is no significant agreement among the judges (or respondents) in the ranking of different color packages is rejected.
  • 13. We can safely conclude that there exists a considerable but significant agreement among the judges as to the ranking of different colored packages is concerned. Thus, it is evident that at least one colored package is ranked significantly higher than the other. Compare the calculated value and critical value:
  • 14. END Thank You Statistics Sat. 1-4 pm Dr. Nasie Seneriches, PHD
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