To apply the H test or the Kruskal-Wallis test to this problem, we begin by ranking all the given figures from the highest to the lowest, indicating besides each the number of the method as under.

Marks Obtained Rank Assigned Number of the method

90 1 II

87 2 II

85 3 II

80 4 III

79 5 III

78 6 I

77 7 II

76 8 II

75 9 III

74 10 III

73 11 I

71 12 I

62 13 I

60 14 III

58 15 I

As the 3 samples have 5 items each the sampling distribution approximately closely with X (Chi) square distribution

H0: The teacher equally well with the 3 methods

Now for finding the values of R i , we arrange the above table as under.

Marks obtained with different methods and corresponding rank.

Method I Rank Method II Rank Method III Rank

78 6 90 1 80 4

73 11 87 2 79 5

71 12 85 3 75 9

62 13 77 7 74 10

58 15 76 8 60 14

n1 = 5 R1=57 n2=5 R2=21 n3=5 R3=42

Now we calculate H stastic as under

H = (12/n(n+1)) (Sigma i = 1 to k (Ri square/ni))-3(n+1)

= (12/15(15+1)){(57)*(57)/5 + 21*21/5 + 42*42/5} - 3(15+1)

= 0.05 x 5454/5 - 48

= 54.54 - 48

Therefore H cal =6.54

Now Xsquare tab(3-1,005) = X square tab (2,005) = 5.99

THere X square cal < X square tab

Note : Please note X is Chi in greek, X square is X* X.

COnclusion

There is no difference between teaching methods

## Saturday, October 18, 2008

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