In the table below, contains the information after initial nonparametric Kruskal-Wallis test ANOVA in data set with different samples sizes in each group and with 20 groups (k=20) that yielded a highly signigicant p value. Assume that the C12 column of Minitab contains the sample sizes for different groups and C14 contains the average ranks for each group. One wishes to do pair-wise comparions for all the possible 190 pairs i.e k(k-1)/2 to identify where the difference exists. Alternatively, if one could wish to compare with a base-line value at a particular time period. In such a case, there would be 19 pair-wise comparisons i.e (k-1).

C11	C12	C13	C14
1	41		534.5
2	56		670.1
3	50		298
4	82		628
5	76		793.5
6	29		393.2
7	74		573.1
8	51		336.9
9	53		722.6
10	73		755.4
11	42		247.6
12	67		424.8
13	15		669.3
14	74		169.3
15	38		795
16	12		118.5
17	24		282.6
18	25		789.4
19	78		655.6
20	99		403.7

The macro invoked by the following command assuming the macro text file is name phft.mac

%phkw c12 c14

Aternatively the macro could be invoked by named cloumns

%phft ‘sskw’ ‘arkw’

After the macro is invoked, the user is asked whether one wishes to do all pair-wise comparisons or

The macro uses the input from two columns in the Minitab’s worksheet: one column with sample sizes for different groups and average ranks in another column. The macro is invoked by the following command: %phft c12 c14, if the sample sizes and average ranks are entered in Columns 12 and 14 respectively of Mintab’s worksheet. After the macro is invoked, the user is asked whether the all pair-wise comparisons are required or comparisons with baseline value are required. In the latter case, the user is asked the group number to be compared. After the appropriate response from the user, the macro performs the required calculations and yields an output.

Description of output in the sessions window of Minitab from 1 to 10 columns respectively are serial number of comparisons, rank sums, group number of time periods, pair of time periods that are being compared, pair of corresponding rank sums, difference in average ranks, significance at 0.05 level (1 for yes, 0 for no) and significance at 0.01.

Invoking and macro output for all pair-wise comparisons

MTB > %phkw c12 c14

Executing from file: C:\MTBWIN\MACROS\phkw.MAC

This is a macro for Posthoc analysis after Friedman test either multigroup comparison or comparison againt a single control .

For computational details refer to

Nonparametric statistics for behavioural sciences

Siegel S and Castellan NJ, 2nd edition, 1988 , McGraw Hill, Inc, New York

, page 213-215

PLEASE REMEMBER TO ENTER THE AVERAGE RANKS IN THE INPUT COLUMN

What type of post hoc analysis you wish to perform

Type YES & enter for multipgroup comparison. Type NO & enter for single

group comparison

yes

Data Display

Row C14 ccgb ccga dcolb dcola diffcol sig05 sig01

1 534.5 1 2 534.5 670.1 135.600 0 0

2 670.1 1 3 534.5 298.0 -236.500 1 0

3 298.0 1 4 534.5 628.0 93.500 0 0

4 628.0 1 5 534.5 793.5 259.000 1 1

5 793.5 1 6 534.5 393.2 -141.300 0 0

6 393.2 1 7 534.5 573.1 38.600 0 0

7 573.1 1 8 534.5 336.9 -197.600 0 0

8 336.9 1 9 534.5 722.6 188.100 0 0

9 722.6 1 10 534.5 755.4 220.900 1 0

10 755.4 1 11 534.5 247.6 -286.900 1 1

11 247.6 1 12 534.5 424.8 -109.700 0 0

12 424.8 1 13 534.5 669.3 134.800 0 0

13 669.3 1 14 534.5 169.3 -365.200 1 1

14 169.3 1 15 534.5 795.0 260.500 1 0

15 795.0 1 16 534.5 118.5 -416.000 1 1

16 118.5 1 17 534.5 282.6 -251.900 0 0

17 282.6 1 18 534.5 789.4 254.900 0 0

18 789.4 1 19 534.5 655.6 121.100 0 0

19 655.6 1 20 534.5 403.7 -130.800 0 0

20 403.7 2 3 670.1 298.0 -372.100 1 1

21 2 4 670.1 628.0 -42.100 0 0

22 2 5 670.1 793.5 123.400 0 0

23 2 6 670.1 393.2 -276.900 1 0

24 2 7 670.1 573.1 -97.000 0 0

25 2 8 670.1 336.9 -333.200 1 1

26 2 9 670.1 722.6 52.500 0 0

27 2 10 670.1 755.4 85.300 0 0

28 2 11 670.1 247.6 -422.500 1 1

29 2 12 670.1 424.8 -245.300 1 1

30 2 13 670.1 669.3 -0.800 0 0

31 2 14 670.1 169.3 -500.800 1 1

32 2 15 670.1 795.0 124.900 0 0

33 2 16 670.1 118.5 -551.600 1 1

34 2 17 670.1 282.6 -387.500 1 1

35 2 18 670.1 789.4 119.300 0 0

36 2 19 670.1 655.6 -14.500 0 0

37 2 20 670.1 403.7 -266.400 1 1

38 3 4 298.0 628.0 330.000 1 1

39 3 5 298.0 793.5 495.500 1 1

40 3 6 298.0 393.2 95.200 0 0

41 3 7 298.0 573.1 275.100 1 1

42 3 8 298.0 336.9 38.900 0 0

43 3 9 298.0 722.6 424.600 1 1

44 3 10 298.0 755.4 457.400 1 1

45 3 11 298.0 247.6 -50.400 0 0

46 3 12 298.0 424.8 126.800 0 0

47 3 13 298.0 669.3 371.300 1 1

48 3 14 298.0 169.3 -128.700 0 0

49 3 15 298.0 795.0 497.000 1 1

50 3 16 298.0 118.5 -179.500 0 0

51 3 17 298.0 282.6 -15.400 0 0

52 3 18 298.0 789.4 491.400 1 1

53 3 19 298.0 655.6 357.600 1 1

54 3 20 298.0 403.7 105.700 0 0

55 4 5 628.0 793.5 165.500 0 0

56 4 6 628.0 393.2 -234.800 0 0

57 4 7 628.0 573.1 -54.900 0 0

58 4 8 628.0 336.9 -291.100 1 1

59 4 9 628.0 722.6 94.600 0 0

60 4 10 628.0 755.4 127.400 0 0

61 4 11 628.0 247.6 -380.400 1 1

62 4 12 628.0 424.8 -203.200 1 0

63 4 13 628.0 669.3 41.300 0 0

64 4 14 628.0 169.3 -458.700 1 1

65 4 15 628.0 795.0 167.000 0 0

66 4 16 628.0 118.5 -509.500 1 1

67 4 17 628.0 282.6 -345.400 1 1

68 4 18 628.0 789.4 161.400 0 0

69 4 19 628.0 655.6 27.600 0 0

70 4 20 628.0 403.7 -224.300 1 1

71 5 6 793.5 393.2 -400.300 1 1

72 5 7 793.5 573.1 -220.400 1 1

73 5 8 793.5 336.9 -456.600 1 1

74 5 9 793.5 722.6 -70.900 0 0

75 5 10 793.5 755.4 -38.100 0 0

76 5 11 793.5 247.6 -545.900 1 1

77 5 12 793.5 424.8 -368.700 1 1

78 5 13 793.5 669.3 -124.200 0 0

79 5 14 793.5 169.3 -624.200 1 1

80 5 15 793.5 795.0 1.500 0 0

81 5 16 793.5 118.5 -675.000 1 1

82 5 17 793.5 282.6 -510.900 1 1

83 5 18 793.5 789.4 -4.100 0 0

84 5 19 793.5 655.6 -137.900 0 0

85 5 20 793.5 403.7 -389.800 1 1

86 6 7 393.2 573.1 179.900 0 0

87 6 8 393.2 336.9 -56.300 0 0

88 6 9 393.2 722.6 329.400 1 1

89 6 10 393.2 755.4 362.200 1 1

90 6 11 393.2 247.6 -145.600 0 0

91 6 12 393.2 424.8 31.600 0 0

92 6 13 393.2 669.3 276.100 0 0

93 6 14 393.2 169.3 -223.900 0 0

94 6 15 393.2 795.0 401.800 1 1

95 6 16 393.2 118.5 -274.700 0 0

96 6 17 393.2 282.6 -110.600 0 0

97 6 18 393.2 789.4 396.200 1 1

98 6 19 393.2 655.6 262.400 1 0

99 6 20 393.2 403.7 10.500 0 0

100 7 8 573.1 336.9 -236.200 1 1

101 7 9 573.1 722.6 149.500 0 0

102 7 10 573.1 755.4 182.300 0 0

103 7 11 573.1 247.6 -325.500 1 1

104 7 12 573.1 424.8 -148.300 0 0

105 7 13 573.1 669.3 96.200 0 0

106 7 14 573.1 169.3 -403.800 1 1

107 7 15 573.1 795.0 221.900 0 0

108 7 16 573.1 118.5 -454.600 1 1

109 7 17 573.1 282.6 -290.500 1 0

110 7 18 573.1 789.4 216.300 0 0

111 7 19 573.1 655.6 82.500 0 0

112 7 20 573.1 403.7 -169.400 0 0

113 8 9 336.9 722.6 385.700 1 1

114 8 10 336.9 755.4 418.500 1 1

115 8 11 336.9 247.6 -89.300 0 0

116 8 12 336.9 424.8 87.900 0 0

117 8 13 336.9 669.3 332.400 1 0

118 8 14 336.9 169.3 -167.600 0 0

119 8 15 336.9 795.0 458.100 1 1

120 8 16 336.9 118.5 -218.400 0 0

121 8 17 336.9 282.6 -54.300 0 0

122 8 18 336.9 789.4 452.500 1 1

123 8 19 336.9 655.6 318.700 1 1

124 8 20 336.9 403.7 66.800 0 0

125 9 10 722.6 755.4 32.800 0 0

126 9 11 722.6 247.6 -475.000 1 1

127 9 12 722.6 424.8 -297.800 1 1

128 9 13 722.6 669.3 -53.300 0 0

129 9 14 722.6 169.3 -553.300 1 1

130 9 15 722.6 795.0 72.400 0 0

131 9 16 722.6 118.5 -604.100 1 1

132 9 17 722.6 282.6 -440.000 1 1

133 9 18 722.6 789.4 66.800 0 0

134 9 19 722.6 655.6 -67.000 0 0

135 9 20 722.6 403.7 -318.900 1 1

136 10 11 755.4 247.6 -507.800 1 1

137 10 12 755.4 424.8 -330.600 1 1

138 10 13 755.4 669.3 -86.100 0 0

139 10 14 755.4 169.3 -586.100 1 1

140 10 15 755.4 795.0 39.600 0 0

141 10 16 755.4 118.5 -636.900 1 1

142 10 17 755.4 282.6 -472.800 1 1

143 10 18 755.4 789.4 34.000 0 0

144 10 19 755.4 655.6 -99.800 0 0

145 10 20 755.4 403.7 -351.700 1 1

146 11 12 247.6 424.8 177.200 0 0

147 11 13 247.6 669.3 421.700 1 1

148 11 14 247.6 169.3 -78.300 0 0

149 11 15 247.6 795.0 547.400 1 1

150 11 16 247.6 118.5 -129.100 0 0

151 11 17 247.6 282.6 35.000 0 0

152 11 18 247.6 789.4 541.800 1 1

153 11 19 247.6 655.6 408.000 1 1

154 11 20 247.6 403.7 156.100 0 0

155 12 13 424.8 669.3 244.500 0 0

156 12 14 424.8 169.3 -255.500 1 1

157 12 15 424.8 795.0 370.200 1 1

158 12 16 424.8 118.5 -306.300 0 0

159 12 17 424.8 282.6 -142.200 0 0

160 12 18 424.8 789.4 364.600 1 1

161 12 19 424.8 655.6 230.800 1 1

162 12 20 424.8 403.7 -21.100 0 0

163 13 14 669.3 169.3 -500.000 1 1

164 13 15 669.3 795.0 125.700 0 0

165 13 16 669.3 118.5 -550.800 1 1

166 13 17 669.3 282.6 -386.700 1 0

167 13 18 669.3 789.4 120.100 0 0

168 13 19 669.3 655.6 -13.700 0 0

169 13 20 669.3 403.7 -265.600 0 0

170 14 15 169.3 795.0 625.700 1 1

171 14 16 169.3 118.5 -50.800 0 0

172 14 17 169.3 282.6 113.300 0 0

173 14 18 169.3 789.4 620.100 1 1

174 14 19 169.3 655.6 486.300 1 1

175 14 20 169.3 403.7 234.400 1 1

176 15 16 795.0 118.5 -676.500 1 1

177 15 17 795.0 282.6 -512.400 1 1

178 15 18 795.0 789.4 -5.600 0 0

179 15 19 795.0 655.6 -139.400 0 0

180 15 20 795.0 403.7 -391.300 1 1

181 16 17 118.5 282.6 164.100 0 0

182 16 18 118.5 789.4 670.900 1 1

183 16 19 118.5 655.6 537.100 1 1

184 16 20 118.5 403.7 285.200 0 0

185 17 18 282.6 789.4 506.800 1 1

186 17 19 282.6 655.6 373.000 1 1

187 17 20 282.6 403.7 121.100 0 0

188 18 19 789.4 655.6 -133.800 0 0

189 18 20 789.4 403.7 -385.700 1 1

190 19 20 655.6 403.7 -251.900 1 1

Description of columns : Input column i.e Average ranks

nsrno=Group serial number; ccgb=base group; ccga=comparative group

dcolb=Average rank of base group; dcola=Average rank of comparative group

diffcol=Difference in Average ranks

sig05= 1 implies significance at 0.05 level and 0 implies not signficant

sig01= 1 implies significance at 0.01 level and 0 implies not signficant

Invoking and macro output for comparison with a single group assuming time period 3 is the group to be compared

MTB > %phkw c12 c14

Executing from file: C:\MTBWIN\MACROS\phkw.MAC

This is a macro for Posthoc analysis after Friedman test either multigroup comparison or

comparison againt a single control .

For computational details refer to

Nonparametric statistics for behavioural sciences

Siegel S and Castellan NJ, 2nd edition, 1988 , McGraw Hill, Inc, New York

, page 213-215

PLEASE REMEMBER TO ENTER THE AVERAGE RANKS IN THE INPUT COLUMN

What type of post hoc analysis you wish to perform

Type YES & enter for multipgroup comparison. Type NO & enter for single

group comparison

What is the comparative group. Enter the number 1 or 2 or 3 etc and press

enter key

DATA> 3

Data Display

Row C14 ccgb ccga dcolb dcola diffcol sig05 sig01

1 534.500 3 1 298 534.500 236.500 1 1

2 670.100 3 2 298 670.100 372.100 1 1

3 298.000 3 4 298 628.000 330.000 1 1

4 628.000 3 5 298 793.500 495.500 1 1

5 793.500 3 6 298 393.200 95.200 0 0

6 393.200 3 7 298 573.100 275.100 1 1

7 573.100 3 8 298 336.900 38.900 0 0

8 336.900 3 9 298 722.600 424.600 1 1

9 722.600 3 10 298 755.400 457.400 1 1

10 755.400 3 11 298 247.600 -50.400 0 0

11 247.600 3 12 298 424.800 126.800 0 0

12 424.800 3 13 298 669.300 371.300 1 1

13 669.300 3 14 298 169.300 -128.700 0 0

14 169.300 3 15 298 795.000 497.000 1 1

15 795.000 3 16 298 118.500 -179.500 0 0

16 118.500 3 17 298 282.600 -15.400 0 0

17 282.600 3 18 298 789.400 491.400 1 1

18 789.400 3 19 298 655.600 357.600 1 1