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Note that S 2 is just the variance of the ranks. When the number of ties is moderate, there will be little difference between Equations 15-11 and 15-12 and the simpler form (Equation 15-11) may be used. EXAMPLE 15-7 Montgomery (2001) presented data from an experiment in which ve different levels of cotton content in a synthetic ber were tested to determine whether cotton content has any effect on ber tensile strength. The sample data and ranks from this experiment are shown in Table 15-4. We will apply the Kruskal-Wallis test to these data, using 0.01.

Table 15-4 Data and Ranks for the Tensile Testing Experiment Percentage of Cotton 15 ranks 20 ranks 25 ranks 30 ranks 35 ranks y1j r1j y2j r2j y3j r3j y4j r4j y5j r5j 7 2.0 12 9.5 14 11.0 19 20.5 7 2.0 7 2.0 17 14.0 18 16.5 25 25.0 10 5.0 15 12.5 12 9.5 18 16.5 22 23.0 11 7.0 11 7.0 18 16.5 19 20.5 19 20.5 15 12.5 9 4.0 18 16.5 19 20.5 23 24.0 11 7.0 ri. 27.5 66.0 85.0 113.0 33.5

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An event method must be created in the code-behind page to set the EditItemIndex of the DataList when a button is clicked. Do this by clicking the Class Name drop-down list and then clicking DataList1. In the Method drop-down list, click EditCommand, which inserts code for this event. In this method, add code to set the EditItemIndex, and call the BindEmployees method as follows:

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Since there is a fairly large number of ties, we use Equation 15-12 as the test statistic. From Equation 15-13 we nd s2 1 N c r2 1 ia ja ij 1 1 251262 2 d 2

12 2

Private Sub DataList1_EditCommand(ByVal source As Object, _ ByVal e As System.Web.UI.WebControls.DataListCommandEventArgs) _ Handles DataList1.EditCommand DataList1.EditItemIndex = e.Item.ItemIndex BindEmployees() End Sub

12 2

1 c 5245.7 53.54 19.06

The CancelCommand must be modified to set the EditItemIndex to minus one (-1) if editing is cancelled:

2512622 d 4

2 Since h 13.28, we would reject the null hypothesis and conclude that treatments 0.01,4 differ. This same conclusion is given by the usual analysis of variance F-test.

Private Sub DataList1_CancelCommand(ByVal source As Object, _ ByVal e As System.Web.UI.WebControls.DataListCommandEventArgs) _ Handles DataList1.CancelCommand If DataList1.EditItemIndex = -1 Then DataList1.SelectedIndex = -1 Else DataList1.EditItemIndex = -1 End If BindEmployees() End Sub

15-5.2

The procedure used in the previous section whereby the observations are replaced by their ranks is called the rank transformation. It is a very powerful and widely useful technique. If we were to apply the ordinary F-test to the ranks rather than to the original data, we would obtain F0 1N H 1a 12 1 H2 1N

as the test statistic. Note that as the Kruskal-Wallis statistic H increases or decreases, F0 also increases or decreases. Now, since the distribution of F0 is approximated by the F-distribution,

The selected item template has been changed to have an Edit button beside the Hide Details button. Also, an edit item template needs to be added to the DataList. The following is the revised selected item template and the new edit item template:

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