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15-4.1

Let X11, X12, . . . , X1n1 and X21, X22, . . . , X2n2 be two independent random samples of sizes n1 n2 from the continuous populations X1 and X2 described earlier. We wish to test the hypotheses H0: H1:

6

17 16

1 1 2 2

The test procedure is as follows. Arrange all n1 n2 observations in ascending order of magnitude and assign ranks to them. If two or more observations are tied (identical), use the mean of the ranks that would have been assigned if the observations differed. Let W1 be the sum of the ranks in the smaller sample (1), and de ne W2 to be the sum of the ranks in the other sample. Then, W2 1n1 n2 21n1 2 n2 12 W1 (15-7)

Figure 6.8 The effect of setting the RepeatColumns to 3, the RepeatDirection to Horizontal, the GridLines to Both, and the BorderColor to Black.

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Now if the sample means do not differ, we will expect the sum of the ranks to be nearly equal for both samples after adjusting for the difference in sample size Consequently, if the sums of the ranks differ greatly, we will conclude that the means are not equal Appendix Table IX contains the critical value of the rank sums for 005 and 001 assuming the two-sided alternative above Refer to Appendix Table IX with the appropriate sample sizes n1 and n2, and the critical value w can be obtained The null H0: 1 2 is rejected in favor of H1: 1 if either of the observed values w1 or w2 is less than or equal 2 to the tabulated critical value w The procedure can also be used for one-sided alternatives.

If the alternative is H1: 1 2, reject H0 if w1 w ; for H1: 1 , reject H0 if w2 w For these one-sided tests, the tabu2 lated critical values w correspond to levels of signi cance of 0025 and 0005 EXAMPLE 15-6 The mean axial stress in tensile members used in an aircraft structure is being studied Two alloys are being investigated Alloy 1 is a traditional material, and alloy 2 is a new aluminum-lithium alloy that is much lighter than the standard material Ten specimens of each alloy type are tested, and the axial stress is measured The sample data are assembled in Table 15-3 Using = 005, we wish to test the hypothesis that the means of the two stress distributions are identical We will apply the eight-step hypothesis-testing procedure to this problem: 1.

As the list of employees gets longer, it will be necessary to come up with a way to fill the screen with employees instead of having a narrow column of employees. That is where the RepeatColumns and RepeatDirection come into play. Figure 6.8 shows an example of setting the RepeatColumns to three and the RepeatDirection to Horizontal. In this example, the GridLines property is set to Both and the BorderColor is set to Black. Notice that the RepeatDirection can also be set to Vertical, which will cause the employee list to be rendered downward in vertical columns. Selecting an Item The DataList can allow a user to select an item. This is usually desirable when only a small amount of data is being displayed and more details are desired. Making a selection involves setting the SelectedIndex to a number other than minus one (-1), which is the default. This can be done by creating an ItemCommand method, which will change the selection number. There is one small problem, which is that the SelectedIndex must be set before the data is bound to the DataList. Currently, our data is being bound in the Page_Load method. This is only acceptable when the data is not being posted to the server (the first time to the page). The code to create the employees will be placed into a procedure called BindEmployees as follows:

The parameters of interest are the means of the two distributions of axial stress 2 H0: 1 2 3 H1: 1 2 4 005 5 We will use the Wilcoxon rank-sum test statistic in Equation 15-7, 1n1 n2 21n1 2 n2 12.

w2 6.

Private Sub Page_Load(ByVal sender As System.Object, _ ByVal e As System.EventArgs) Handles MyBase.Load If Not IsPostBack() Then BindEmployees() End If End Sub

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