【正文】 aduate School of Quality Management ? 86 ?Here, we see the 95% confidence intervals for the two populations. Since they overlap, we know that we will fail to reject the null hypothesis. ?The F test results are shown here. We can see from the PValue of .263 that again we would fail to reject the null hypothesis. Note that the F test assumes normality ?Note that we get a graphical summary of both sets of data as well as the relevant statistics…. Analyzing the data…. ?Levene’s test also pares the variance of the two samples and is robust to nonnormal data. Again, the PValue of .229 indicates that we would fail to reject the null hypothesis. ?Here we have box plot representations of both populations. 169。The National Graduate School of Quality Management ? 87 Lets test the data with a 2 Sample t Test ?Under Stat… Basic Statistics…. We see several of the hypothesis tests which we discussed in class. In this example we will be using a 2 Sample t Test…. ?Go to Stat…. Basic Statistics.. 2 Sample t….. 169。The National Graduate School of Quality Management ? 88 ?Since we already have our data stacked, we will load C4 for our samples and C3 for our subscripts. Setting up the test…. ?Since we have already tested for equal variances, we can check off this box… ?Now select Graphs…. 169。The National Graduate School of Quality Management ? 89 Setting up the test…. ?We see that we have two options for our graphical output. For this small a sample, Boxplots will not be of much value so we select “Dotplots of data” and hit “OK”. Hit OK again on the next screen…. 169。The National Graduate School of Quality Management ? 90 ?In the session window we have each population’s statistics calculated for us.. ?Note that here we have a P value of .922. We therefore find that the data does not support the conclusion that there is a significant difference between the means of the two populations... Interpreting the results…. 169。The National Graduate School of Quality Management ? 91 ?The dotplot shows how close the datapoints in the two populations fall to each other. The close values of the two population means (indicated by the red bar) also shows little chance that this hypothesis could be rejected by a larger sample Interpreting the results…. 169。The National Graduate School of Quality Management ? 92 Paired Comparisons ? In paired parisons we are trying to “pair” observations or treatments. An example would be to test automatic blood pressure cuffs and a nurse measuring the blood pressure on the same patient using a manual instrument. ? It can also be used in measurement system studies to determine if operators are getting the same mean value across the same set of samples. ? Let’s look at an example: 169。The National Graduate School of Quality Management ? 93 ? In this example we are trying to determine if shoe material “A” wear rate is different from shoe material “B”. ? Our data has been collected using ten boys, whom were asked to wear one shoe made from each material. Ho: Material “A” wear rate = Material “B” wear rate Ha: Material “A” wear rate ? Material “B” wear rate 169。The National Graduate School of Quality Management ? 94 Paired Comparison ?Go to Stat…. ?Basic Statistics… ? Paired t….. 169。The National Graduate School of Quality Management ? 95 Paired Comparison ?Select the samples… ?Go to Graphs…. 169。The National Graduate School of Quality Management ? 96 Paired Comparison ?Select the Boxplot for our graphical output.. ?Then select OK.. 169。The National Graduate School of Quality Management ? 97 Paired Comparison We see how the 95% confidence interval of the mean relates to the value we are testing. In this case, the value falls outside the 95% confidence interval of the data mean. This gives us confirmation that the shoe materials are significantly different. 169。The National Graduate School of Quality Management ? 98 CONTINGENCY TABLES (CHI SQUARE) 169。The National Graduate School of Quality Management ? 99 Entering the data…. ?Enter the data in a table format. For this example, load the file Contingency ... 169。The National Graduate School of Quality Management ? 100 Let’s set up a contingency table…. ?Contingency tables are found under Stat…. Tables… Chi Square Test…. 169。The National Graduate School of Quality Management ? 101 ?Select the columns which contain the table. Then select “OK” Setting up the test…. 169。The National Graduate School of Quality Management ? 102 Note that you will have the critical population and test statistics displayed in the session window. ?Minitab builds the table for you. Note that our original data is presented and directly below, Minitab calculates the expected values. ?Here, Minitab calculates the Chi Square statistic for each data point and totals the result. The calculated Chi Square statistic for this problem is . Performing the Analysis…. 169。The National Graduate School of Quality Management ? 103 ANalysis Of VAriance ANOVA 169。The National Graduate School of Quality Management ? 104 Let’s set up the analysis ?Load the file Anova … ?Stack the data in C4 and place the subscripts in C5 169。The National Graduate School of Quality Management ? 105 Set up the analysis…. ?Select Stat… ?ANOVA… ?One way… 169。The National Graduate School of Quality Management ? 106 ?Select ? C4 Responses ? C5 Factors ?Then select Graphs…. Set up the analysis…. 169。The National Graduate School of Quality Management ? 107 ?Choose boxplots of data... ?Then OK Set up the analysis….