1. Copy Data to Minitab Statistical Tests Open Excel File > Highlight All Data & Column Headings > Copy Launch Minitab: Start > Programs > Minitab > Minitab Paste Data into Minitab Put the Data into Minitab for Analysis Remember to paste in cell above row labeled 1 – This brings column headings and data in without confusing Minitab

2. Do you have Normal Data?  H o : Data distribution = Normal Distribution H a : Data distribution  Normal Distribution Continuous Non Normal Normal If the p-value >.05 …… Then H o is true and there is no difference in the groups you had me test(Accept H o ) The Data is normal If the p-value <.05 …... Then H o is false and there is a statically significant difference (Reject H o ) The Data is not Normal Normality Test

3. MINITAB: Stat> Basic Statistics> Display Descriptive statistics> Normality Test> If the p-value >.05 …… Then H o is true and there is no difference in the groups you had me test(Accept H o ) The Data is normal If p-value <.05 …... Then H o is false and there is a statically significant difference (Reject H o ) The Data is not Normal If the p-value >.05 …… Then H o is true and there is no difference in the groups you had me test(Accept H o ) The Data is normal If p-value <.05 …... Then H o is false and there is a statically significant difference (Reject H o ) The Data is not Normal P-value = 0.000 < 0.05 Therefore The data is NOT Normal Normality Test

4. Capability MINITAB: Stat> Quality tools Capability analysis Nonnormal

5. Visualize The Data – Box Plots Statistical Tests Minitab: Graph > Box Plots > Y=Cycle Time > X1 = Department X2 = Band X3 = Agent Which Xs Look they effect the Cycle Time (Mean, Median, Variance)? If they look like they have an impact they probably do and we can prove it with Statistics Which Xs Look they effect the Cycle Time (Mean, Median, Variance)? If they look like they have an impact they probably do and we can prove it with Statistics

6. We have these tests to choose from because the Data is NOT NORMAL Statistical Tests Variances HOV Levine’s Correlation Sign test Wilcoxon Mann- Whitney Mood’s Friedman Continuous Non Normal Medians Non Normal Data Variance Tests Homogeneity of Variance - Levine’s - Compares two or more sample variances. Medians Tests Sign Test - Tests if a sample median is equal to a known or target value. Wilcoxon Test - Tests if a sample median is equal to a known or hypothesized value. Mann-Whitney Test - Test if two sample medians are equal. Mood’s Median Test - Test if two or more sample medians are equal. Friedman Test - Tests if medians from samples classified by two categories are equal. Correlation - Tests linear relationship between two variables.

7. Staffing cycle time is exceeding 75 days 88% of the time Measurement Variation Process (or product) Variation Measurement System Valid Time to Time Department to Department Job type to Job type Band to Band Agent To Agent Other? Let’s see what we can eliminate from our suspect list Let’s start with Department to department Check the variances Check the means Let’s start with Department to department Check the variances Check the means Statistical Tests

8. HOV Staffing cycle time is exceeding 75 days 88% of the time Process (or product) Variation Department to Department Department to Department - Variances Appropriate Test: HOV-Levine’s H o : Variances are the same department to department H a : Variances are different Response = Cycle Time Factor = Department Statistical Tests Variances HOV Levine’s Non Normal MINITAB: Stat> ANOVA Test of equal variances

9. Remember: Min I.Tab can only give us a P-value, we have to determine what it means Statistical Tests HOV If the p-value >.05 …… Then H o is true and there is no difference in variances (Accept H o ) If the p-value <.05 …... Then H o is false and there is a statically significant difference in variances (Reject H o ) P-value = 0.000 95% Confident that the variances are different – Validates what we saw on the Box Plot (more scatter in IT Data)

10. Department to Department - Medians Appropriate Test: Mood’s Median H o : Cycle Time Medians are the same department to department H a : Cycle Time Medians are different Response = Cycle Time Factor = Department Staffing cycle time is exceeding 75 days 88% of the time Process (or product) Variation Department to Department Statistical Tests Moods Median Correlation Sign test Wilcoxon Mann- Whitney Mood’s Friedman Non Normal Medians MINITAB: Stat> Nonparametrics Mood’s Median test

11. If the p-value >.05 …… Then H o is true and there is no difference in Means (Accept H o ) If the p-value <.05 …... Then H o is false and there is a statically significant difference in Means (Reject H o ) P-value = 0.06 The Department Medians are NOT different at 95% Confidence Level – but close Statistical Tests Moods Median Mood Median Test Mood median test for Cycle Ti Chi-Square = 7.42 DF = 3 P = 0.060 Individual 95.0% CIs Departme N Median Q3-Q1 -------+---------+---------+--------- Engineer 3 5 84.6 5.3 (-+-) Finance 3 8 84.5 3.1 (+-) IT 4 3 66.7 43.5 (-------------------+--------------) Sourcing 7 1 81.4 3.2 (+-) -------+---------+---------+--------- 45 60 75 Overall median = 83.6

12. Means t - test 1 - sample 2 - sample ANOVA One way Two way Normal Department to Department - Means Appropriate Test: One-Way ANOVA, ( Tests if more than two sample means are equal) H o : Cycle Time Means are the same department to department H a : Cycle Time Means are different Staffing cycle time is exceeding 75 days 80% of the time Process (or product) Variation Department to Department Statistical Tests ANOVA If our staffing cycle time data had been normal... Samples MUST BE NORMAL

13. Staffing cycle time is exceeding 75 days 88% of the time Measurement Variation Process (or product) Variation Measurement System Valid Agent To Agent Department to Department Band to Band Let’s see what we can eliminate from our suspect list Moods p-value = 0.060 HOV p-value = 0.000 Continue to work through until you find the Red X or X’s Statistical Tests Staffing Cycle Time

14. Staffing cycle time is exceeding 75 days 88% of the time Measurement Variation Process (or product) Variation Measurement System Valid Agent To Agent Department to Department Band To Band Staffing Cycle Time Statistical Tests Department to Department is the Red X Moods p-value = 0.060 HOV p-value = 0.000 Moods p-value = 1.000 HOV p-value = 0.0166 Moods p-value = 0.211 HOV p-value = 0.067

15. Statistical Tests What if you have Attribute data? 75 days Anything less than 75 days is Good Anything greater than 75 days is a Defect Hypothesis Testing Continuous Non-Continuous Chi-sq Correlation Staffing cycle time is exceeding 75 days 88% of the time Measurement Variation Process (or product) Variation Time to Time Department to Department Band to Band Operator to Operator Attribute Data

16. Non-Continuous Chi-sq Correlation H o : All Departments are the same H a : Departments are different If the p-value >.05 …… Then H o is true and there is no difference in the groups you had me test(Accept H o ) Departments are the same If the p-value <.05 …... Then H o is false and there is a statically significant difference (Reject H o ) Departments are different Staffing cycle time is exceeding 75 days 88% of the time Process (or product) Variation Department to Department PassFail Engineering Finance Sourcing Department to Department Counts of pass / fail Chi 2 Statistical Tests 75 days Anything less than 75 days is Good Anything greater than 75 days is a Defect

17. Statistical Tests If the p-value >.05 …… Then H o is true and there is no difference in the groups you had me test(Accept H o ) Departments are the same If the p-value <.05 …... Then H o is false and there is a statically significant difference (Reject H o ) Departments are different P-value >.05 There is no difference between departments Chi 2 MINITAB: Stat> Tables Chi Square test Chi-Square Test: Defects, Good Expected counts are printed below observed counts Chi-Square contributions are printed below expected counts Defects Good Total 1 7 1 8 6.12 1.88 0.127 0.414 2 9 2 11 8.41 2.59 0.041 0.134 3 3 4 7 5.35 1.65 1.034 3.361 4 7 1 8 6.12 1.88 0.127 0.414 Total 26 8 34 Chi-Sq = 5.652, DF = 3, P-Value = 0.130 4 cells with expected counts less than 5.