L. Goch – February 2011

1. Basic Statistics Using Minitab L. Goch – February 2011

2. Agenda • Comparing 1 Group to a Target / Specification OR Comparing 2+ Groups to Each Other: • Stability – Run Chart (Feb 4th) or Control Chart (Mar 4th) • Shape – Histogram (Feb 4th) or Probability Plot • Spread – Test for Equal Variances • Centering – 1-Sample T-test, 1-Sample Sign, Paired T, 2-Sample T-test, ANOVA or Mood’s Median Test • Comparing Proportions - 1 Proportion, 2 Proportion • Basic Linear Regression – Fitted Line Plot • Chi-Squared – Cross Tabulation and Chi-Square • Trend Analysis – Under Stat > Time Series: We won’t be covering in this class. See Tutorials for more information.

3. Probability plot: Graph > Probability Plot

4. Probability Plot: Graph > Probability Plot • Use to display overlaid probability plots of multiple variables and/or multiple groups on the same graph. Open worksheet FlameRTD.mtw

5. Probability Plot

6. Test for Equal Variances: Stat > ANOVA > Test for Equal Variances

7. Test for Equal Variances: Stat > ANOVA > Test for Equal Variances • Use to display overlaid probability plots of multiple variables and/or multiple groups on the same graph. Open worksheet FlameRTD.mtw

8. Test for Equal Variances (Session window & Graph Results) Use for Normal Data Use for Non-Normal Data

9. Centering Comparison Analyses

10. 1-Sample T-test: Stat > Basic Statistics > 1-Sample t

11. 1-Sample T-test: Stat > Basic Statistics > 1-Sample t • Performs a one-sample t-test or t-confidence interval for the mean. Open worksheet EXH_Stat.mtw

12. 1-Sample T (Session window & Graph Results) Note: For n<30, data is assumed to be Normally Dist’d 95% of the time the True Avg will be between 4.5989 & 4.9789 The sample Avg is significantly different from the Target of 5.

13. 1-Sample Sign: Stat > NonParametrics> 1-Sample Sign

14. 1-Sample Sign: Stat > NonParametrics> 1-Sample Sign • Performs a one-sample t-Sign or t-confidence interval for the median. Open worksheet EXH_Stat.mtw

15. 1-Sample Sign (Session window Results) The sample Median is NOT significantly different from the Target of 115. 95% of the time the True Median will be between 108.5 & 211.7

16. Paired T-test: Stat > Basic Statistics > Paired t

17. Paired T-test: Stat > Basic Statistics > Paired t Open worksheet EXH_Stat.mtw • Tests the mean difference between paired (related) observations.

18. Paired T (Session window & Graph Results) 95% of the time the True Avg Difference will be between -0.687& -0.133 which does NOT contain ZERO. The sample Avgs are significantly different from each other.

19. 2-Sample T-test: Stat > Basic Statistics > 2-Sample t

20. 2-Sample T-test: Stat > Basic Statistics > 2-Sample t Open worksheet Furnace.mtw • Performs a two-sample t-test or t-confidence interval for the mean difference.

21. 2-Sample T (Session window & Graph Results) 95% of the time the True Avg Difference will be between -1.450 & 0.980 which contains ZERO. The sample Avgs are NOT significantly different from each other.

22. One-Way ANOVA: Stat > ANOVA > One-way

23. One-Way ANOVA: Stat > ANOVA > One-way Open worksheet Exh_AOV.mtw • Compares the Averages for 2 or more Groups.

24. One-Way ANOVA (Session window & Graph Results) At least 1 Pair of Avgs are significantly different from each other.

25. Mood’s Median Test: Stat > NonParametrics> Mood’s Median Test

26. Mood’s Median Test: Stat > NonParametrics> Mood’s Median Test • Compares the Medians of 2 or more Groups. Open worksheet Cartoon.mtw

27. Mood’s Median Test (Session window Results) At least one group’s median is significantly different from the others. Group 2 is significantly different from groups 0 & 1 since the 95% CI’s do NOT overlap.

28. 1-Proportion Test: Stat > Basic Statistics > 1-Proportion

29. 1-Proportion: Stat > Basic Statistics > 1-Proportion • Performs a one-sample proportions test or p-confidence interval for a proportion. No worksheet is needed for this test.

30. 1-Proportion: (Session window Results) Note: Proportion Testing Should NOT be done when the sample size n<30!! 95% of the time the True Proportion will be between 55.74% & 62.10% The sample Proportion is significantly different from the Target of 65%.

31. 2-Proportion Test: Stat > Basic Statistics > 2-Proportions

32. 2-Proportions: Stat > Basic Statistics > 2-Proportions • Performs a two-sample proportions test or p-confidence intervals for a proportion. No worksheet is needed for this test.

33. 2-Proportions: (Session window Results) Note: Proportion Testing Should NOT be done when the sample size for any one group is <30!! 95% of the time the True Difference between the Proportions will be between -9.58% & 17.58% The difference in Proportions is NOT significantly different.

34. Basic Linear Regression: Stat > Regression > Fitted Line Plot

35. Regression: Stat > Regression > Fitted Line Plot • Performs a Regression Analysis on 1 Input (X) and 1 Output (Y). Open worksheet Exh_REGR.mtw

36. Regression: (Graph Results) The line does NOT fit the curved data. Need a quadratic, cubic or transformation of the data.

37. Regression: (Session window & Graph Results) The Regression Equation shows that Machine Setting explains 93.1% of the variability in Energy Consumption. The Quadratic Term is significant in the model. NOTE: If a higher order term is significant than the lower order term must remain in the model.

38. Cross Tabulation and Chi-Square: Stat > Tables > Cross Tabulation and Chi-Square

39. Chi-Square: Stat > Tables > Cross Tabulation and Chi-Square Open worksheet Exh_TABL.mtw • Performs a Chi-Squared Analysis on Count Data.

40. Chi-Square Analysis: (Session Window Results) No significant association between Gender and Activity

41. Conclusions • Results need to be Supported by data • Not based on conjecture or intuition • Shown in 1) Graphical & 2) Statistical format • Make sense from an 3) Engineering standpoint • Use P-values to determine if Results could have happened by Chance!! Need Significant Differences for Reliable Conclusions !!