Basic Statistics Using Minitab L GOCH FEBRUARY 2011

Basic Statistics Using Minitab L. GOCH – FEBRUARY 2011

AGENDA Comparing 1 Group to a Target / Specification OR Comparing 2+ Groups to Each Other: 1) 2) 3) 4) Stability – Run Chart (Feb 4 th) or Control Chart (Mar 4 th) Shape – Histogram (Feb 4 th) 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.

PROBABILITY PLOT: GRAPH > PROBABILITY PLOT

PROBABILITY PLOT: GRAPH > PROBABILITY PLOT Use to display overlaid probability plots of multiple variables and/or multiple groups on the same graph. Open worksheet Flame. RTD. mtw

PROBABILITY PLOT

TEST FOR EQUAL VARIANCES: STAT > ANOVA > TEST FOR EQUAL VARIANCES

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 Flame. RTD. mtw

TEST FOR EQUAL VARIANCES (SESSION WINDOW & GRAPH RESULTS) Use for Normal Data Use for Non-Normal Data

CENTERING COMPARISON ANALYSES

1 -SAMPLE T-TEST: STAT > BASIC STATISTICS > 1 -SAMPLE T

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

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.

1 -SAMPLE SIGN: STAT > NONPARAMETRICS> 1 SAMPLE SIGN

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

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

PAIRED T-TEST: STAT > BASIC STATISTICS > PAIRED T

PAIRED T-TEST: STAT > BASIC STATISTICS > PAIRED T Tests the mean difference between paired (related) observations. Open worksheet EXH_Stat. mtw

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.

2 -SAMPLE T-TEST: STAT > BASIC STATISTICS > 2 -SAMPLE T

2 -SAMPLE T-TEST: STAT > BASIC STATISTICS > 2 SAMPLE T Performs a two-sample t-test or t-confidence interval for the mean difference. Open worksheet Furnace. mtw

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.

ONE-WAY ANOVA: STAT > ANOVA > ONE-WAY

ONE-WAY ANOVA: STAT > ANOVA > ONE-WAY Compares the Averages for 2 or more Groups. Open worksheet Exh_AOV. mtw

ONE-WAY ANOVA (SESSION WINDOW & GRAPH RESULTS) At least 1 Pair of Avgs are significantly different from each other.

MOOD’S MEDIAN TEST: STAT > NONPARAMETRICS> MOOD’S MEDIAN TEST

MOOD’S MEDIAN TEST: STAT > NONPARAMETRICS> MOOD’S MEDIAN TEST Compares the Medians of 2 or more Groups. Open worksheet Cartoon. mtw

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.

1 -PROPORTION TEST: STAT > BASIC STATISTICS > 1 -PROPORTION

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.

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%.

2 -PROPORTION TEST: STAT > BASIC STATISTICS > 2 -PROPORTIONS

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.

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.

BASIC LINEAR REGRESSION: STAT > REGRESSION > FITTED LINE PLOT

REGRESSION: STAT > REGRESSION > FITTED LINE PLOT Performs a Regression Analysis on 1 Input (X) and 1 Output (Y). Open worksheet Exh_REGR. mtw

REGRESSION: (GRAPH RESULTS) The line does NOT fit the curved data. Need a quadratic, cubic or transformation of the data.

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.

CROSS TABULATION AND CHI-SQUARE: STAT > TABLES > CROSS TABULATION AND CHISQUARE

CHI-SQUARE: STAT > TABLES > CROSS TABULATION AND CHI-SQUARE Performs a Chi-Squared Analysis on Count Data. Open worksheet Exh_TABL. mtw

CHI-SQUARE ANALYSIS: (SESSION WINDOW RESULTS) No significant association between Gender and Activity

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 !!