l. g och – f ebruary 2011 basic statistics using minitab
TRANSCRIPT
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L. GOCH – FEBRUARY 2011L. GOCH – FEBRUARY 2011
Basic Statistics Using Basic Statistics Using MinitabMinitab
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AGENDA
Comparing 1 Group to a Target / Specification OR Comparing 2+ Groups to Each Other:
1) Stability – Run Chart (Feb 4th) or Control Chart (Mar 4th)2) Shape – Histogram (Feb 4th) or Probability Plot3) Spread – Test for Equal Variances 4) 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.
Basic Statistics using Minitab.mtb
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PROBABILITY PLOT: PROBABILITY PLOT:
GRAPH > PROBABILITY PLOT
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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.mtwFlameRTD.mtw
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PROBABILITY PLOT
5.04.54.03.53.02.52.0
99
95
90
80
70
6050
40
30
20
10
5
1
Fabric1
Per
cent
90
3.54
4
3.18
5
4.30
4
3.013 0.4138 15 0.321 0.4972.727 0.3575 15 0.545 0.1333.573 0.5700 15 0.310 0.517
Mean StDev N AD P
ABNone
Coating
Probability Plot of Fabric1Normal
is NORMALLY DISTRIBUTED.0.05, conclude each data setSince all p-values are >
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TEST FOR EQUAL TEST FOR EQUAL VARIANCES: VARIANCES:
STAT > ANOVA > TEST FOR EQUAL VARIANCES
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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.mtwFlameRTD.mtw
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TEST FOR EQUAL VARIANCES (SESSION WINDOW & GRAPH RESULTS)
None
B
A
1.11.00.90.80.70.60.50.40.30.2
Coat
ing
95% Bonferroni Confidence Intervals for StDevs
Test Statistic 3.19P-Value 0.203
Test Statistic 1.42P-Value 0.253
Bartlett's Test
Levene's Test
Test for Equal Variances for Fabric1
Use for Normal Data
Use for Non-Normal Data
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CENTERING COMPARISON CENTERING COMPARISON ANALYSESANALYSES
Analysis # of Grps Comparison Statistic1-Sample T 1 Target Average1-Sample Sign 1 Target Median
Paired T 2Paired Data (e.g. before
vs after)Difference
2-Sample T 2 Each Other AverageANOVA 2+ Each Other AverageMood’s Median Test 2+ Each Other Median
Response is Numeric & Factors are Text or Numeric
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1-SAMPLE T-TEST: 1-SAMPLE T-TEST:
STAT > BASIC STATISTICS > 1-SAMPLE T
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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.mtwEXH_Stat.mtw
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1-SAMPLE T (SESSION WINDOW & GRAPH RESULTS)Note: For n<30, data is assumed to be Normally Dist’d
5.15.04.94.84.74.64.54.4
X_
Ho
Values
Boxplot of Values(with Ho and 95% t-confidence interval for the mean)
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.
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1-SAMPLE SIGN: 1-SAMPLE SIGN:
STAT > NONPARAMETRICS> 1-SAMPLE SIGN
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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.mtwEXH_Stat.mtw
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1-SAMPLE SIGN (SESSION WINDOW RESULTS)
95% of the time the True Median will be between 108.5 & 211.7
The sample Median is NOT significantly different from the Target of 115.
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PAIRED T-TEST: PAIRED T-TEST:
STAT > BASIC STATISTICS > PAIRED T
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PAIRED T-TEST: STAT > BASIC STATISTICS > PAIRED T
Tests the mean difference between paired (related) observations.
Open worksheet EXH_Stat.mtwEXH_Stat.mtw
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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.
0.0-0.3-0.6-0.9-1.2
X_
Ho
Differences
Boxplot of Differences(with Ho and 95% t-confidence interval for the mean)
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2-SAMPLE T-TEST: 2-SAMPLE T-TEST:
STAT > BASIC STATISTICS > 2-SAMPLE T
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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.mtwFurnace.mtw
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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.
21
20
15
10
5
Damper
BTU
.In
Boxplot of BTU.In
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ONE-WAY ANOVA: ONE-WAY ANOVA:
STAT > ANOVA > ONE-WAY
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ONE-WAY ANOVA: STAT > ANOVA > ONE-WAY
Compares the Averages for 2 or more Groups.
Open worksheet Exh_AOV.mtwExh_AOV.mtw
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ONE-WAY ANOVA (SESSION WINDOW & GRAPH RESULTS)
At least 1 Pair of Avgs are significantly different from each other.
4321
22.5
20.0
17.5
15.0
12.5
10.0
7.5
5.0
Carpet
Dura
bility
Boxplot of Durability
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MOOD’S MEDIAN TEST: MOOD’S MEDIAN TEST:
STAT > NONPARAMETRICS> MOOD’S MEDIAN TEST
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MOOD’S MEDIAN TEST: STAT > NONPARAMETRICS> MOOD’S MEDIAN TEST
Compares the Medians of 2 or more Groups.
Open worksheet Cartoon.mtwCartoon.mtw
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MOOD’S MEDIAN TEST (SESSION WINDOW RESULTS)
Group 2 is significantly different from groups 0 & 1 since the 95% CI’s do NOT overlap.
At least one group’s median is significantly different from the others.
210
140
130
120
110
100
90
80
70
ED
Otis
Boxplot of Otis
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1-PROPORTION TEST: 1-PROPORTION TEST:
STAT > BASIC STATISTICS > 1-PROPORTION
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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.
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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%.
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2-PROPORTION TEST: 2-PROPORTION TEST:
STAT > BASIC STATISTICS > 2-PROPORTIONS
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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.
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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.
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BASIC LINEAR BASIC LINEAR REGRESSION: REGRESSION:
STAT > REGRESSION > FITTED LINE PLOT
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REGRESSION: STAT > REGRESSION > FITTED LINE PLOT
Performs a Regression Analysis on 1 Input (X) and 1 Output (Y).
Open worksheet Exh_REGR.mtwExh_REGR.mtw
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REGRESSION: (GRAPH RESULTS)
3025201510
40
30
20
10
0
MachineSetting
Energ
yConsu
mption
S 12.1825R-Sq 2.3%R-Sq(adj) 0.0%
Fitted Line PlotEnergyConsumption = 1.25 + 0.3218 MachineSetting
The line does NOT fit the curved data. Need a quadratic, cubic or transformation of the data.
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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.
3025201510
100
10
1
MachineSetting
Energ
yConsu
mption
S 0.167696R-Sq 93.1%R-Sq(adj) 91.1%
Fitted Line Plotlog10(EnergyConsumption) = 7.070 - 0.6986 MachineSetting
+ 0.01740 MachineSetting**2
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CROSS TABULATION CROSS TABULATION AND CHI-SQUARE: AND CHI-SQUARE:
STAT > TABLES > CROSS TABULATION AND CHI-SQUARE
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CHI-SQUARE: STAT > TABLES > CROSS TABULATION AND CHI-SQUARE
Performs a Chi-Squared Analysis on Count Data.Open worksheet Exh_TABL.mtwExh_TABL.mtw
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CHI-SQUARE ANALYSIS: (SESSION WINDOW RESULTS)
No significant association between Gender and Activity
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CONCLUSIONS
Results need to be Supported by data Not based on conjecture or intuition Shown in 1) Graphical & 2) Statistical 1) Graphical & 2) Statistical
formatformat Make sense from an 3) Engineering 3) Engineering
standpointstandpoint Use P-values to determine if Results could have
happened by Chance!!Need Significant Differences Need Significant Differences for Reliable Conclusions !!for Reliable Conclusions !!Need Significant Differences Need Significant Differences for Reliable Conclusions !!for Reliable Conclusions !!