A05 Continuous One Variable Stat Tests

Determine Critical X’s Statistical Tests for a Continuous Single Variable Deliverable 10A

Define Module Roadmap Define 1D – Define VOC, VOB, and CTQ’s 2D – Define Project Boundaries 3D – Quantify Project Value 4D – Develop Project Mgmt. Plan Measure 5M – Document Process 6M – Prioritize List of X’s 7M – Create Data Collection Plan 8M – Validate Measurement System 9M – Establish Baseline Process Cap. Analyze 10A – Determine Critical X’s Improve 12I – Prioritized List of Solutions 13I – Pilot Best Solution Control 14C – Create Control System 15C – Finalize Project Documentation Green 11G – Identify Root Cause Relationships Queue 1 Queue 2

Deliverables – Analyze # Deliverable Deliverable Concept & Tasks Primary Tool(s) Secondary Tool(s) 10A Determine Critical X’s Using the data gathered after deliverable 8M, we need to assess which X’s cause changes in the Y. When viewing raw data or even charts, people can come to incorrect conclusions. 10A uses statistics to be the arbiter in deciding which X’s are important. ,[object Object],[object Object],[object Object]

10A – Determine Critical X’s # Deliverable Deliverable Concept & Tasks Primary Tool(s) Secondary Tool(s) 10A Determine Critical X’s Using the data gathered after deliverable 8M, we need to assess which X’s cause changes in the Y. When viewing raw data or even charts, people can come to incorrect conclusions. 10A uses statistics to be the arbiter in deciding which X’s are important. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Objectives – Determine Critical Xs ,[object Object],[object Object],[object Object],[object Object]

Statistical Tests Continuous Y Discreet Y Discreet X 2 Sample t Test Test for Equal Variance One-Way ANOVA (Tukeys) Moods Median Paired t Test Two Way ANOVA GLM CHI Square TOA Two Proportion Continuous X Correlation Simple Linear Regression Multiple Linear Regression These tools are not taught as part of Black Belt training Vs. Target Normality 1 Sample T One Sample Sign CHI Square GOF One Proportion

Hypothesis Test Categories Continuous Y, Continuous X(s) Tests Continuous Y, Discrete X(s) Tests Discrete Y, Continuous X(s) Tests Discrete Y, Discrete X(s) Tests Continuous Y? Y N Continuous X(s)? Continuous X(s)? Y N N Y Start

Continuous Y, Discrete X(s) Test for Normality ( Shape = normal) Residuals Normal? ResidualsEqual Variance? Residuals Stable? Y Y See MBB N N N Y Done Testing vs. a Target Value(s)? Y N 1 Sample t  1 Sample Sign (m = #) Data Symmetric? 1 Sample Wilcoxon (m = #) Y N Not Normal Normal Done No of X’s? 1 > 2 2 Sample t (Assume equal variance) (  No of levels? 2 Data Paired? N Y > 3 Paired t (  See MBB 1 Way ANOVA (  General Linear Model (  Go to “B” Perform Box-Cox Transform and Reanalyze Data already Transformed? N Y

Testing for Normality One Variable, Continuous Data H o : The data is normally distributed H a : The data is not normally distributed

Review – Test for Normality ,[object Object],[object Object],[object Object],[object Object],[object Object]

Descriptive Statistics Graphical Output Is the data normal?

Normality Test Graphical Output

Alternate Normality Tests ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

1 Sample t Test Normally Distributed Continuous Data vs. Target H o :  a = Target H a :  a ≠ Target

1 Sample t Test ,[object Object],[object Object],[object Object],[object Object],[object Object]

Chlorine Residuals Graphical Summary Data is normal!

1 Sample t Test ,[object Object]

1 Sample t Test Check ‘histogram of the data’ Make the test one-tailed by choosing ‘greater than’ The test mean is 0.03 Summarized data would go here

1 Sample t Test One-Sample T: PPM Chlorine Test of mu = 0.3 vs > 0.3 95% Lower Variable N Mean StDev SE Mean Bound T P PPM Chlorine 55 0.335889 0.045808 0.006177 0.325552 5.81 0.000 P value < 0.05, reject the null and conclude the mean is greater than 0.3 Target Value (H o ) Confidence interval for the lower bound H o :  =0.3 H a :  >0.3

Class Exercise ,[object Object],10 Min

One Sample Sign Test Non-Normally Distributed Continuous Data vs. a Target H o : Median = Target H a : Median ≠ Target

One Sample Sign Test ,[object Object],[object Object],[object Object],[object Object],[object Object]

1-Sample Sign Test ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

1-Sample Sign Test ,[object Object]

Vacation Days Example First, determine if the data is normal… Did this catch you? Don’t forget to check for normality. Technically, we should use a 1 sample t test of the mean for this data. However, let’s proceed with a 1- sample sign test for the median for illustration.

Vacation Days Example ,[object Object],H o : median=15 H a : median>15

Vacation Days Example Sign Test for Median: Vacation Days Sign test of median = 15.00 versus > 15.00 N Below Equal Above P Median Vacation Days 78 30 5 43 0.0801 18.00 Note the lack of power in a nonparametric statistical test. 43 of 78 data points are above 15 yet there is still insufficient evidence to prove the population is above 15. What if we had used the 1-sample t after all? The number of observations below the test median. The number of observations above the test median. The number of observations equal to the test median.

Vacation Days Revisited One-Sample T: Vacation Days Test of mu = 15 vs > 15 95% Lower Variable N Mean StDev SE Mean Bound T P Vacation Days 78 16.6154 7.6145 0.8622 15.1800 1.87 0.032 There is enough data to confirm the mean is >15!

1-Sample Sign Homework ,[object Object]

Learning Check – Determine Critical Xs ,[object Object],[object Object],[object Object],[object Object]

A05 Continuous One Variable Stat Tests

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