The document provides an agenda and overview for a Champion Training module on basic analytics. It includes definitions of descriptive and inferential statistics, how to monitor descriptive statistics over time, examples of numeric display terms like mean, median, and standard deviation, definitions of defects and defective units, and a table for calculating sigma levels and associated defects per million. The training aims to provide champions with knowledge and skills to lead process improvement projects.

1. Action plan and SOP for
Special Cause Variation
Determine new Goals
(UCL, LCL)

2. Module 8: Basic Analytics
Welcome to Champion Training
Facilitated by Kaplan’s Process Improvement Team

3. Agenda of Champion Training Modules
# Module # Pages
1 Introduction 19
2 Project Selection and Engaging Process Improvement 22
3 Champion Role through Project Lifecycle 26
4 Calculating Financial Benefit/ the Cost of Poor Quality 13
5 Define Overview & Tools 26
6 Measure Overview & Tools 27
7 Analyze Overview & Tools 18
8 Basic Analytics 21
9 Improve Overview & Tools 33
10 Control Overview & Tools 28
11 How to Effectuate Change Using Change Management 31
12 Kaplan’s Work Out 15

4. Purpose of This Training
Provide Kaplan champions with the knowledge and skills to be
effective leaders and coaches to their people engaged in Process
Improvement/Six Sigma projects
“Everything should be made as simple as
possible, but not too simple.”
Albert Einstein

5. Types of Statistics
Descriptive Statistics are used to describe the basic features of the data
in a study. They provide simple summaries about the sample and the
measures. Together with simple graphics analysis, they form the basis of
virtually every quantitative analysis of data. With descriptive statistics you
are simply describing what is, what the data shows.
Inferential Statistics investigate questions, models and hypotheses. In
many cases, the conclusions from inferential statistics extend beyond the
immediate data alone. For instance, we use inferential statistics to try to
infer from the sample data what the population thinks. Or, we use inferential
statistics to make judgments of the probability that an observed difference
between groups is a dependable one or one that might have happened by
chance in this study. Thus, we use inferential statistics to make inferences
from our data to more general conditions; we use descriptive statistics
simply to describe what's going on in our data.

6. Monitor Descriptive Statistics
Monitor
performance of
the Xs and Ys
over time
Verify that the
improvement
actions on the
Xs have made
the desired
improvement in
the Y
Mean, Median, Mode
Standard Deviation

7. Numeric Display Terms
• The number of data points with non-missing values in the data
set.N
• The Average
Mean (Arithmetic Mean)
• The middle data point in the data set.Median (50th Percentile)
• The Value that occurs the most frequently in a data set.Mode
• The average distance from the mean.StDev (Standard
Deviation)
• The highest value form the lowest 25% of the ranked data.
Q1 (First Quartile or 25th
Percentile)
• The lowest value from the highest 25% of the ranked data.
Q3 (Third Quartile or 75th
Percentile)

8. Defects
• A DEFECT is failure to conform to customer
requirements
• DEFECTIVE is when an entire unit fails to
meet acceptance criteria, regardless of the
number of defects within the unit.
Defective
Defect
Defective

9. How to Calculate Sigma
3.4
5
8
10
20
30
40
70
100
150
230
330
480
680
960
1,350
1,860
2,550
3,460
4,660
6,210
8,190
10,700
13,900
17,800
22,700
28,700
35,900
44,600
54,800
66,800
80,800
96,800
115,000
135,000
158,000
184,000
212,000
242,000
274,000
308,000
344,000
382,000
420,000
460,000
500,000
540,000
0.34
0.5
0.8
1
2
3
4
7
10
15
23
33
48
68
96
135
186
255
346
466
621
819
1,070
1,390
1,780
2,270
2,870
3,590
4,460
5,480
6,680
8,080
9,680
11,500
13,500
15,800
18,400
21,200
24,200
27,400
30,800
34,400
38,200
42,000
46,000
50,000
54,000
0.034
0.05
0.08
0.1
0.2
0.3
0.4
0.7
1.0
1.5
2.3
3.3
4.8
6.8
9.6
13.5
18.6
25.5
34.6
46.6
62.1
81.9
107
139
178
227
287
359
446
548
668
808
968
1,150
1,350
1,580
1,840
2,120
2,420
2,740
3,080
3,440
3,820
4,200
4,600
5,000
5,400
0.0034
0.005
0.008
0.01
0.02
0.03
0.04
0.07
0.1
0.15
0.23
0.33
0.48
0.68
0.96
1.35
1.86
2.55
3.46
4.66
6.21
8.19
10.7
13.9
17.8
22.7
28.7
35.9
44.6
54.8
66.8
80.8
96.8
115
135
158
184
212
242
274
308
344
382
420
460
500
540
0.00034
0.0005
0.0008
0.001
0.002
0.003
0.004
0.007
0.01
0.015
0.023
0.033
0.048
0.068
0.096
0.135
0.186
0.255
0.346
0.466
0.621
0.819
1.07
1.39
1.78
2.27
2.87
3.59
4.46
5.48
6.68
8.08
9.68
11.5
13.5
15.8
18.4
21.2
24.2
27.4
30.8
34.4
38.2
42
46
50
54
99.99966%
99.9995%
99.9992%
99.9990%
99.9980%
99.9970%
99.9960%
99.9930%
99.9900%
99.9850%
99.9770%
99.9670%
99.9520%
99.9320%
99.9040%
99.8650%
99.8140%
99.7450%
99.6540%
99.5340%
99.3790%
99.1810%
98.930%
98.610%
98.220%
97.730%
97.130%
96.410%
95.540%
94.520%
93.320%
91.920%
90.320%
88.50%
86.50%
84.20%
81.60%
78.80%
75.80%
72.60%
69.20%
65.60%
61.80%
58.00%
54.00%
50%
46%
6.0
5.9
5.8
5.7
5.6
5.5
5.4
5.3
5.2
5.1
5.0
4.9
4.8
4.7
4.6
4.5
4.4
4.3
4.2
4.1
4.0
3.9
3.8
3.7
3.6
3.5
3.4
3.3
3.2
3.1
3.0
2.9
2.8
2.7
2.6
2.5
2.4
2.3
2.2
2.1
2.0
1.9
1.8
1.7
1.6
1.5
1.4
Long-Term Yield
ST Process
Sigma
Defects Per
1,000,000
Defects Per
100,000
Defects Per
10,000
Defects Per
1,000
Defects Per
100
3.4
5
8
10
20
30
40
70
100
150
230
330
480
680
960
1,350
1,860
2,550
3,460
4,660
6,210
8,190
10,700
13,900
17,800
22,700
28,700
35,900
44,600
54,800
66,800
80,800
96,800
115,000
135,000
158,000
184,000
212,000
242,000
274,000
308,000
344,000
382,000
420,000
460,000
500,000
540,000
0.34
0.5
0.8
1
2
3
4
7
10
15
23
33
48
68
96
135
186
255
346
466
621
819
1,070
1,390
1,780
2,270
2,870
3,590
4,460
5,480
6,680
8,080
9,680
11,500
13,500
15,800
18,400
21,200
24,200
27,400
30,800
34,400
38,200
42,000
46,000
50,000
54,000
0.034
0.05
0.08
0.1
0.2
0.3
0.4
0.7
1.0
1.5
2.3
3.3
4.8
6.8
9.6
13.5
18.6
25.5
34.6
46.6
62.1
81.9
107
139
178
227
287
359
446
548
668
808
968
1,150
1,350
1,580
1,840
2,120
2,420
2,740
3,080
3,440
3,820
4,200
4,600
5,000
5,400
0.0034
0.005
0.008
0.01
0.02
0.03
0.04
0.07
0.1
0.15
0.23
0.33
0.48
0.68
0.96
1.35
1.86
2.55
3.46
4.66
6.21
8.19
10.7
13.9
17.8
22.7
28.7
35.9
44.6
54.8
66.8
80.8
96.8
115
135
158
184
212
242
274
308
344
382
420
460
500
540
0.00034
0.0005
0.0008
0.001
0.002
0.003
0.004
0.007
0.01
0.015
0.023
0.033
0.048
0.068
0.096
0.135
0.186
0.255
0.346
0.466
0.621
0.819
1.07
1.39
1.78
2.27
2.87
3.59
4.46
5.48
6.68
8.08
9.68
11.5
13.5
15.8
18.4
21.2
24.2
27.4
30.8
34.4
38.2
42
46
50
54
99.99966%
99.9995%
99.9992%
99.9990%
99.9980%
99.9970%
99.9960%
99.9930%
99.9900%
99.9850%
99.9770%
99.9670%
99.9520%
99.9320%
99.9040%
99.8650%
99.8140%
99.7450%
99.6540%
99.5340%
99.3790%
99.1810%
98.930%
98.610%
98.220%
97.730%
97.130%
96.410%
95.540%
94.520%
93.320%
91.920%
90.320%
88.50%
86.50%
84.20%
81.60%
78.80%
75.80%
72.60%
69.20%
65.60%
61.80%
58.00%
54.00%
50%
46%
6.0
5.9
5.8
5.7
5.6
5.5
5.4
5.3
5.2
5.1
5.0
4.9
4.8
4.7
4.6
4.5
4.4
4.3
4.2
4.1
4.0
3.9
3.8
3.7
3.6
3.5
3.4
3.3
3.2
3.1
3.0
2.9
2.8
2.7
2.6
2.5
2.4
2.3
2.2
2.1
2.0
1.9
1.8
1.7
1.6
1.5
1.4
Long-Term Yield
ST Process
Sigma
Defects Per
1,000,000
Defects Per
100,000
Defects Per
10,000
Defects Per
1,000
Defects Per
100
3.4
5
8
10
20
30
40
70
100
150
230
330
480
680
960
1,350
1,860
2,550
3,460
4,660
6,210
8,190
10,700
13,900
17,800
22,700
28,700
35,900
44,600
54,800
66,800
80,800
96,800
115,000
135,000
158,000
184,000
212,000
242,000
274,000
308,000
344,000
382,000
420,000
460,000
500,000
540,000
0.34
0.5
0.8
1
2
3
4
7
10
15
23
33
48
68
96
135
186
255
346
466
621
819
1,070
1,390
1,780
2,270
2,870
3,590
4,460
5,480
6,680
8,080
9,680
11,500
13,500
15,800
18,400
21,200
24,200
27,400
30,800
34,400
38,200
42,000
46,000
50,000
54,000
0.034
0.05
0.08
0.1
0.2
0.3
0.4
0.7
1.0
1.5
2.3
3.3
4.8
6.8
9.6
13.5
18.6
25.5
34.6
46.6
62.1
81.9
107
139
178
227
287
359
446
548
668
808
968
1,150
1,350
1,580
1,840
2,120
2,420
2,740
3,080
3,440
3,820
4,200
4,600
5,000
5,400
0.0034
0.005
0.008
0.01
0.02
0.03
0.04
0.07
0.1
0.15
0.23
0.33
0.48
0.68
0.96
1.35
1.86
2.55
3.46
4.66
6.21
8.19
10.7
13.9
17.8
22.7
28.7
35.9
44.6
54.8
66.8
80.8
96.8
115
135
158
184
212
242
274
308
344
382
420
460
500
540
0.00034
0.0005
0.0008
0.001
0.002
0.003
0.004
0.007
0.01
0.015
0.023
0.033
0.048
0.068
0.096
0.135
0.186
0.255
0.346
0.466
0.621
0.819
1.07
1.39
1.78
2.27
2.87
3.59
4.46
5.48
6.68
8.08
9.68
11.5
13.5
15.8
18.4
21.2
24.2
27.4
30.8
34.4
38.2
42
46
50
54
99.99966%
99.9995%
99.9992%
99.9990%
99.9980%
99.9970%
99.9960%
99.9930%
99.9900%
99.9850%
99.9770%
99.9670%
99.9520%
99.9320%
99.9040%
99.8650%
99.8140%
99.7450%
99.6540%
99.5340%
99.3790%
99.1810%
98.930%
98.610%
98.220%
97.730%
97.130%
96.410%
95.540%
94.520%
93.320%
91.920%
90.320%
88.50%
86.50%
84.20%
81.60%
78.80%
75.80%
72.60%
69.20%
65.60%
61.80%
58.00%
54.00%
50%
46%
6.0
5.9
5.8
5.7
5.6
5.5
5.4
5.3
5.2
5.1
5.0
4.9
4.8
4.7
4.6
4.5
4.4
4.3
4.2
4.1
4.0
3.9
3.8
3.7
3.6
3.5
3.4
3.3
3.2
3.1
3.0
2.9
2.8
2.7
2.6
2.5
2.4
2.3
2.2
2.1
2.0
1.9
1.8
1.7
1.6
1.5
1.4
Long-Term Yield
ST Process
Sigma
Defects Per
1,000,000
Defects Per
100,000
Defects Per
10,000
Defects Per
1,000
Defects Per
100
Long-Term Yield
ST Process
Sigma
Defects Per
1,000,000
Defects Per
100,000
Defects Per
10,000
Defects Per
1,000
Defects Per
100
A KU student expected to speak in person to
their Financial Aid Officer every time they contact
the FAO.
500 Defects = 100,000 Defects Per
5000 Opportunities Million Opportunities
2.8 Sigma
A DEFECT is any time that the
customers’ requirement is not met.

10. Shift The Mean And Reduce Variation
Calculate new process capability after implementing the improvement or design
Determine if the new process capability (process sigma) meets stated goals
See if you achieved the desired shift, variance reduction, or DPMO reduction

11. Sigma and Normal Distribution
As you can see, the curve is divided into a series of equal increments, each
representing one standard deviation from the mean.

12. Histogram
100806040200-20
25
20
15
10
5
0
DAYS
Frequency
Mean 29.41
StDev 24.45
N 68
Days it Takes for FAO to Return calls
Spec Limit is 5 days maximum

13. Causes for Greenbelts Not Completing Project
55
25
8
6 3 3
Not enough
time
Sponsor does
not understand
value
Did not pass
exam
Unclear of
what needed
to be done on
template
Lost template Office closed for
a month
55%
80%
88%
94%
100%97%
Causes
CumulativePercent

14. Central Limit Theorem
http://www.intuitor.com/statistics/CentralLim.html
If a random sample is drawn from any population, the sampling distribution of the sample
mean is approximately normal for a sufficiently large sample size. The larger the sample
size, the more closely the sampling distribution of the sample mean will resemble a normal
distribution
1 3 15 30

15. Yields
Rolled
Throughput
Yield
Receive request for Financial Aid
45,000 DPMO wasted
Step 1 in Financial Aid
28,650 DPMO wasted
Step 2 in Awarding Financial Aid
51,876 DPMO wasted
Financial Aid Awarded
Right
First
Time
125,526 DPMO
wasted opportunities
95.5% Yield (YTP)
97% Yield (YTP)
94.4% Yield (YTP)
Yields can be multiplied with many
process steps. Assumes independent
sources of defects.
YRT = .955*.97*.944 = 87.5%

16. Correlations are not Necessarily Causal
• City of Oldenburg, Germany
• 1930- 1936
• X-axis: stork population
• Y-axis: human population
What your mother told you about
babies when you were three is still
not right, despite the strong
correlation “evidence”.
Causal means that one variable results in the other thing occurring. In general, it is
extremely difficult to establish causality between two correlated events or observances.
There are many statistical tools to establish a statistical significant correlation.
Source: Box, Hunter, hunter Statistics For Experiments 1978

17. Regression
Regression can be used for prediction, inference, hypothesis testing, and
modeling of causal relationships
The procedure calculates estimates of the relationship between the
independent variables (advertising, price, etc.) and the dependent variable
(sales).
Simple Linear
Regression Analysis:
Y = b0 + b1X

18. The Control Chart or Shewhart Chart
Observation
IndividualValue
28252219161310741
60
50
40
30
20
10
0
_
X=29.06
UCL=55.24
LCL=2.87
1
Control Chart of Recycle
Process
Center
(usually the Mean)
Special Cause
Variation
Detected
Control
Limits
Common
Cause
Variation

19. Common Distributions
Sample size - Normal Distributions
• As the number of samples measured increases, to 30, the distribution
becomes more representative of the population.
Population
sample
NORMAL DISTRIBUTION’S IMPORTANCE
Most variables are approximately normally
distributed. This means we can use the
normal distribution as a model to help us
better understand these variables.
NORMALITY TESTS
Normality tests are used to determine if any
group of data fits a standard normal
distribution

20. Confirm New Capability
Calculate new
process capability
Determine if the
new process sigma
meets stated goals

21. Action plan and SOP for
Special Cause Variation
Determine new Goals
(UCL, LCL)

22. Module Wrap Up
•Questions/Comments
•Discussions of Process
Improvement Projects in Your Area
•Discuss Next Module
•Establish Time/Date of Next
Meeting