DATA CONFUSION

DATA CONFUSION

How to confuse yourself and others with Data Analysis

AGENDA FOR TODAY’S TALK

• Good Graphs – Bad Graphs• The Law of Averages• PTBD Analysis• Enumerative & Analytical Problems• PARC Analysis• Wrong Methods of Analysis

“There are three kinds of lies:

Lies, damned lies and statistics”Attributed to Benjamin Disraeli by Mark Twain

GOOD GRAPHS AND BAD GRAPHS

DATA RELEVANCE

• Graphs are only as good as the data they display

• No amount of creativity can produce good graphs from dubious data

DATA CONTENT

• Don’t produce graphs from very small amounts of data

• The human brain can grasp 1, 2 or 3 numbers without a graph

RULES FOR PRODUCING GOOD GRAPHS

• KEEP IT SIMPLE AND STUPID– Jesse Ventura

• Tell the truth – don’t distort the data

GOOD GRAPHS

• Portray information without distortion

• Contain no distracting elements

– No false third dimensions, irrelevant decoration, or colour (chartjunk)

• Use an appropriate scale

• Label axes and tick marks properly, including measurement units

• Have a descriptive title and/ or caption and legend

• Have a low ink – to – information ratio

Temperature (degC) of Air and Subject during one day

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BAD GRAPH GOOD GRAPH

BAD GRAPH EVEN BETTER GRAPH

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Boxplot of A, B, C, D, E

Project: more chewchat data.MPJ; Worksheet: Worksheet 1; 12/04/2006; Graham Errington

BAD GRAPH

GOOD GRAPH GOOD GRAPH

Data17.016.516.015.515.014.514.013.513.012.512.011.5

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Dotplot of A, B, C, D, E

Project: more chewchat data.MPJ; Worksheet: Worksheet 1; 12/04/2006; Graham Errington

GRAPHS THAT CONFUSE

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GRAPHS THAT TELL A STORYNo. REJ

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Time Series Plot of No. REJECTS

Project: Untitled; Worksheet: Worksheet 3; 04/04/2006; Graham Errington

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I-MR Chart of No. REJECTS by YEAR

Project: Data for ChewChat 13 Apr 2006.MPJ; Worksheet: Worksheet 3; 04/04/2006; Graham Errington

HISTOGRAMS

• No meaningless gaps

• Reasonable Choice of bins

• Easy to choose or adjust bins

• Good aspect ratio

• Meaningful labels on axes

• Appropriate labels on bin tick marks

Histogram

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Histogram of C20

Project: DATA FOR CHEWCHAT 13 APR 2006.MPJ; Worksheet: Worksheet 1; 07/04/2006; Graham Errington

TRENDING RANDOM VARIATION

“Upward trend”

“Downturn”

“Rebound”

“Setback”

“Turnaround”

“Downward trend”

THE LAW OF AVERAGES

“If I sit in a freezer and plunge my head into a pan of boiling chip fat. . . . .

on average, I’m quite comfortable.”

SHEWHART’S RULES FOR PRESENTATION OF DATA

• Rule One

– Data should always be presented in a way that preserves the evidence in the data

• Rule Two

– When an average, standard deviation or histogram is used to summarize data, the user should not be misled into to taking action they would not take if the data were presented in a time series

USING THE WRONG METHODS

Descriptive Statistics: A, B, C, D

Variable N Mean StDev CoefVar Minimum Maximum

A 20 11.950 0.102 0.85 11.83 12.08

B 20 11.950 0.100 0.84 11.85 12.25

C 20 11.950 0.102 0.86 11.75 12.15

D 20 11.950 0.100 0.84 11.81 12.14

Process: A B C D

1 11.85 11.85 11.75 12.14

2 11.83 11.86 11.95 12.01

3 11.87 11.87 11.8 11.88

4 11.84 11.87 11.94 12.07

5 11.85 11.88 11.95 11.95

6 11.86 11.89 12 11.87

7 11.85 11.89 12.05 12.06

8 11.85 11.9 11.85 11.94

9 11.84 11.92 11.94 11.84

10 11.86 11.91 11.85 12.05

11 12.05 11.93 12.05 11.93

12 12.06 11.93 11.85 11.83

13 12.03 11.95 12.05 12.04

14 12.02 11.97 11.95 11.92

15 12.03 11.96 11.95 11.82

16 12.04 11.99 11.95 12.03

17 12.06 12 11.85 11.91

18 12.06 12 12.1 11.81

19 12.04 12.16 12 12.01

20 12.08 12.25 12.15 11.81

NO SIGNIFICANT DIFFERENCE HERE!

One-way ANOVA: A, B, C, D Source DF SS MS F P Factor 3 0.0000 0.0000 0.00 1.000 Error 76 0.7746 0.0102 Total 79 0.7746 S = 0.1010 R-Sq = 0.00% R-Sq(adj) = 0.00% Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev --------+---------+---------+---------+- A 20 11.950 0.102 (-----------------*-----------------) B 20 11.950 0.100 (-----------------*-----------------) C 20 11.950 0.102 (-----------------*-----------------) D 20 11.950 0.100 (-----------------*-----------------) --------+---------+---------+---------+- 11.925 11.950 11.975 12.000 Pooled StDev = 0.101

NO DIFFERENCE?!?

Sample

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2018161412108642

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A B

C D

Project: ENUMERATIVE VS ANALYTICAL STUDIES.MPJ; Worksheet: Worksheet 1; 05/04/2006; Graham Errington

FOUR PROCESSES WITH SAME MEAN AND SDMean = 11.95, SD = .10

ALWAYS CARRY OUT PTBD ANALYSIS

PLOT THE B….. DOTS!

TYPES OF STATISTICAL STUDIES

• Descriptive

• Enumerative

• Analytic

DESCRIPTIVE STUDY

• Count all fish in barrel

• Count number of goldfish

• Proportion of goldfish applies to the fish population in this barrel and no other barrels of fish

ENUMERATIVE STUDY

• Take a sample of fish from the barrel, and count the number of goldfish in the sample

• Point estimate of the proportion of goldfish in the barrel population

• Many statistical procedures do this

• Cannot make any inference about any other barrels of fish

ANALYTICAL STUDY

• Will we get the same proportion of goldfish in the future as we got in the past?

• An analytical study allows prediction within limits

Fish Packing Process over Time

ANALYTICAL STUDY

• Proportion of goldfish is stable over time

• Fish packing process is predictable within limits

• We can expect, on average, 4 goldfish per barrel, but as many as 10 and as few as 0 in any single barrel

Week No.

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C Chart of No goldfish per Barrel

Project: ENUMERATIVE VS ANALYTICAL STUDIES.MPJ; Worksheet: Fish in Barrel; 05/04/2006; Graham Errington

ENUMERATIVE vs ANALYTICAL METHODS

• Enumerative methods – seek to provide numeric summaries, confidence intervals,etc– use significance tests, ANOVA, descriptive stats, etc.,

assume single, stable population • Analytical methods

– seek to understand the system under study– use primarily graphical tools such as run charts, control

charts, histograms, box plots, etc– in the real world, most problems are analytical

“Analysis of variance, t-tests, confidence intervals, and other statistical techniques taught in books,….., are inappropriate because they provide no basis for prediction and because they bury the information contained in the order of production.”

W.E. Deming, Out of the Crisis

Traditional statistical methods have their place, but are widely abused in the real world. When this is the case, statistics do more to cloud the issue than to enlighten.

PARC ANALYSIS

Practical

Accumulated

Records

Compilation

Passive

Analysis (by)

Regression

Correlations

Planning

After

Research

Completed

Profound

Analysis

Relying (on)

Computers

note inverse relationship with

Continuous

Recording (of)

Administrative

Procedures

Constant

Repetition (of)

Anecdotal

Perceptions

PLANNING A PROCESS IMPROVEMENT STUDY

• Why collect the data?• What statistical methods for analysis?• What data will be collected?• How much data do we need?• How will the data be measured?• How good is the measurement system?• When and where will data be collected?• Who will collect the data?• Remember:

GARBAGE IN – GARBAGE OUT

WHAT’S SIGNIFICANT?

Two-sample T for C1 vs C2

N Mean StDev SE Mean

A 5 13.652 0.487 0.22

B 5 14.369 0.646 0.29

Difference = mu (C1) - mu (C2)

Estimate for difference: -0.716615

95% CI for difference: (-1.551531, 0.118301)

T-Test of difference = 0 (vs not =): T-Value = -1.98 P-Value = 0.083 DF = 8

Both use Pooled StDev = 0.5725

Two-sample T for C3 vs C4

N Mean StDev SE Mean

A 200 13.510 0.501 0.035

A 200 13.667 0.492 0.035

Difference = mu (C3) - mu (C4)

Estimate for difference: -0.157292

95% CI for difference: (-0.254935, -0.059649)

T-Test of difference = 0 (vs not =): T-Value = -3.17 P-Value = 0.002 DF = 398

Both use Pooled StDev = 0.4967

Mean A = 13.7, Mean B = 14.4

Not significant?

Mean A = 13.5, Mean B = 13.7

Significant?

WHAT SHOULD I DO WITH OUTLIERS?

• Data point far away from the rest of the data

• Don’t remove outliers to make data “look good”

• Do you know why it is different?

• If you do, remove it. If you don’t, leave it in

• Could have a big impact on the analysis

• Re – run analysis without outlier, and compare results

“REGRESSION” WITH EXCEL

• Usually means drawing an X-Y plot, fitting a straight line and coming up with an R2 value.

• As long as R2 is high, everything’s hunky-dory.

WRONG!

“REGRESSION” WITH EXCEL

Defects vs Cure Time

y = 0.1913x - 5.5192

R2 = 0.5079

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Relationship is clearly not linear, and should not be presented as such

“REGRESSION” WITH EXCEL• Regression model checking – in Excel?

• Residual plots:

– Normally distributed

– Random pattern when plotted vs fitted values

OK Variance not homogeneous

Model incorrect

PITFALLS OF REGRESSION ANALYSIS

• Non-Linear Relationships

• Influential Points

• Extrapolating

• Lurking Variables

• Summary Data

• Assuming Causation

• THAT’S (WITH REASONABLE PROBABILITY) THE END FOLKS!

And remember,

• With statistics, you never have to say you’re certain!

• THANK YOU FOR YOUR ATTENTION• ARE THERE ANY QUESTIONS?

• GOOD LUCK!!

Documents

DATA CONFUSION