INTRODUCTION TO CLINICAL RESEARCH How To Make A Bad Plot Karen Bandeen-Roche, Ph.D. July 13, 2010

How to display data badly Karl W Broman Department of Biostatistics and Medical Informatics University of Wisconsin

Using Microsoft Excel to obscure your data and annoy your readers Karl W Broman Department of Biostatistics

4 Inspiration This lecture was inspired by H Wainer (1984) How to display data badly. American Statistician 38(2): Dr. Wainer was the first to elucidate the principles of the bad display of data. The now widespread use of Microsoft Excel has resulted in remarkable advances in the field.

5 General principles The aim of good data graphics: Display data accurately and clearly. Some rules for displaying data badly: –Display as little information as possible. –Obscure what you do show (with chart junk). –Use pseudo-3d and color gratuitously. –Label badly –Use a poorly chosen scale. –Ignore sig figs.

6 Displaying data well Be accurate and clear. Let the data speak. –Show as much information as possible, taking care not to obscure the message. Science not sales. –Avoid unnecessary frills — esp. gratuitous 3d. In tables, every digit should be meaningful. Don’t drop ending 0’s.

7 Displaying data well Show “typical”, “average” values Convey extent of “spread”, “variability” in values Compare groups clearly Label explicitly

8 Einarsson K, et al (NEJM 313:277, 1985; reprinted in D-S & T, p st ed) Supersaturation of bile with cholesterol necessary for cholesterol gall stones Female gender and increasing age are risk factors for gall stones Is either gender or age associated with percentage cholesterol saturation of bile? Cross-sectional data on 60 healthy Swedish subjects (31 men, 29 women) who were not obese Supersaturation of Bile Data Set

9 Bile Data Set

10 “Average” -- typical or representative value; where the distribution is “centered” Different measures of the center -- usually, all the same for symmetric distributions (ones that look on right or left of center Median -- value such that half the observations are less than it and half are greater than it (50th percentile) MalesFemales 86% 84% Mode -- value where the distribution achieves maximum -- most likely value MalesFemales 80-90% (85%)80-90 (85%) Mean -- sum of values divided by the number of values = MalesFemales 84.5%88.5% Measures of the “Average”

11 Spread -- variability among the observations Different measures of spread, like averages, represent distinct aspects of distribution Interquartile range –75th-25th percentiles -- range of values that contains middle 50% of data MenWomen = 40.0% =40.5% Measures of Spread

12 Variance = (standard deviation) 2 = mean squared error deviation from the mean variance = standard deviation = square root of variance Men Women (24.0%) 2 =574(% 2 )(26.6%) 2 =761(% 2 ) to n from i=1 SUM Measures of Spread (cont’d)

13 Displays for continuous data –Histograms / Stem and leaf plots –Boxplots Displays for categorical data: tables Displays for relationships of two variables (on same “people”) to each other –Continuous data: scatterplots –Categorical data: cross-tabulations Some common data displays

14 4* 07 5* * 567 7* * * 0 10* 66 11* * 3 13* 7 Stem and Leaf Plot: % Saturation, Men

15 Boxplots of Bile Data

16 Scatterplot: SBP vs DBP SBP DBP

Some really bad plots

18 Example 1

19 Example 2 Distribution of genotypes AA21% AB48% BB22% missing 9%

20 Example 3

21 Example 4

22 Example 5

23 Example 6

24 Example 7

25 Example 8

26 Main points once again Be accurate and clear. Let the data speak. –Show as much data as possible, taking care not to obscure the message. Science not sales. –Avoid unnecessary frills –Go for the cleanest display that conveys the necessary info In tables, every digit should be meaningful. Don’t drop ending 0’s.

27 Displaying data well Show “typical”, “average” values Convey extent of “spread”, “variability” in values Compare groups clearly Label explicitly

28 Further reading ER Tufte (1983) The visual display of quantitative information. Graphics Press. ER Tufte (1990) Envisioning information. Graphics Press. ER Tufte (1997) Visual explanations. Graphics Press. WS Cleveland (1993) Visualizing data. Hobart Press. WS Cleveland (1994) The elements of graphing data. CRC Press.