Basics and Beyond: Displaying Your Data

Mario Davidson, PhDVanderbilt University School of Medicine

Department of BiostatisticsInstructor

Objectives

1.Understand the types of data and levels of measurement

2.Understand how a Table 1 typically looks

3.Be able to interpret all of the basic graphs.

4.Know the type of displays that may be used dependent upon the type of data and level of measurement

5.Be introduced to less familiar displays of the data

Types of Data (Obj1)●Qualitative Data

● Consist of attributes, labels, or non-numerical entries.● If you can’t perform mathematical operations or order data,

it’s qualitative.● Ex: Colors in a box of crayons; names; county

●Quantitative Data● Consist of numerical measurements or counts.

● Ordering is a dead give away● Ex: BMI; age; numerical grade

Levels of Measurement (Obj1)

●Nominal● Qualitative● Categorized using names, qualities, or labels● Ex: Top 5 movies, jersey numbers, type of drug

●Ordinal● Quantitative or Qualitative● Can order● Differences between data are not meaningful.● Ex: Letter grade, Likert scale such as very dissatisfied to very satisfied

Levels of Measurement (Obj1)

●Interval Level of Measurement● Quantitative● Can order ● Can calculate meaningful differences● No Value that means “nothing/none.” A zero entry merely

represents a position on a scale (i.e. no inherent zero).● Ex: Time of day, temperature

●Ratio Level of Measurement● Quantitative● Can order● Can calculate meaningful differences● There’s a value that means “nothing/none.”● Ex: Age, weight, test score

Popular Displays

Description of Table 1 (Obj2) Typically summarizes baseline characteristics of the data. Compares statistics between groups May provide means, medians, confidence intervals,

percentiles, percentages, p-values, standard deviations, etc.

Summaries of all types of data (e.g. continuous, categorical, nominal, ordinal, interval, ratio) may be used.

Likert scale: Scale indicating degree of agreement (e.g. Rate the following statement: I have a had a difficult time focusing on my studies this semester: SD D N A SA

Example of a Table 1 (Obj2)

Test Your Knowledge

Interpret the following graphs.

Test Your Knowledge

Interpret the following graphs.

Cherry or Apple Pies sold the most in January. “Other” pies sold the least

Nearly 15 subjects chose Saturday as their favorite day. Sunday was the least chosen.

Pie Charts (Obj3)

Features (Obj4)– Nominal or Ordinal– Compares Levels of One

CharacteristicAdvantages:

Easily Interpreted • Larger Area; Greater

Proportion Easy to Create

Disadvantages Difficult to Judge Areas Wastes Ink

Bar Plots (Obj3)

Features (Obj4)– Nominal and

Ordinal – Compares

Advantages Same as Pie Chart

Disadvantages Similar to Pie Chart No such thing as an

Analyte 2.5 Ordering can Change

Perception

Test Your Knowledge

Interpret the following graphs

Test Your Knowledge

The most frequent BMI seems to be approximately around 24-26.

There were 8 subject weighing approximately 0 grams. There was only one weighing 10 grams.

Histograms (Obj3)

Features

– Shows Distribution

– Continuous

– One Characteristic (Obj4)

Advantages Easy to Interpret Easy to Produce

Disadvantages Size of Bins can Change

Perception Cannot Read Exact Values

Dot Plot (Obj3) Features (Obj4)

–One Characteristic

–Ordinal Advantages

Good for Small and Moderate Data

Easily Interpreted Disadvantages

May not be Best Option with Large Data

Not Produced in all Packages

Stem and Leaf Plot (Obj3)

Features (Obj4)

– One Characteristic

– Ordinal Advantages

Useful with Small Data and May be Used with Large Data

Can be produce by hand Easily Interpreted Useful with Numeric

Disadvantages May be Difficult to Measure

Center Not Appealing

The most frequent USMLE1 scores in our data were in the 220's, 230's, and 260's. The highest and lowest scores were 190 and 278 respectively.

Test Your Knowledge

Why is this graph difficult to interpret?

What is the trend?

What is the trend?

An outlier is data that is a numerical distance from the rest. Can you find one?

Test Your Knowledge

There is no y-label.

R is a statistical software.

From Jan-Dec, there is an upward trend.

Seems to be a slight positive trend: as age increases so does POMS.

The arrows suggest 2 possibly outliers.

Line Graph (Obj3)

Features (Obj4)– One Characteristic

– Used with Ordinal and Continuous

– Displays Associations, Trends, and Range

Advantages Produced in Most

Packages

Line Graph with Rugplot

Scatterplot (Obj3)

Features (Obj4)

– Continuous and Ordinal

– Shows Associations

– Shows Trend

Advantages Shows all of Data Produced in Most Packages –

not the Line Exact values shown Easily Interpreted

Disadvantage May not be Best Way for Large

Data

Less Familiar Graphs

Boxplot (Obj3 and Obj5)

Features Continuous by Nominal or

Ordinal (Obj4) May Compare Groups

Advantages Good Summary: Min, 1Q,

2Q(median), 3Q, Max Disadvantages

Does not Display All the Data

Not as Appealing Cannot be Created in All

Packages May not be as Recognized

by Some

Boxplot

The median tooth length for orange juice at 1dose of Vitamin C was roughly 25 units.

The first quartile length for 1 dose of ascorbic acid was approx. 15.

As Vitamin C doses increase tooth length increases. Overall, it appears that those using orange juice had greater length given the same dose and excluding possibly a Vitamin C dose of two.

There was an outlier for the ascorbic acid at dose 1.

Boxplot Overlayed with Stripchart (Obj5)

Features– Same as

Boxplot Advantages

Same as Boxplot Can See All of the

Data Disadvantage

Many Programs Cannot Create

Dot Chart (Obj5) Features

Nominal, Ordinal Characteristics with a Continuous Outcome (Obj4)

–Can Compare Levels and Groups

Advantages Easily Interpreted Size of Data Irrelevant

Disadvantage Not as Recognized as

Bar Graphs and Pie Charts

Kaplan Meier Curve (Obj5)

Demonstrates the probability of survival

The plot suggests that males have a more favorable rate of survival over the years.

Can be created in most programs

Number at Risk

Probably Even Less Familiar Graphs

Spaghetti Plot (Obj5)

●Alzheimer's Disease

●Verbal IQ – Words that could not be sounded out (e.g. Depot)

Spaghetti Plot

Features (Obj4)

– Continuous, Longitudinal

– Two Characteristics

– Shows Trend

Advantages Shows all of the Data

Disadvantages Not Available in All

Packages May be Difficult to

Interpret

Age(yrs)

Earnings(thsd of dollars)

The overall trend suggest that as age increases so do earnings.

Dendogram: Cluster (Obj5)

Useful for Determining Clustering

May Help to Remove Variables (Data Reduction)

PGY clustered Clinical Year

Scatter Plot with Marginal Histograms (Obj5)

Continuous Virtually appealing Shows trends,

associations, and the distributions of the data

Cannot be created in many programs

Large Data Sets

Sunflower Plot (Obj5)

Large data sets The more ink used,

the more dense the data

Ordinal More fresh embryos

to the uterine were transferred on day 3.

Heat Map (Obj5) ●Encephalitis●Red

● Proportion of Presence

●Green● Proportion of

Absence●White

● Missing●Light/Dark

● Intensity of Presence of Attribute

Heat Map Similar to the

Hexagon Plot Lightness or

Darkness Indicates Intensity

May not be Created in Some Programs

Nomogram (Obj5)

May Provide Risk, Probability, etc.

Useful in Providing Predictive Scores

Sum the “Points” for each category, find the “Total Points,” then look at the corresponding “Risk of Death.”

40 yo, Male, 200 Cholesterol, and 170 BP has Approximately a 48% Risk of Death

Multidimensional Plot (Obj5) http://data.vanderbilt.edu/rapache/bbplot/

Multidimensional Plot (Obj5)

Conclusion

Always try to think of the best way to display your story (data).

Consider your target audience. When publishing, color may cost.

References

Hamid, et al. BMC Infectious Diseases 2010, 10:364. http://www.biomedcentral.com/1471-2334/10/364

Grober, E, Hall, CB, Lipton, RB, Zonderman, AB, Resnick, SM, and Kawas, C (2009). Memory impairment, executive dysfunction, and intellectual decline in preclinical Alzheimer's disease. Journal of the International Neuropsychological Society, 14(2), 266-278.

http://data.vanderbilt.edu/rapache/bbplot/