Organizing data in tables and charts: Criteria for effective presentation Jane E. Miller, Ph.D. Rutgers University

About the author  Author: The Chicago Guide to Writing about Multivariate Analysis (Chicago, 2005) and The Chicago Guide to Writing about Numbers (Chicago, 2004), and other articles about statistical literacy and quantitative communication.The Chicago Guide to Writing about Multivariate Analysis The Chicago Guide to Writing about Numbersarticles about statistical literacy and quantitative communication  Professor, Rutgers University Institute for Health, Health Care Policy and Aging Research. Institute for Health, Health Care Policy and Aging Research. Edward J. Bloustein School of Planning and Public Policy. Edward J. Bloustein School of Planning and Public Policy.

Learning objectives  To learn the different types of variables and how they affect choices for organizing data.  To become aware of different principles for organizing variables in tables or charts.  To learn the strengths and weaknesses of tables, charts, and prose for organizing and conveying numeric information.

Performance objectives  To be able to choose among different criteria for organizing data for a particular task.  To be able to identify whether to use a table or chart to present data for a specific objective.  To understand how to write a prose description to coordinate with a table or chart.

Why does order of variables matter?  The arrangement of items in a table or chart should coordinate with order they are mentioned in the prose description. Avoid zigzagging back and forth across a chart or among rows and columns of a table.  Usually describe a pattern based on observed numeric values, e.g., most to least common.  Often a hypothesis includes some theoretical basis of how items relate to one another.

Ordinal and continuous variables  Values of ordinal, interval, and ratio variables have an inherent numeric order. E.g., age groups, dates, blood pressure.  Numeric or chronological order of values is the principle for organizing those values in a table or chart.

Nominal variables  Values of nominal variables have no inherent numeric order. E.g., categories of race, gender, or region.  Need an organizing principle to determine sequence of items.  Same issue if you have >1 variable to present. Several different causes of death. Prevalence of >1 symptoms, attitudes, etc.

+ and - of different tools

Complementary use of prose, tables & charts  Use tables and charts to present full set of numeric values.  Use prose to describe the pattern or address the hypothesis.  Use same ordering principle in table or chart and its accompanying prose. Improves clarity of narrative line.

Prose description of a pattern  Objectives: Describe size and shape of the pattern. Explain whether it matches hypothesis.  Specify direction and magnitude of association. Direction: “Which is higher? Magnitude: “How much higher?”

Direction for different types of variables  Direction for ordinal, interval or ratio variable: Is the relationship positive, negative, or level? E.g., as income rises, do death rates increase, decrease or remain constant?  For nominal variables: Which category has the highest value? E.g., which gender has the higher death rate?

Principles for organizing data  Alphabetical order  Order of items on original data collection instrument  Empirical order  Theoretical groupings  Arbitrary order – NEVER a good idea! Think about how the data will be used, and choose one of the above principles!

For tables and charts accompanied by prose Pattern description or hypothesis testing

Example: Attitudes about legal abortion “Please tell me whether or not you think it should be possible for a pregnant woman to obtain a legal abortion” % of respondents who agree If the woman wants it for any reason 43.7 If there is a strong chance of defect in the baby 79.8 If the woman's own health is seriously endangered by the pregnancy 88.2 If she is not married and does not want to marry the man 42.5 If she becomes pregnant as a result of rape 80.8 If she is married and does not want any more children 44.4 From the 2000 U.S. General Social Survey

Order of items from questionnaire

Alphabetical order

Empirical order (descending)

Theoretical grouping

Combining theoretical & empirical criteria

Pattern with a third variable * difference between men and women is statistically significant at p<.05

Pattern with a third variable * difference between men and women is statistically significant at p<.05

Identifying theoretical criteria  Consult the published literature on your topic to learn about theoretical criteria for organizing your variables.  In new research areas, empirical sorting may yield clusters with similar response patterns that can then be explored for conceptual overlap.

For self-guided data lookup  Why is it important? When is it used? Researchers look up data for own research questions, then organize the data using empirical or theoretical criteria.  How to organize data for such tasks? Alphabetical order Order of items from data collection instrument Standard ordering used in periodic reports

Alphabetical order  Widely familiar principle, e.g., used in  Phone book  Daily stock market report  Learned at an early age  Facilitates self-guided lookup

Ordering for a public data source  Order of items on original data collection instrument Users can refer to codebook Easy to find the variables they need  Ordering used in periodic reports  Standardized from year to year for a given topic

Summary  There is no one principle for organizing numeric data that fits all possible tasks.  Determine your main objective Hypothesis testing or pattern description Data reporting for others’ use  Choose the organizing principle accordingly.