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Presenting Your Findings - A Practical Guide for Creating Tables


reviewed by Howard Wainer - 2001

coverTitle: Presenting Your Findings - A Practical Guide for Creating Tables
Author(s): Adelheid A. M. Nicol and Penny M. Pexman
Publisher: American Psychological Association, Washington, DC
ISBN: 1557985936, Pages: 157, Year: 1999
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Presenting Your Findings is a book whose goal is to guide the novice through the preparation of tables that report the results of statistical analyses. The authors have followed APA standards carefully and found examples of representative tables within the psychological literature and reproduced them within the book. The prospective users merely complete whatever analysis they are doing, look up that method of analysis in the book and reproduce the included table after substituting their own labels and numbers. Unfortunately, the preparation of good tabular displays is not this simple.

Each chapter of Presenting Your Findings provides a very brief description of a specific statistical method and then lays out what the authors feel is a suitable tabular display for that methodology. The table of contents of the book provides the reader with an insight into both what is strongest and what is weakest about this book. The chapters are ordered alphabetically. The book begins with analysis of covariance (chapter 2), gets to tables of means in chapter 13, and finishes with word tables in chapter 21. This makes any particular section easy to find, but prevents the kinds of natural connections that could have been made if the organization had been on the basis of content.1 Even cookbooks put all of the salad recipes together.

 I found it revealing to compare this book with another published 63 years earlier (Walker & Durost, 1936). Remarkably these two books, nominally on the same subject, have almost no topics in common. Indeed 28 of the 30 subheadings in Walker and Durost's slim volume were not mentioned in the index of Presenting Your Findings.  Among the missing topics were:

1. Ordering of columns

2. Ordering of rows

3. Inclusion of Totals

4. Spacing

5. Rounding

6. Dealing with Omissions (missing data)

 

These seem to be startling omissions from a book on tabular presentation. Moreover Presenting Your Findings contains no references to any other work; neither prior work on data display nor sources for the examples used.

Since Presenting Your Findings has been published by the American Psychological Association, it seems likely that it will have a large audience. Presenting such a shallow description of display methods seems a waste of a good audience. To get some sense of what's missing, and what might be gained from a less superficial viewpoint, let us consider how the inclusion and utilization of some fundamental precepts on tabular presentation might help us to construct more informative, alternative tables.  As is always the case when one is trying to determine the most sensible design for a display, it is crucial that we begin with an explicit statement of purpose.2 Data displays can have at least four purposes: (i) exploration, (ii) communication, (iii) storage, and (iv) decoration. Unfortunately, these goals often suggest contradictory directions in design. The sort of detail that may be critical for an accurate archive usually makes a display too Byzantine for easy comprehension.

Modern displays, bound for inclusion in scientific journals, should focus on communication; archival purposes are far better served with electronic storage than tabular. This said, let us consider a two panel data table from Presenting Your Findings that includes a summary of the data in the first panel and the analysis of covariance summary in the second panel.

Figure 1. These are the first two tables (Tables 2.1 and 2.2) from Nichol & Pexman (1999) that purport to show how to display results from a typical analysis of covariance (p. 11)

Table 2.1

Table X

Pre- and Postest Mean Scores and Standard Deviations as A Function of Instruction Condition and Tutor Help


 

Pretest

Posttest

Source

M

SD

M

SD


No instruction

 

 

 

 

Tutor help

56.12

12.11

76.90

11.22

No tutor help

54.33

11.93

73.96

12.34

Written instruction

 

 

 

 

Tutor help

58.34

12.05

83.66

12.36

No tutor help

55.09

12.17

74.01

11.78

Demonstration

 

 

 

 

Tutor help

64.05

11.89

86.14

10.80

No tutor help

65.12

12.34

76.44

11.24


Table 2.2 (This table, along with Table 2.1 for means and standard deviations, is the "Play It Safe" table for ANCOVA tables.)

Table X

Analysis of Covariance of Posttest Knowledge Scores as a Function of Instruction Condition and Tutor Help, with Pretest Knowledge Scores as Covariate


Source

df

SS

MS

F

w2


Covariate

1

39.31

9.31

4.22**

.05

Instruction condition (IC)

2

38.78

19.39

2.50*

.03

Tutor help (TH)

1

30.26

30.26

3.90**

.04

IC X TH

2

76.04

38.02

4.90**

.06

Error

54

419.04

7.76

 

 

Total

60

573.43

9.56

 

 


*p < .05 **p < .01.

What does the reader learn from looking at these two tables? It appears that both main effects are significant as is their interaction. Moreover, the covariate (performance on the pretest) is related significantly to the outcome. Would we learn more if the data were arrayed differently?

Let us consider a more reasoned display in Figure 2. The experimental design is fundamentally a two way design (tutoring or not vs. three instructional conditions). We note in passing that we are interested in comparing the mean performances to one another, not to their standard deviations, so it seems wasteful of space to place them next to one another. Moreover, since the standard deviations are all about the same (roughly between 11 and 12), it is probably enough to merely note that they are all about that and leave them be for a moment while we focus our attention on the summary of more direct importance, the cell means. When we do this, first for the posttest situation, then for the pretest, and finally for the difference between them3, one number sticks out.  We see that the smallest change (11) took place when no tutor was paired with a demonstration.

Working backward from this we see that this small change was due to the unusually large pretest score in this cell.  Thus it appears that it would be a mistake to spend much time interpreting the results from what might have been just a few anomalous observations. Instead we ought to look at the raw data that went into this cell and see if, because of an outlier or two a more robust analysis is called for. Note that the medians (more robust to the effects of outliers than means) suggest that, contrary to the significant Fs in Table 2.2, none of the experimental treatments seem to be having much effect.

This path of discovery was formed by following just three simple rules of table formation: (i) order the rows and columns of the data to suit the structure of the inferences we want to make while (ii) rounding the entries to a level that suits the precision of the experiment, and (iii) only including in the table those data values of immediate interest.

Figure 2. An alternative display of the cell means from the same experiment with the rows and columns permuted and the entries rounded. One unusual entry is emphasized in red along with the unusual change score it generated.

Posttest

Tutor

No Tutor


No Instruction

77

74

Written Instruction

84

74

Demonstration

86

76

Pretest

Tutor

No Tutor


No Instruction

56

54

Written Instruction

58

55

Demonstration

64

65

Posttest - Pretest

Tutor

No Tutor

Median


No Instruction

21

20

20

Written Instruction

26

19

22

Demonstration

22

11

17


Median

22

19

20

Statistical graphics came into widespread use following the publication of Playfair's influential Atlas in 1786. Graphics became so popular that within a century the tabular method was being publicly derided.

The graphical method has considerable superiority for the exposition of statistical facts over the tabular. A heavy bank of figures is grievously wearisome to the eye, and the popular mind is as incapable of drawing any useful lessons from it as of extracting sunbeams from cucumbers. (Farquhar & Farquhar, 1893, p. 55)

Such derision is not fully deserved. Tables hold an honorable place in the pantheon of display technologies, but to be deserving of this honor they must be used appropriately and formed thoughtfully.4 Although I am sympathetic to the goals of Presenting Your Findings, I am forced to conclude that we are less in need of a cookbook for tabular construction then we are for a guide to gastronomy.

References

Ehrenberg, A. S. C. (1977). Rudiments of numeracy. Journal of the Royal Statistical Society, Series A, 140, 277-297.

Farquhar, A. B. & Farquhar, H. (1891). Economic and Industrial Delusions.
New York: G. P. Putnam's Sons.

Holland, P. W., & Rubin, D. B. (1983). On Lord's paradox. In H. Wainer & S. Messick (Eds.), Principals of Modern Psychological Measurement (pp. 3-25).Hillsdale, NJ: Lawrence Erlbaum Associates.


Playfair, W. (1786). The Commercial and Political Atlas. London: Corry.

Wainer, H. (1991). Adjusting for differential base-rates: Lord's Paradox again. Psychological Bulletin, 109, 147-151.

Wainer, H. (1996). Depicting error. The American Statistician, 50, 101-111.

Wainer, H. (1997). Improving tabular displays: with NAEP tables as examples and inspirations. Journal of Educational and Behavioral Statistics, 22, 1-30.

Wainer, H. (1998). Rounding Tables. Chance, 11, 46-50.

Wainer, H. (2000). Visual Revelations: Graphical Tales of Fate and
Deception from Napoleon Bonaparte to Ross Perot
. (2nd edition) Hillsdale, N. J.: Lawrence Erlbaum Associates.


Walker, H. M. & Durost, W. N. (1936). Statistical Tables: Their Structure and Use. New York: Bureau of Publications, Teachers College, Columbia University.

End Notes

  1. If the book is ever translated into other languages the order of the chapters will change. I suspect that mathematicians will be delighted to have such a fine example of an ordering that is not invariant with respect to translation.
  2. Indeed, knowing the purpose is crucial in the design of anything.
  3. It is hard to know, in the absence of the associated research study, what were the goals of the investigators, but I suspect they were trying to measure the causal effects of both the instructional situation and the presence or absence of tutoring. If this was indeed the case, it is likely that they would want to look at the change scores, rather than use the pretest scores as a covariate (Holland & Rubin, 1983; Wainer, 1991), thus a sensible summary should focus on the changes from pre- to post.
  4. In addition to Walker & Durost (1936) mentioned previously, there are a substantial number of  more recent treatments on various aspects of effective tabular display (Ehrenberg, 1977; Wainer,  1996, 1997, 1998, 2000 chapter 10)


Cite This Article as: Teachers College Record Volume 103 Number 1, 2001, p. 93-98
https://www.tcrecord.org ID Number: 10582, Date Accessed: 5/21/2022 8:42:12 AM

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About the Author
  • Howard Wainer
    Educational Testing Service
    E-mail Author
    Howard Wainer is Principal Research Scientist in the Research Statistics Group at the Educational Testing Service. He does research in statistical graphics, psychometrics, and computerized testing. He has recently published Visual Revelations (2000), Computerized Adaptive Testing, 2nd edition (2000), and Drawing Inferences from Self-Selected Samples (2000). His new book (with David Thissen) Test Scoring will appear later this year.
 
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