7.5: Presenting Results

Learning Objectives

1. Recognize the importance of tables and graphs in presenting information.
2. Identify how to format tables, graphs, and their titles in APA Style.

Tables are where you put rows or columns of numbers, like a frequency table or your calculation results. A figure is a chart/graph or other picture. Often, these are used to present statistical information, but they could also be used to present lists (like for words that participants were asked to memorize) or pictures that were presented to participants.

Presenting Descriptive Statistics in Writing

APA Style includes several rules for presenting numerical results in the text (see 4.31–4.34 in the APA Publication Manual) . These include using words only for numbers less than 10 that do not represent precise statistical results and using numerals for numbers 10 and higher. However, statistical results are always presented in the form of numerals rather than words and are usually rounded to two decimal places (e.g., “2.00” rather than “two” or “2”). When you have a small number of results to report, it is often most efficient to write them out.

Examples of Statistical Results in the Narrative

• The mean age of the participants was 22.43 years with a standard deviation of 2.34.
• Among the participants with low self-esteem, those in a negative mood expressed stronger intentions to have unprotected sex (M = 4.05, SD = 2.32) than those in a positive mood (M = 2.15, SD = 2.27).
• The treatment group had a mean of 23.40 (SD = 9.33), while the control group had a mean of 20.87 (SD = 8.45).
• The test-retest correlation was .96.
• There was a moderate negative correlation between the alphabetical position of respondents’ last names and their response time (r = −.27).

Notice that when presented in the narrative, the terms mean and standard deviation are written out, but when presented parenthetically, the symbols M and SD are used instead. Notice also that it is especially important to use parallel construction to express similar or comparable results in similar ways. The third example is much better than the following nonparallel alternative: The treatment group had a mean of 23.40 (SD = 9.33), while 20.87 was the mean of the control group, which had a standard deviation of 8.45.

An additional consideration is needed when writing about comparisons between social groups. As noted in Russel et al. (2022), researchers often write about differences between social identity groups as if the difference is caused by the group membership itself. As an example from Russell et al. (2022), educational research on the achievement differences between White and Black elementary students seem to imply that it's the fact of being Black that affects achievement while ignoring policies and institutional practices that contribute to educational outcomes. For example, public school funding is based based on property taxes, but red-lining practices through the early 1900's have excluded from upper and middle class neighbors, resulting in many African American families being forced to live in poorer neighborhoods that do not have the tax base to fully support their community schools. Another example is the use of testing to track students into remedial or advanced coursework, even while we know that academic tests are culturally biased (Russell et al., 2022). To counter this "deficit narrative," Russell et al. (2022) urged researchers to frame any differences between social identity groups to be caused by institutional influences (racism, biased policies), rather than imply that the difference is caused by any inadequacies of groups disadvantaged by institutional policies, or imply the superiority of groups already advantaged by the past and current systems. In terms fo race, "one should consider race a proxy for the impacts of racism," (Russell et al., 2022, 5).

Presenting Descriptive Statistics in Figures

When you have a large number of results to report, you can often do it more clearly and efficiently with a graphical depiction of the data, such as frequency line graphs, bar graphs, or scatterplots. In an APA style research report, these graphs are presented as figures. Figures also include pictures. When you prepare figures for an APA Style research report, there are some general guidelines that you should keep in mind. First, the figure should always add important information rather than repeat information that already appears in the text or in a table (if a figure presents information more clearly or efficiently, then you should keep the figure and eliminate the text or table.) Second, figures should be as simple as possible. For example, the Publication Manual discourages the use of color in manuscripts unless it is absolutely necessary (although color can still be an effective element in posters, slide show presentations, or textbooks.) Third, figures should be interpretable on their own. A reader should be able to understand the basic result based only on the figure and its caption and should not have to refer to the text for an explanation.

There are also several more technical guidelines for presentation of figures that include the following (see the APA Publication Manual section 5.20 through 5.30):

• Layout of graphs
  • In general, scatterplots, bar graphs, and line graphs should be slightly wider than they are tall.
  • The independent variable should be plotted on the x-axis and the dependent variable on the y-axis.
  • Values should increase from left to right on the x-axis and from bottom to top on the y-axis.
  • The x-axis and y-axis should begin with the value zero.
• Axis Labels and Legends
  • Axis labels should be clear and concise and include the units of measurement if they do not appear in the caption.
  • Axis labels should be parallel to the axis.
  • Legends should appear within the figure.
  • Text should be in the same simple font throughout and no smaller than 8 point and no larger than 14 point.
• Captions
  • Captions are titled with the word “Figure”, followed by the figure number in the order in which it appears in the text, and terminated with a period. This title is italicized.
  • After the title is a brief description of the figure terminated with a period (e.g., “Reaction times of the control versus experimental group.”)
  • Following the description, include any information needed to interpret the figure, such as any abbreviations, units of measurement (if not in the axis label), units of error bars, etc.

“Convincing” retrieved from http://imgs.xkcd.com/comics/convincing.png (CC-BY-NC 2.5)

Expressing Descriptive Statistics in Tables

Like graphs, tables can be used to present large amounts of information clearly and efficiently. The same general principles apply to tables as apply to graphs. They should add important information to the presentation of your results, be as simple as possible, and be interpretable on their own. Again, we focus here on tables for an APA Style manuscript.

The most common use of tables is to present several means and standard deviations—usually for complex research designs with multiple independent and dependent variables. Table \(\PageIndex{1}\), for example, shows the results of a hypothetical study similar to the one by MacDonald and Martineau (2002). MacDonald and Martineau (2002) categorized participants as having low or high self-esteem, put them into a negative or positive mood, and measured their intentions to have unprotected sex. MacDonald and Martineau (2002) also measured participants’ attitudes toward unprotected sex. Notice that the table includes horizontal lines spanning the entire table at the top and bottom, and just beneath the column headings. Furthermore, every column has a heading—including the leftmost column—and there are additional headings that span two or more columns that help to organize the information and present it more efficiently. Finally, notice that APA Style tables are numbered consecutively starting at 1 and given a brief but clear and descriptive title.

Table \(\PageIndex{1}\): Sample APA Style Table Presenting Means and Standard Deviations. Means and Standard Deviations of Intentions to Have Unprotected Sex and Attitudes Toward Unprotected Sex as a Function of Both Mood and Self-Esteem.

Another common use of tables is to present correlations—usually measured by Pearson’s r—among several variables. This kind of table is called a correlation matrix. Table \(\PageIndex{2}\) is a correlation matrix based on a study by McCabe et al. (2010). McCabe et al. (2010) were interested in the relationships between working memory and several other variables. We can see from the table that the correlation between working memory and executive function, for example, was an extremely strong .96, that the correlation between working memory and vocabulary was a medium 0.27, and that all the measures except vocabulary tend to decline with age. Notice here that only half the table is filled in because the other half would have identical values. For example, the Pearson’s r value in the upper right corner (working memory and age) would be the same as the one in the lower left corner (age and working memory). The correlation of a variable with itself is always 1.00, so these values are replaced by dashes to make the table easier to read.

Table \(\PageIndex{2}\): Sample APA-Style Table (Correlation Matrix) Based on Research by McCabe and Colleagues. Correlations Between Five Cognitive Variables and Age.

As with graphs, precise statistical results that appear in a table do not need to be repeated in the text. Instead, the writer can note major trends and alert the reader to details (e.g., specific correlations) that are of particular interest.

Formatting Tables and Figures

That introduction gave you some indication of the formatting of tables and figures. And as previously mentioned, the 7^th Edition allows you to put the tables and figures in the main body of the paper, but you can also put them on their own pages at the end of your paper. Here are some more specific information on now to format tables and figures:

• Tables and Figures can be single-spaced.
• Tables and Figures must be numbered, in bold (Example: Figure 1 or Table 1). The table or figure number should be on a line above the title.
• Tables and Figures must have a title (in italics) on the line below the number.
• In a Table, the column titles should be underlined.
• There should be a line across the whole bottom edge of each table.

If you are putting a table or figure in an appendix, then each set of tables or figures should be started on a new page [Insert a Page Break, don’t hit enter a bunch of times].

Example Table Formatting

Table 3

Measures of Central Tendency and Standard Deviation

Table \(\PageIndex{3}\)- Example of APA Style Table Formatting

Groups	N	Mean	Median	Mode	SD
Group 1	34	9	2	6.50	2.51
Group 2	550	246.99	45.5	22.22	5.54
Note: “SD” is “standard deviation.

Table \(\PageIndex{3}\): Example of number, title, and table formatted in APA Style.. (CC-BY-NC-SA; Michelle Oja)

Example Chart Formatting

Figure 1

Frequency of Final Exam Scores

Figure \(\PageIndex{1}\): Example of number, title, and chart formatted in APA Style. (CC-BY-NC-SA; created by Michelle Oja with data from OpenIntro.org)

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References

MacDonald, T. K., & Martineau, A. M. (2002). Self-esteem, mood, and intentions to use condoms: When does low self-esteem lead to risky health behaviors? Journal of Experimental Social Psychology, 38, 299–306.

McCabe, D. P., Roediger, H. L., McDaniel, M. A., Balota, D. A., & Hambrick, D. Z. (2010). The relationship between working memory capacity and executive functioning. Neuropsychology, 24(2), 222–243. doi:10.1037/a0017619

Russell, M., Oddleifson, C., Russell Kish, M., & Kaplan, L. (2022). Countering deficit narratives in quantitative educational research. Practical Assessment, Research, and Evaluation, 27(14), 1-18. DOI: https://doi.org/10.7275/k44e-sp84 Available at: https://openpublishing.library.umass...ticle/id/1328/