Data support factual premises.

In the Results section, data support the factual premises necessary to test Measurable Hypotheses. Therefore, data do not need to be isolated and presented without context. Data can be objectively collected and and presented, but also placed in context by contributing to strong reasoned arguments that help readers understand conclusions.

Clearly presenting data involves presenting data as simply as possible. Three principles can help present data effectively and simply:

1) Present only data necessary to test Measurable Hypotheses.

2) Present data as completely and objectively as possible.

3) Help readers put data into perspective.

1) Present only data necessary to test Measurable Hypotheses.

Collecting and analyzing data can be grueling, and involve years or decades of work. Consequently, when preparing a paper to disseminate their findings, researchers often (understandably) have a desire to present all of the data they labored so hard to collect. However, the purpose of scientific papers is to advance understanding, not simply to archive data (online databases like Genbank and supplemental data available with many journals provide opportunities to archive raw data). Therefore, the Results section needs to present ONLY data that are used as premises for arguments to test Measurable Hypotheses.

Even with modestly complex datasets, there are many ways to present data, and many comparisons that could potentially be made. Presenting only data necessary to test Measurable Hypotheses is a reasonable standard for deciding which data to include in the Results. Therefore, data that do not support premises for reasoned arguments need not be included in a paper (or can be removed if included).

One way to determine if data support premises is to ensure that all data are referred to by premises in the Results. Figures and tables should contain only the data necessary to support the premises that reference the figure or table.

2) Present data as completely and objectively as possible.

A scientific paper must present ALL data relevant to testing measurable hypotheses. Datasets sometimes contain data from individual participants, or individual experimental trials, that are outliers that do not seem representative of the remainder of the data. If data are outliers for clear reasons that affect the validity of experimental measurements (e.g. malfunctioning equipment), then there is cause to exclude outliers from a dataset. However, when excluding outliers, it is important to verify the validity of all other measurements at the same time to avoid confirmation bias. Without definitive and justified cause, data cannot be removed from quantitative datasets.

Data are typically presented in one of three ways: the body text of the paper, in tables, and in figures.

The primary purpose of the body text is to put data into the context of arguments to test the Measurable Hypotheses. The amount of data that can be included in body text is limited. Moreover, extensive data can be difficult to read and thus detract from the reasoning of the Results. Therefore, scientific papers typically use tables and figures to report the bulk of the data.

Tables are typically used for data where reporting precise values is important. Data in tables must be clearly-presented and labeled. All labels must include the units used to express numbers. Numbers in tables should be presented to an appropriate number of significant figures based on the precision of underlying measurements. Only data used to support the premises of reasoned arguments should be included in a table. For example, the following table reports numeric data from several different variables, along with the results of statistical tests:

Figures can help readers understand the data. Unlike tables, the primary purpose of figures is often not to report data (although figures can be economical ways of reporting large data sets such as time series or continuous relationships between variables), but to provide a convincing visual representation of data to help readers understand an argument. Therefore, figures are strongest when they clearly convey at least one "main message" that is self-evident in the figure.

For example, even without providing context, some things are evident from the figure below.

Figure 1. Mean braking force for different mass (M) and rotational inertia (I) conditions. Values represent averages across individuals for each condition. Error bars represent one standard deviation.

Clearly, the two dashed lines (red squares and blue triangles) are more similar to each other than they are to the solid black line. Moreover, the dashed lines remain relatively constant over the five conditions on the abscissa (x-axis), whereas the black line clearly decreases. Of course, comparing the three variables with each other or among conditions requires statistics. However, the figure suggests that there are unlikely to be significant or substantial differences between the three variables in the M 0%, I 1 condition to the left, but the potential for substantial differences among variables for the M 17%, I 4 condition at the right. Therefore, there is at least one clear "main message" conveyed by the figure.

Just as with tables, axes and other elements must be clearly labeled and include units. Data that are presented without labels and corresponding units are meaninglessand accomplish nothing more than to confuse readers. Therefore, it is essential to ensure that all figures are properly labeled with appropriate units.

Figure titles can be descriptive.

Tables and figures include titles that describe the table or figures. Titles can be either above or below the table or figure. Figure titles are the ONE place in a scientific paper where text can be purely descriptive, where text is not part of an argument or other framework. Table and figure titles typically start with a one-sentence summary description of the figure, then provide concise descriptions of the elements of the table or figure.

Use repetition to help readers understand figures.

Use the principle of repetition in figures. Within a figure, when possible use the SAME scale for each axis when plotting data of the same units against one another. Use a systematic labeling convention that is consistent with the text of the paper. When creating multiple figures, make all figures as consistent with each other as possible. Variables, symbols, colors, order of presentation should be as consistent as possible across figures.

Color information can be unreliable.

Printers may not print color, or computer screens may not render colors accurately. More importantly, not all people are capable of distinguishing among all colors. Therefore, although using color figures is acceptable, color should not be the ONLY way to differentiate variables.

Seek additional insight into graphical display of information.

We have barely scratched the surface. Creating effective figures and graphics is a science in and of itself. How readers interpret figures is determined by the human visual system, which can be biased and misled in many ways (Franconeri, 2021). Creating figures and graphical frameworks that convey specific information and clearly support conclusions without confusing or misleading readers is a challenge (Tufte, 2001). Creating strong figures involves creativity, inspiration, and collaboration (feedback) from others, but is a worthwhile investment of time and thought.

3) Help readers put data into perspective.

If tables and figures present the majority of data in a paper, is there any reason to include data in the text?

Yes. Including data in the text can be helpful for several reasons. For example, individual measurements that are not repeated or numerous enough to warrant a table are appropriate for the text. For example, in the "Study participants" section of the Methods, participant characteristics like age, body mass, gender, etc. are commonly reported in the text.

More importantly, presenting data in the body text of a paper can help readers put the data into context, or perspective. Putting data into perspective involves helping readers to understand importance of individual elements of data. Examples of perspective include expressing the magnitude of data relative to some baseline, or comparing different measurements to each other. Therefore, the purpose of data presented in body text is not simply to report numbers, but to help readers gain a conceptual understanding of the contribution of the values to the conclusions of the Results.

Percentages are a useful way to put data into perspective.

One effective way to put data into perspective is to express data as percentages, or relative changes. For example, writing "leg ground-reaction force during acceleration was 50 N more than during constant-speed running" is a reasonably specific statement (N refers to "Newtons", or units of force). However, how much is 50 N? A little? A lot? Enough to potentially cause injury? Even experienced scientists may have difficulty understanding how important a change of 50 N represents.

However, expressing the statement as "leg ground-reaction force was 25% higher during acceleration than during constant-speed running" expresses the change in force as a percentage that readers can clearly understand (25% is a fairly substantial change). Therefore, percentages are an effective way to report data that help readers conceptually understand the Results.

Although providing perspective can help readers understand data, the scope of the Results section is limited to the data collected in the study and the Measurable Hypotheses. Putting data into perspective does not include comparisons to other research or any information outside the data collected for the study (providing broader context is an important objective of the Discussion). Therefore, the Results section typically does not contain references to other studies.

The purpose of text in the Results section is not solely to report data. Most sentences in the Results section of a scientific paper are premises that support conclusions about Measurable Hypotheses. The purpose of data are to support premises in the text. Therefore, representations of data that help place the data into perspective (e.g. percentages) can be included in text of the premises. However, place references to tables, figures, and statistical tests parenthetically at the END of sentences.

For example, a paragraph from the Results section could read:

"Sinusoids were sufficient to reconstruct forces in the initial movement direction (imd) over stance. Sinusoidal reconstructions of ground-reaction forces (GRF) accounted for 64 ± 11 % of the variance in GRF over the entire step (Table 1). However, sinusoidal reconstructions did not capture transients associated with leg impact in the first 50 ms of stance (Fig. 2 B). After the first 50 ms of stance, reconstructions accounted for 78 ± 6 % of GRF (Table 1). The variance accounted for (VAF) of sinusoidal reconstructions after the first 50 ms was significantly greater than for the entire stance period (P<0.001). Therefore, although sinusoids did not model transient forces at leg impact, sinusoids could accurately reconstruct leg forces during 85% of stance."

The purpose of text in the Results section is to explain how measured data support or reject Measurable Hypotheses. Therefore, the majority of data can be presented descriptively in tables and figures. Text in the Results can include data that help readers put findings into perspective. Otherwise, references to data or calculations should be placed parenthetically at the END of sentences.