3.5: Reporting Results
- Page ID
- 50003
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Results in the behavioral and social sciences are often reported in sentences or, for more complex analyses, paragraphs. When statisticians report their results, they must take care to do so accurately and clearly. To be accurate means that what is reported is correct and that there have been no miscalculations. This requires that the statistician takes care to learn the proper procedures and formulas and that they carry out the steps with precision. It is also a good habit to double-check one’s work again before reporting the results, the same way it is a good idea to proofread a paper before submitting it to one’s professor. Clarity refers to reporting things in a way which is comprehensible. In practice, this means that results sentences should be specific rather than vague and that they be written simply and directly whenever possible. As noted earlier in this chapter, APA format provides some useful guidelines which are meant to enhance clarity such as the rule that decimals be rounded and shown to the hundredths place when reported as results. When reporting results in sentences, do each of the following:
- Ensure results are accurate and shown to the proper decimal place.
- Replace any vague words or language with specific terms and phrases.
- Edit for simplicity where possible such as by removing unnecessary words.
Understanding statistics, research, and sciences can sometimes be challenging so it is beneficial to audiences when writing is direct.
Let’s take a look at an example of a results sentence that would benefit from revision.
When the average was computed for the data using the mean formula, the result for the variable age was 29.0000000.
Reading this results sentence is painful, but it doesn’t have to be this way. Let’s edit following the three recommended steps from above. First, let’s round following APA format:
When the average was computed for the data using the mean formula, the result for the variable age was 29.00.
It’s starting to look better but could still be improved. Let’s identify any vague language. The word “average” is not specific so it should be replaced. The measure of central tendency which was used was the mean so let’s make that clear:
When the mean was computed for the data using the mean formula, the result for the variable age was 29.00.
We are getting there but this sentence is cumbersome. We want to focus on the main points so let’s identify what those are. We want to indicate what the variable was. It was age. We want to indicate which measure of central tendency was used. It was the mean. Finally, we want to state what the statistic was. It was 29.00. The rest of the information in the sentences is unnecessary. We don’t need to state that a computation occurred because our audience will know this simply because we are reporting the result of that computation. We also don’t need to say we are giving a result; instead we can simply give the result. Further, we do not need to state that the data were for a variable because means are only computed for variables. Taken together, this means we can remove several parts of the sentence to leave just the things we need like so:
When the mean was computed for the data using the mean formula, the result for the variable age was 29.00.
Now we have a simple and clear results sentence which states:
The mean age was 29.00.
Much better. Reread the initial sentence and the final draft of the sentence one more time. You may experience two differences while reading the final draft of the sentence compared to the first: 1. Less stress and 2. More confidence that you understood what the writer wanted you to know. When you report results you have the same power to reduce emotional and cognitive strain for your reader by following the three recommendations for editing. These recommendations can be used when reporting any results, including the mean, median, and mode. When reporting results, be kind and helpful to your readers through editing.
Reading Review 3.3
Simplify each sentence using the three recommendations for editing.
- The median GPA for a sample of students can be summarized as 2.80.
- The GPA that was the most common in a data set was 3.00.
- When an average GPA was computed by summing the sample GPAs and dividing it by the sample size, the average was 2.67.