4.4: Summarizing Results in Sentences
- Page ID
- 50010
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)If the SD for the age variable in Data Set 4.1 was 9.39 when rounded to the hundredths place. Let’s now focus on how to report results like these in American Psychological Association (APA) format. When summarizing Data Set 4.1, one could write:
Data were collected from 22 people. They ranged in age from 14 to 47 (M = 29.00, SD = 9.39).
The summary sentences use a format referred to as APA. In APA format, symbols can be written in parentheses to provide important results in a concise way. When a mean is reported in parenthesis, the symbol M is used. When a standard deviation is reported in parenthesis, the symbol SD is typically used. The summary sentences clearly and succinctly give a lot of information about the data to the audience. The audience knows the sample size. The audience knows that the lowest age was 14 and the highest age was 47. The audience also knows that the mean score was 29.00 but that individual ages varied around the mean quite a bit. By always presenting the mean and standard deviation together we get a nice snapshot. Image you were reading a paper and it contained this sentence:
Data were collected from 50 people. The mean age in the sample was 15.00 (SD = 0.00).
What do we know about this dataset? Well, the standard deviation reflects how far people tend to fall from the mean and it is reported as 0.00. Thus, everyone was 15 years of age! Remember, when a standard deviation is 0.00 it means that everyone had the exact same score and there is no variation in the data.
Examples of APA Summaries for Data Set 4.1
There are several ways that data for a variable can be summarized using APA format. Here are a few examples of different ways to summarize the same data:
Option 1: Data were collected from 22 people. They ranged in age from 14 to 47 (M = 29.00, SD = 9.39).
Option 2: Data were collected about age (n = 22). The exclusive range for age was 33.00 (M = 29.00, SD = 9.39).
Option 3: Age varied (M = 29.00, SD = 9.39) in a sample of 22 persons.
Often sample size is already reported elsewhere in a report, in which case a simpler sentence focused on the mean and standard deviation can be used like so:
Option 4: The mean age was 29.00 (SD = 9.39).
Option 5: The mean age was 29.00 with a standard deviation of 9.39.
The symbols M and SD are used to represent the mean and standard deviation, respectively, when these are presented in parenthesis as part of a sentence. Sample size is represented with the symbol n.
Reading Review 4.2
- What symbols should be used for the mean and standard deviation when they are reported within parentheses in a sentence?
- What does the standard deviation add to the summary which is why it is usually reported with the mean?
- Do the symbols for mean and standard deviation always need to be used when summarizing each in sentences?