MPH 560 Module 1 Descriptive Statistics Example

Describing the Data Before Testing It: Descriptive Statistics With Blood Pressure Readings

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Master of Public Health Program, Aspen University

MPH 560: Applied Biostatistics for Public Health

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Month Day, Year

Describing the Data Before Testing It: Descriptive Statistics With Blood Pressure Readings

Every statistical analysis begins with description. Before testing hypotheses, researchers must know what their data look like: where values center, how spread out they are and whether the distribution is symmetric or skewed. This paper explains the main descriptive statistics used in public health through a composite sample of 20 adults' systolic blood pressure readings, placing the example in the context of national hypertension data.

Why Blood Pressure

Hypertension is one of the most common and important conditions in public health. National examination survey data for 2017 to 2018 found an age-adjusted hypertension prevalence of 45.4% among US adults, higher among men at 51.0% than women at 39.7% (Ostchega et al., 2020). Describing blood pressure distributions accurately is therefore a routine task for public health analysts.

Types of Data

The type of variable determines which summaries apply. Categorical variables, such as sex or hypertension status, are summarized with counts and percentages. Numerical variables, such as systolic blood pressure in millimeters of mercury, are summarized with measures of center and spread. Ordinal variables, such as pain ratings, fall in between and are often summarized with medians.

The Composite Sample

The sample consists of systolic readings from 20 adults at a community screening event: 112, 118, 121, 124, 126, 128, 129, 131, 132, 134, 135, 137, 139, 141, 144, 147, 152, 158, 166 and 184 mm Hg. The table summarizes them.

Measures of Center

The mean, 137.9, is the sum of values divided by 20. The median, 134.5, is the average of the 10th and 11th ordered values, 134 and 135. The mean is higher because a few high readings, especially 184, pull it upward. When a distribution has a long tail to the right, the mean exceeds the median, and the median may better describe a typical person.

Measures of Spread

The standard deviation of 17.2 mm Hg describes how far readings typically fall from the mean. The interquartile range, from 127.5 to 144.75, contains the middle half of readings and is less affected by extreme values. For skewed data, reporting the median with the interquartile range is often more informative than the mean with the standard deviation (Whitley & Ball, 2002).

Shape of the Distribution

A histogram of the readings would show most values between 120 and 150, with a tail stretching toward higher readings. Skewness matters because many statistical tests assume approximately normal distributions. Describing shape before analysis helps choose the right test later in the course.

Standard Deviation Versus Standard Error

Variability among people is captured by the standard deviation, while the standard error, which shrinks as the sample grows, tells how precisely the sample mean pins down the population mean; for these readings, 17.2 over the root of 20 gives 3.85. Here the standard error is 17.2 divided by the square root of 20, or 3.85. Authors sometimes report standard errors when describing data, which makes variability look smaller than it is; the standard deviation should be used to describe spread among individuals (Altman & Bland, 2005).

Categorical Summary

Using the common threshold of 130 mm Hg for elevated systolic pressure, 13 of the 20 adults, or 65%, had readings at or above 130. This proportion is much higher than the national prevalence, which is expected because people attending a screening event may be more likely to have concerns about blood pressure. Such selection effects must be considered before generalizing.

Presenting Results

Good practice is to report the sample size, use appropriate summaries for the data type and shape, give units, avoid excessive decimal places and use tables or figures that make patterns clear. A box plot would display the median, quartiles and the outlying reading of 184 at a glance. Tables should label units in column headings and state the number of missing values, if any, so readers know how complete the data are.

Why Description Matters

Descriptive statistics reveal data entry errors, outliers and patterns that shape later analysis. An analyst who skips description may apply tests that do not fit the data or miss important findings, such as a subgroup with extreme values. In public health reports, clear descriptive statistics are often the most useful results for decision-makers.

Descriptive Statistics in Public Health Reports

Health departments publish descriptive statistics constantly: rates of disease by county, median ages of cases, percentages of residents screened. Readers use these numbers to set priorities, so accuracy and clear presentation matter. Reporting the denominator, the time period and whether figures are age-adjusted helps readers interpret them correctly.

Checking Data Quality

Descriptive statistics also catch errors. A systolic reading of 1,340 would signal a typing error, and a minimum of zero would suggest missing data coded as zero. Reviewing the range, frequencies and a quick plot before analysis prevents such errors from distorting results.

Comparing Groups Descriptively

Descriptive statistics can compare groups before formal testing. If readings were split by sex or age group, reporting the median and interquartile range for each would reveal differences worth testing. Tables that place groups side by side are often the clearest way to show such comparisons.

Software and Reproducibility

Most analysts calculate descriptive statistics with software such as R, SAS, Stata or Excel. Recording the steps, for example in a script, lets others reproduce the results and makes it easy to rerun analyses when data are updated. Reproducibility is part of good statistical practice, not an extra.

Conclusion

Descriptive statistics summarize data by center, spread and shape. In the composite blood pressure sample, the mean of 137.9 exceeded the median of 134.5 because of right skew, the standard deviation of 17.2 described individual variability and the standard error of 3.85 described the precision of the mean. Choosing summaries that fit the data, and distinguishing standard deviations from standard errors, is the foundation for sound statistical inference.

References

Altman, D. G., & Bland, J. M. (2005). Standard deviations and standard errors. BMJ, 331(7521), 903. https://doi.org/10.1136/bmj.331.7521.903

Ostchega, Y., Fryar, C. D., Nwankwo, T., & Nguyen, D. T. (2020). Hypertension prevalence among adults aged 18 and over: United States, 2017-2018 (NCHS Data Brief No. 364). National Center for Health Statistics. https://www.cdc.gov/nchs/products/databriefs/db364.htm

Whitley, E., & Ball, J. (2002). Statistics review 1: Presenting and summarising data. Critical Care, 6(1), 66-71. https://doi.org/10.1186/cc1455