Statistics: read the numbers, the comparison and the uncertainty
Statistics helps summarise data and reason about what they may show. The calculation is only one part of the task. A useful interpretation also identifies what was measured, who was included and which question the number is intended to answer.
Identify what each value represents before combining values
Data used to summarize statistics could be based upon categories, counts, or measurements. Depending on the units and definitions of the collected data, some comparisons are more appropriate than others. For example, total visits represent something different than total individuals since one person may attend more than once. Similarly, percentages require a defined base to accurately assess. Using clear labeling ensures that no matter how accurate your final calculation is, it addresses the question you expect your readers to ask rather than a different question they might assume you answered.
Identify whether each line item of a fictional Service Report represents an individual, an appointment, or test. Determine whether an individual can have multiple representations. Finally, define the time frame during which these items were recorded. Many times, defining the units of measure prior to determining the most suitable analytical approach provides greater clarity regarding the appropriateness of your subsequent analyses.
The mean and median describe the centre differently
The mean is determined by summing all of the values and dividing by the number of values. The median is determined by placing all of the values in order and identifying the middle value (or average of the two middle values if there is an even number of values). Differences can occur depending upon the distribution of the values within your data set. Additionally, both measures leave out information regarding the variability among the observations.
Use five fictional waiting times: 2, 2, 2, 2 and 12 minutes. The mean is 4 minutes and the median is 2 minutes. Neither calculation gives the entire story. Explain how the 12-minute value affects the mean, and describe the range of 2 to 12 minutes alongside the central values.
State the baseline as well as the change
Absolute change compares numbers through subtraction. Relative comparisons compare one number against another. Use the following fictional example to demonstrate both types: Moving from 10 cases/100 persons to 5 cases/100 persons means there is a decrease of 5 percentage points but a relative decline of 50%. Both forms of reporting must use the same outcome, population base, and observational time period.
One form does not have inherent merit over the other. Both forms answer different questions. If provided, recreate the original and end values when reporting a result. Do not interpret a relative change without having access to the baseline and do not turn a math instruction example into a statement that a real-world treatment actually produces that type of change.
An estimate should be read alongside its limitations
Estimates based upon samples may deviate from the true population value. Confidence intervals express uncertainty due to a particular estimation method given specific assumptions. Confidence interval interpretations belong with study design and data quality. A narrower interval does not compensate for sampling bias nor indicate that a statistically significant observed difference is practically important.
To revise write three sentences: What does the estimate tell us? What uncertainty is reported? What does the study design NOT tell us? Statistically significant does not equate to the size or practical importance of an effect. There is no singular standard that defines both conclusions. Reporting estimates effectively communicates what was numerically reported while making uncertainty and relevant limitations evident.
Check your understanding
A short quiz, with an explanation after each answer.
What is the median of 2, 2, 2, 2 and 12?
Return to the section you found hardest and explain its example without looking at the page. Check the explanation, then repeat the quiz later. Being able to describe the reasoning is more useful than remembering the position of a correct answer.