Chapter 26

Descriptive Statistics

Overview

• For most papers in the health sciences, the goal of analysis should be to use the simplest statistics possible to make the results of the study clear.

• Most research studies do not require the use of complex statistics like regression (and using advanced statistical tests incorrectly is never helpful).

FIGURE 26- 1 Analytic Plan

Types of Variables

• A variable is a characteristic that can be assigned more than one value.

• The value of a variable for an individual does not have to vary (change) over time, but the response among individuals within a population should be something that might differ.

Types of Variables

There are several ways to classify variables:•Ratio variables •Interval variables

– Continuous variables– Discrete variables

•Ordinal variables (ranked variables)•Nominal variables (categorical variables)

– Binomial variables

FIGURE 26- 2 Types of Variables

Measures of Central Tendency

There are several ways to report the average response to a variable in a population:•For ratio and interval variables, the central tendency can be described using means, medians, and modes. •For ordinal variables, a median or mode can be reported. •A mode can be reported for categorical variables.

FIGURE 26-3 Example of a Mean, Median, and Mode

Measures of Spread

Measures of spread, also called “dispersion,” are used to describe the variability and range of responses.•range •median•quartiles •interquartile range (IQR)

FIGURE 26-4 Sample Boxplot

Measures of Spread

• A normal distribution of responses has a bell-shaped curve with one peak in the middle

• Not all numeric variables have a normal distribution. The distribution may instead be left-skewed, right-skewed, bimodal, or uniform.

FIGURE 26-5 Sample Histogram

Standard Deviation

For variables with a relatively normal distribution the standard deviation describes the narrowness or wideness of the range of responses. •68% of responses fall within one standard deviation above or below the mean.•95% of responses are within two standard deviations above or below the mean.•More than 99% of responses are within three standard deviations above or below the mean.

Z-scores

A z-score indicates how many standard deviations away from the sample mean an individual’s response is. •An individual whose age is exactly the mean age in the population will have a z-score of 0. •A person whose age is one standard deviation above the mean in the population will have a z-score of 1. •A person whose age is two standard deviations below the population mean will have a z-score of –2.

FIGURE 26-6 Example of the Distribution of Responses for a Normally Distributed Numeric Variable

Categorical Responses

• A histogram or boxplot cannot be used to display the responses to categorical variables.

• The distribution of responses must instead be displayed in a bar chart (or, less often, a pie chart).

FIGURE 26-7 Sample Bar Chart

FIGURE 26-8 Common Descriptive Statistics by Variable Type

Statistical Honesty

• Failure to correctly report the results of statistical analyses is a form of research misconduct.

• Statistical honesty requires more than merely avoiding falsification, fabrication, and plagiarism. It also requires adherence to accepted statistical practices.

• Statistical analysis is about discovering the true story in a data set, not about creatively manipulating data toward a preferred result.

Statistical Consultation

If answering the study question adequately requires the use of elaborate analytic techniques, invite a statistical expert to serve as a collaborator and as a coauthor on the resulting paper.