This chapter discusses descriptive statistics and different types of variables. It covers measures of central tendency like means, medians, and modes to describe averages, and measures of spread like ranges and standard deviations to describe variability. Different types of graphs like histograms and bar charts are used to display distributions of numeric and categorical variables. The chapter emphasizes using simple and transparent statistics to clearly present results and avoiding incorrect use of complex analyses.
3. 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).
5. 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.
6. 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
8. 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.
10. 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)
12. 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.
14. 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.
15. 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.
16. FIGURE 26-6 Example of the Distribution of
Responses for a Normally Distributed Numeric Variable
17. 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).
20. 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.
21. 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.