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83341 ch26 jacobsen
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.

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83341 ch26 jacobsen

  • 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).
  • 4. FIGURE 26- 1 Analytic Plan
  • 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
  • 7. FIGURE 26- 2 Types of 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.
  • 9. FIGURE 26-3 Example of a Mean, Median, and Mode
  • 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.
  • 13. FIGURE 26-5 Sample Histogram
  • 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).
  • 18. FIGURE 26-7 Sample Bar Chart
  • 19. FIGURE 26-8 Common Descriptive Statistics by Variable Type
  • 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.