Brief introduction to contingency table

1. Contingency Table
Dr. Weam Banjar; DDS, MS

2. “The work of epidemiology is related to unanswered
questions, but also to unquestioned answers.”
Patricia Buffler, University of California epidemiologist speaking at the North American Congress of Epidemiology in Montreal
in June 2011

3. Overview
• Contingency tables, also called crosstabs or two-way tables are
used in statistics to summarize relationship between several
categorical variables.
• A special type of frequency distribution table, where two
variables are shown simultaneously
• Data arrays containing counts of observations that are recorded
in cross-classification by a number of discrete factors predictors
• Contingency tables are summaries of response data where
predictor variables (exposure, confounder) are discrete factors
or categorical variables and where the response are counts

4. Factors and Contingency Tables:
• a categorical (discrete) variable taking a small number of values
that represent the levels of the factor.
• Examples:
• Gender: Two levels; 0= male ad 1= female
• Marital status: Five levels; 0= single, 1= married, 2= divorced, 3=
widow, and 4= separated
• Data description:
• Frequencies of factor levels and their combinations
• To assess whether factors are related

5. Factors and Contingency Tables:
• Data summary:
• Categorical data are often summarized by reporting the proportion or
percentage in each category
• Alternatively, a summary of the relative proportion (odds) in each
category might be calculated (relative to a baseline category)
• Testing:
• Assessing the relation between the factors could be achieved using 2
test.

6. Factors and Contingency Tables:
• Dependent variable:
• Outcome of interest
• What do you intend to measure?
• Independent variable:
• Exposure of interest
• What do you intend to investigate?
• Confounder:
• Any factors other than dependent and independent variables that may
influence the results

7. Factors and Contingency Tables:
• Example:
• A total of 30 subjects where enrolled; 20 male and 10 female, to assess
the effect of electronic smoking on development of ginigivitis.
• Identify:
Dependent variable Development of gingivitis
Independent variable Electronic smoking use
Confounder Gender

8. Understanding Contingency Tables:
Outcome

9. Understanding Contingency Tables:
Exposure

10. Understanding Contingency Tables:
• Count: number of observation within the cell
• Row percentage:

11. Understanding Contingency Tables:
• Count: number of observation within the cell
• Row percentage:
• Column percentage:

12. Understanding Contingency Tables:
• Count: number of observation within the cell
• Row percentage
• Column percentage:
• Total percentage:

13. Understanding Contingency Tables:
• In cohort studies (prospective and retrospective):
• Dichotomization based on the exposure
• Relative risk might be calculated
• 𝑅𝑅 =
A/(𝐴+𝐵)
𝐶/(𝐶+𝐷)

14. Understanding Contingency Tables:
• In case control studies:
• Dichotomization based on the outcome
• Odds ratio might be calculated
• 𝑂𝑅 =
A/𝐵
C/D

15. Tips:
• RR and OR are most widely used measures of association in
epidemiology
• Two main factors influence the discrepancy between RR and
OR:
• Initial risk of an event
• Strength of association between exposure and outcome