STA 205 Lecture Notes - Lecture 6: Contingency Table, Marginal Distribution, Electrocardiography
Packet 6: Chi-Square Test for Independence Textbook pages: 18 – 24; 624 – 631
After completing this material, you should be able to:
• calculate the expected count for any cell of a contingency table.
• find marginal distributions for a contingency table and use those to construct a side-by-side bar graph.
• compute chi-square contributions for any cell of a contingency table.
• conduct the chis-square test (with the aid of StatCrunch output) to determine if two categorical variables are
related.
The legalization of medicinal marijuana has been a hotly contested subject. A survey conducted in April 2015 was
undertaken to investigate whether a relationship exists between feelings on the legalization of medicinal marijuana
(for/against) and political party (Republican/Democrat/Independent).
During this study, a total of 500 individuals were surveyed. For each American adult, what variables were
recorded? Are these variables categorical or quantitative?
Because two variables were recorded for each individual, we need a way to organize this data. A contingency table
categorizes counts on two (or more) categorical variables – in other words, this table summarizes the number of
individuals in all possible combinations of categories. We can summarize the responses to the survey in the table below:
Legalization of Marijuana
Supports
Does not support
Political Party
Democrat
Republican
Independent
Instead of looking at the counts, let’s split the table into marginal
distributions – that is, what percentage of each political party
surveyed gave each of the two responses?
cyategorical i11what is your political party INEl
Feeling on legalization of medical marijuana
11684 200
Ii 429 Yo Ethan
Based on bar graph
eraininion see.io ct
iH3gzH3gzMzeEggz
party Distribution of
support is Not similar
across ALL 3parties
Democrat In200
support 58
NO support 8
Independent h1001
Support 9
5
100
nonsupport foot
Document Summary
After completing this material, you should be able to: The legalization of medicinal marijuana has been a hotly contested subject. A survey conducted in april 2015 was undertaken to investigate whether a relationship exists between feelings on the legalization of medicinal marijuana (for/against) and political party (republican/democrat/independent). During this study, a total of 500 individuals were surveyed. Inel cyategorical i 11 what is your political party. Because two variables were recorded for each individual, we need a way to organize this data. A contingency table categorizes counts on two (or more) categorical variables in other words, this table summarizes the number of individuals in all possible combinations of categories. We can summarize the responses to the survey in the table below: y t r a. Based on bar graph eraininion see. io ctih3gzh3gzmzeeggz party distribution of support is not similar across all 3 parties. In order to determine if the differences are significant, we need to conduct a hypothesis test.
