The table cross-classifies 68,694 passengers in cars and light trucks involved in accidents in the state of Maine by whether or not they were wearing a seat belt and by whether or not they were injured or killed. The study is using seatbelt wearing to predict injury/death. Injured or Killed? Wore Seatbelt? Yes No Total No 3,865 27,037 30,902 Yes 2,409 35,383 37,792 Total 6,274 62,420 68,694 What are the odds that a passenger was injured or killed if he/she did not wear a seatbelt (Row 1 odds)? What are the odds that a passenger was injured or killed if he/she wore a seatbelt (Row 2 odds)? Interpret both results. Describe the strength of the association between seatbelt use and injury/death using the odds ratio. Calculate the odds ratio and interpret the result?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
The table cross-classifies 68,694 passengers in cars and light trucks involved in accidents in the state of Maine by whether or not they were wearing a seat belt and by whether or not they were injured or killed. The study is using seatbelt wearing to predict injury/death.
Injured or Killed?
| Wore Seatbelt? | Yes | No | Total |
| No | 3,865 | 27,037 | 30,902 |
| Yes | 2,409 | 35,383 | 37,792 |
| Total | 6,274 | 62,420 | 68,694 |
What are the odds that a passenger was injured or killed if he/she did not wear a seatbelt (Row 1 odds)? What are the odds that a passenger was injured or killed if he/she wore a seatbelt (Row 2 odds)? Interpret both results. Describe the strength of the association between seatbelt use and injury/death using the odds ratio. Calculate the odds ratio and interpret the result?
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