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Contingency Table

A contingency table presents data for more than one categorical variable over usually five or less levels. In comparison to a frequency table, a contingency table differs because it has a more complex nature. It is basically a multivariate frequency table.

A contingency table can be used to measure and compare the proportions between different variables. When comparing the proportions, different statistical tests can be utilized to measure the significance between the differences of the proportions. A Fisher’s exact test and a Chi-square test are two possible statistical tests which can be used.

Here is an example illustrating when a contingency table is appropriate to use: 

Scenario: Pretend you were comparing sleep patterns between 100 older women and 100 younger women. Older women are considered to be 40 and over, whereas younger women are under 40. In terms of sleep patterns, you ask the women to classify themselves as a morning person or night person. This can be tabulated in a 2x2 contingency table, which is represented by Figure 1 below. 

A contingency table is a useful tool which can be utilized in statistics. When comparing multiple categorical variables and measuring their association with each other, a contingency table resembles a great method of not only presenting the data, but comparing the variables with each other. 

 

Categories within Contingency Table

Cohen's kappa

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Cohen’s kappa is a statistical coefficient, identified as k, which deals with independent raters and measures the degree of agreement between them.

Chi Square Test and Contingency Table

15.2 During last year's budget crunch, several deserving employees of the Bureau of Procedures (BP) were denied promotions. This year, an unusual number of BP employees retired. The bureau chief suspects that the denial of promotions resulted in increased retirements. Of the 115 employees denied promotion, 32 retired. Of the 58

Contingency Table: Formulas and Concepts

The following problems are intended to help you continue working with formulae and concepts pertaining to contingency tables (bivariate frequency tables). Good luck and enjoy! Results on seat belt usage from the 2003 Youth Risk Behavior Survey were published in a USA Snapshot on January 13, 2005. The following table outlin

Contingency Tables: Warranty Repair

Each year, ratings are compiled concerning the performance of new cars during the first 90 days of use. Suppose that the cars have been categorized according to whether the car needs warranty-related repair (yes or no) and the country in which the company manufacturing the car is based (United States or not United States). Based

Probabilities: Contingency Tables

Use the following contingency table: Event A Event B Event C 9 6 Event D 4 21 Event E 7 3 Determine the following probabilities: a) P (A and C) b) P (A and D) c) P B and E) d) P (A and B)

Probability - Excel

4.55. Problem 2.119 on page 65 describes a survey of 40 MBA students (stored in Grade Survey). For these data, construct contingency tables of gender and graduate major, gender and undergraduate major, gender and employment status, graduate major and undergraduate major and graduate major and employment status. ID Num Gender

Data Interpretation and Analysis

Read the data from the fictitious research study regarding diabetes and alcohol consumption, and analyze and interpret the results. The study investigated the effect of drinking alcohol on the risk of diabetes in women. The participants in the study were classified either as alcohol drinkers (any amount of consumption) or non

Statistics: Contingency Table for Beer and Cigars

Four percent (4%) of the customers of a store buy cigars. Half of the customers who buy cigars buy beer and one fourth of those who buy beer buy cigars. The table is given below: Beer No Beer Total Cigars .02 .02 .04 No cigar .06 .90 .96 Total .08 .92

Contingency Tables and Probablity: Cereal will be high calorie, high fiber

See attached template. Using the Cereal worksheet (which we used in the Week 2 Lab for Linear Regression Analysis), the Calorie variable was recoded into "high calorie" and "low calorie" categories. We used 120 calories per serving as the break point (greater than or equal to 120 is "high calorie"). A contingency table wa

Contingency Table and Probability

Many people think that job satisfaction in the workplace is directly related to the annual income. To check the validity of this assumption a survey of 430 active working adults in the U.S was taken that relates their job satisfaction to their annual income. The results are shown in the contingency table below. Annual Income

Design contingency table

Design a contingency table that will hold your data. What are your degrees of freedom and critical value at a 0.05 confidence level? You do not need data to answer this. These are based off of the number of rows and columns in your table. Below is the original question I need to use to create the contigency table. A study

Develop a hypothetical contingency table

Develop a hypothetical contingency table of data using a grid of 3 rows and four columns (label the rows and columns as you see fit. For example, the rows might be age, and the columns might be income level). Insert hypothetical values for each cell in the table. Create four probability questions using the table that you a

Calculate Probabilities from a Contingency Table

Given the following contingency table: C D Total A 10 30 40 B 20 40 60 Total 30 70 100 Find the probability of A and C. a) 33.3% b) 10% c) 25% Find the probability of A or C a) 60% b) 70% c) 10% Find the probability of B given C a) 20% b) 30% c) 66.67%

Relationship between three Contingency Tables

Two contingency tables are related by a common attribute C. Use any relationships between the cell entries, such as, derived probabilities to form a third contingency table directly relating attributes A and B. You may solve for the third table either as a frequency table with cell entries in counts [0..N], or a relative proba

Probabilities -Solution using Set theory & Contingency Table

An insurance company reviews their auto insurance clients and finds the following: a) all insure at least 1 car b) 85% insure more than 1 car C) 23% insure a sports car d) 17% insure more than 1 car including a sports car find the probability that a client, selected at random insures only one car and it is NOT a sports

Expected Value using Contingency Table

A four-year university has decided to implement a new approach to teaching Statistics. Full-time and adjunct professors were surveyed to determine whether they preferred the traditional lecture approach or a computer approach to teaching Statistics. Use hypothesis testing to test the independence of opinion between the two gro

Distributions, frequencies, critical values, and hypothesis tests.

10. What is the critical value at the 0.05 level of significance for a goodness-of-fit test if there are six categories? A) 3.841 B) 5.991 C) 7.815 D) 11.070 E) None of the above 11. Two chi-square distributions were plotted on the same chart. One distribution was for 3 degrees of freedom and the other was f

Calculating relative frequencies in a contingency table

Calculating relative frequencies in a contingency table A survey of a sample of 347 people is conducted. The survey's respondents are classified according to their political affiliation and their opinion on a bill. The results are given in the contingency table below. Opinion on

Contingency table - chi square test

Four brands of light bulbs are being considered for use in the final assembly area of the Saturn plant in Spring Hill, Tennessee. The director of purchasing asked for samples of 100 from each manufacturer. The numbers of acceptable and unacceptable bulbs from each manufacturer are shown below. At the .05 significance level, is t

Set up a contingency table.

1. When we calculate chi-square tests in hypothesis testing we use contingency tables. a. Set up a simple contingency table for me. b. Highlight a cell in your table.