Contingency Tables are used to do which of these? (Note: There are 2 correct answers).

A contingency table, also known as a cross-tabulation, is a fundamental tool for analyzing the relationship between two or more categorical variables. The data used to construct the table must be attribute (or categorical) in nature, where observations are sorted into distinct categories (e.g., pass/fail, machine A/B/C). The cells of the table contain frequency counts for each intersection of categories. A primary statistical application for these tables is the Chi-Square (χ²) test for independence or homogeneity, which effectively compares the proportions of an outcome across several different groups or samples to determine if a statistically significant relationship exists between the variables.

A. Illustrate one-tail proportions. This is incorrect terminology. "One-tail" refers to the directionality of a hypothesis test, not a feature of data presentation in a contingency table.
C. Contrast the Outliers under the tail. Outliers are extreme values typically associated with continuous (variable) data, identified using tools like box plots. Contingency tables use categorical data, where the concept of outliers is not applicable.
D. Analyze the "what if" scenario. "What-if" or sensitivity analysis is typically performed with predictive models like regression. Contingency tables are used to analyze observed frequencies, not to simulate hypothetical outcomes.

1. Montgomery

D. C. (2013). Introduction to Statistical Quality Control (7th ed.). Wiley.

Page 690

Section 15-4.2

Contingency Tables: "The test procedure for the hypothesis of independence in a contingency table is based on the chi-square distribution... The observations... are counts or frequencies." This supports that the data is attribute (counts) in nature (Option E). The section further explains how the test compares observed frequencies to expected frequencies to test for association

which is a method of comparing proportions across categories (Option B).

2. NIST/SEMATECH. (2012). e-Handbook of Statistical Methods. National Institute of Standards and Technology.

Section 1.3.5.13

Contingency Table: "Contingency tables are used to record and analyze the relationship between two or more categorical variables." This directly supports Option E

as it specifies the use for categorical (attribute) data.

Section 7.2.4

Are the proportions of two characteristics in a population the same?: This section describes the Chi-Square test for homogeneity using a contingency table to compare proportions. The principle extends from two proportions to more than two in larger tables (e.g.

r x c tables)

directly supporting Option B.

3. The Pennsylvania State University. (n.d.). STAT 504: Analysis of Discrete Data. Eberly College of Science.

Lesson 1.1 - Types of Variables: This lesson distinguishes between quantitative and categorical (attribute) variables

noting that contingency tables are a primary tool for summarizing categorical data. This supports Option E.

Lesson 2.2 - Chi-Squared Test of Homogeneity: "The Chi-squared test of homogeneity... is used to determine if the distribution of a categorical variable is the same across two or more populations." This is a direct application of comparing more than two sample proportions

supporting Option B.