Which of the following is used to test the significance for the analysis of a Variance Table?

The F-test is the statistical test used in an Analysis of Variance (ANOVA). ANOVA partitions the total variability of a data set into two components: variability between groups and variability within groups. The F-test is conducted by calculating the F-statistic, which is the ratio of the mean square between groups (variance between samples) to the mean square within groups (variance within samples). This ratio is then compared to a critical value from the F-distribution to determine if the observed differences between the means of the groups are statistically significant, or if they could have occurred by random chance.

A. t Test: The t-test is primarily used to compare the means of only two groups. The F-test is a generalization that can compare the means of two or more groups.
C. Chi Square Test: This test is used for analyzing categorical data to assess the goodness of fit of a model or the independence of two variables, not for comparing means of continuous data.
D. Acid Test: This is a financial term (also known as the quick ratio) used to measure a company's short-term liquidity and is completely unrelated to statistical analysis.

1. Montgomery

D. C. (2019). Introduction to Statistical Quality Control (8th ed.). John Wiley & Sons. In Chapter 11

"Design and Analysis of Single-Factor Experiments: The Analysis of Variance

" Section 11-2.2

"Analysis of Variance

" it is stated: "The test procedure for the null hypothesis... is to compute the test statistic F₀ = MSTreatments / MSE... and to reject H₀ if F₀ > Fα

k-1

N-k." This explicitly identifies the F-test as the procedure for ANOVA.

2. The Pennsylvania State University. (n.d.). STAT 501: Regression Methods

Lesson 6: One-Way ANOVA. Eberly College of Science. Retrieved from https://online.stat.psu.edu/stat501/lesson/6. The course material states

"The test statistic for the one-way ANOVA is the F-statistic... The F-statistic is a ratio of the 'average between-group variation' to the 'average within-group variation'."

3. MIT OpenCourseWare. (2011). 15.075J Statistical Thinking and Data Analysis

Fall 2011

Lecture Notes: Analysis of Variance (ANOVA). Massachusetts Institute of Technology. Section 2.1

"The F-test

" describes the F-statistic as the ratio of the Mean Square for Treatments (MST) to the Mean Square for Error (MSE) and its use in testing the hypothesis of equal means.