The distribution used for the hypothesis test is a new one. It is called the F distribution, invented by George Snedecor but named in honor of Sir Ronald Fisher, an English statistician. The F statistic is a ratio (a fraction). There are two sets…
The purpose of a one-way ANOVA test is to determine the existence of a statistically significant difference among several group means. The test actually uses variances to help determine if the means are equal or not. In order to perform a one-way…
This chapter introduces a new probability density function, the F distribution. This distribution is used for many applications including ANOVA and for testing equality across multiple means. We begin with the F distribution and the test of hypothesis of differences…
Figure 12.1 One-way ANOVA is used to measure information from several groups. (credit: modification of work “Magazine Stack” by thebittenword.com/ Flickr, CC BY 2.0) Many statistical applications in psychology, social science, business administration, and the natural sciences involve several groups. For example,…
Facts About the Chi-Square Distribution The chi-square distribution is a useful tool for assessment in a series of problem categories. These problem categories include primarily (i) whether a data set fits a particular distribution, (ii) whether the distributions of two…
Above the χ2 test statistic was used in three different circumstances. The following bulleted list is a summary of which χ2 test is the appropriate one to use in different circumstances.
The goodness–of–fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the test for homogeneity, can be used…
Tests of independence involve using a contingency table of observed (data) values. The test statistic for a test of independence is similar to that of a goodness-of-fit test: Σ(i⋅j)(O–E)2EΣ(i⋅j)(O–E)2E where: There are i⋅ji⋅j terms of the form (O–E)2E(O–E)2E. A test of independence determines whether two factors are…
In this type of hypothesis test, you determine whether the data “fit” a particular distribution or not. For example, you may suspect your unknown data fit a binomial distribution. You use a chi-square test (meaning the distribution for the hypothesis test is…
Thus far our interest has been exclusively on the population parameter μ or it’s counterpart in the binomial, p. Surely the mean of a population is the most critical piece of information to have, but in some cases we are…