BNAD277 Exam 3 CH. 13

General assumptions of One-way ANOVA test for testing c population means:

1. The populations are normally distributed 2. The population standard deviations are unknown but assumed equal 3. The samples are selected independently

A one-way ANOVA test is better than using a series of two-sample t tests because conducting a series of two-sample t tests inflates the risk of committing Type Ⅰ Error

By conducting numerous pairwise comparisons, we inflate the risk of Type Ⅰ Error α but ANOVA avoids this problem with providing one test that simultaneously evaluates the equality of several means

The null and alternative hypotheses look like this:

Ho: μ_1=μ_2=μ_3=μ_4 HA:Not all populations means are equal

Reject the Null if Between-treatments variance > Within-treatments variance

MSTR > MSE Reject the Null

One-way ANOVA test

compares population means based on one categorical variable or factor

One-way ANOVA analysis

does not require that all means differ from one another

Treatments

identify c populations being examined

ANOVA

is a generalization of the two sample t-test with equal but unknown variances

Between-treatments variance

is based on a weighted sum of squared differences of sample means and the overall mean of the data set

The term treatment

is often used to identify the populations being examined for an ANOVA analysis

ANOVA

is statistical technique used to determine if differences exist between the means of three or more populations under independent sampling

X-- X bar bar

is the grand mean (the overall mean of the data set)

The one-way analysis of variance (ANOVA) test

is used to determine if the differences exist between the means of three or more populations

A one-way ANOVA test is based on

the F_(df1,df2) distribution