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