Lecture 13 Flashcards
One Factor ANOVA is used to test for?
Differences in the means of 3 or more populations
What type of data does the one-factor ANOVA use?
Ratio-interval scale data
What assumptions of one-factor ANOVA does it require?
To follow a NORMAL distribution and have equal variances
What is the response variable in ANOVA?
(Dependent variable) the ratio-interval scale variable that you are actually measuring
What are factors in ANOVA?
(Independent variable) the nominal scale variable that will group the data into categories
What defines the type of ANOVA?
The factors
What are levels in ANOVA?
(Groups, type of treatments, or sample) the CATEGORIES themselves contained within the factors
What is the null hyposthesis in One-factor ANOVA?
All the means of each population are equal
What is the alternative hyposthesis in one-factor ANOVA?
At least one population mean is different
What does k stand for?
The number of populations
What does X-double bar, N, and G stand for?
The grand mean, grand sample size, and grand total
What is similar to ANOVA?
Two sample t-test
what can be used to test for normality for ANOVA?
D’Agostino Pearson k^2 test
What can be used to test for homoscedascity in ANOVA?
Bartlett’s test and Levene’s test
Why is a test that looks at differences in the means of three or more populations called analysis of variances?
The analysis of variances explains the different sources of variation in the data
What are the three variations One-factor ANOVA?
Level variation, error variation, and total variation
What is level variation?
The variation among the levels (groups/treatments) of a given factor
What is error variation?
The “within” group (level) variation that is unexplained
What is the total variation
The combination of the “among” group and “within” group variations
What is the test statistic calculated in ANOVA?
ONE TAILED F-test, like variance ratio test
What are the two variances of interest in the one-factor ANOVA?
The among-group variances and within-group variances
Why is there just one within-groups variance value if there are 3 or more groups?
Due to the equal variance assumption being true would be all the same within each group
Which variance goes in the numerator and denominator?
Numerator = among group variance, denominator = within-group variance
What must be the case in order to reject the null hypothesis and conclude that there is a difference among the means of the groups?
The among-group variation must be greater than the within group variation
