Statistics: Analysis of Variance methods Flashcards
When do these methods apply?
When a quantitative response variable has a categorical explanatory variable.
What is meant by ANOVA?
Comparing the means of several groups
What is the difference between one way and two way anova
1 factor, two factors (categorical variables.)
What are the null and alternative hypothesis formats for ANOVA test comparing means
H0: m1=m2=….m(n)
Ha: at least two of the population means are unequal
What are the assumptions of the ANOVA test?
-The population distributions of the response variable
for the g groups are normal, with the same standard
deviation in each group.
-Randomisation
Why is the ANOVA method called analysis of variance?
The test statistic uses evidence about two types of variability; between the means and within the samples.
The mean square of the group row is based on ______ while the mean square error is _______
Variability between groups estimate of the population variance squared; variability within groups estimate sample variance squared of the population variance squared.
What does the error label refer to?
It summarises the error from not being able to predict subject’s responses exactly if we know the only group to which they belong.
How is the mean square calculated
Sum of the squares (SS) divided by the DF
As the sample size increases the normality assumption becomes ______ important
less
Discuss violations of the equal population assumption
Moderate violations are not serious. When the sample sizes are identical the f test still works quite well. When the sample sizes are not equal the f test works quite well as long as the standard deviation is no more than about twice the smaller groups standard deviation.
What is the relationship between the T and F test?
The P-value for the F test is the same as the two sided P-value for the t test.
Why do an F test instead of multiple t tests?
A single test helps control the Type 1 error probability
What is the disadvantage of an F test?
Doesn’t tell us which groups are different or how different they are
What is meant by the fisher method?
The ANOVA F test confidence interval
When can we infer the population means are different?
When the confidence interval contains 0
When is it preferable to use the confidence interval equation from chapter 10?
When the ratio of the largest standard deviation to the smallest is about 2 as it uses separate standard deviations.
What is a multiple comparison method?
Compare pairs of means with a confidence level that applies simultaneously to the entire set of comparisons rather than each comparison.
What is the bonferroni multiple comparison method?
For each level it uses a t score. ie five groups at a 95% confidence level = 0.05/5= 0.01 for each one (99% confidence)
What method would we use?
Tukey Method
