Differences Across Three Groups (ANOVA) Flashcards
What is a Type 1 error?
When you conclude that there is a genuine differnce between the populations when in fact there is not
What is the alpha level?
Probability of having a type 1 error, typically 0.05 using conventional criteria
What is a Type 2 error?
When you conclude that there is no difference between the population when in reality, there is
What is the beta level?
Probability of having a Type 2 error
If the H0 is true and we reject the H0, what type of error is this?
Type 1 error
If the H0 is false and we fail to reject H0, what type of error is this?
Type 2 error
What is the Bonferroni correction?
Way to maintain an overall Type 1 error rate of 5%, by dividing alpha by the number of comparions, k
Name a disadvantage of the Bonferroni correction?
Time consuming
What is ANOVA used for?
Testing the differences in means in three or more groups
What is the null hypothesis for ANOVA?
Group means are identical
What is the F test statistic?
ratio of variability BETWEEN groups/variability WITHIN groups
What is the degrees of freedom for between groups?
k - 1
What is the degrees of freedom for residuals?
Ntot - k
How is the Sum Square column calculated for between groups?
Sum of Squares between, total of the differences between the sample mean for the ith group and sample mean across all groups combined
How is the Sum Square column calculated for residuals?
Sum of Squares within, represents variability within groups
How is the Mean Square column calculated?
Sum of squares divided by the degrees of freedom
What should the F statistic be if H0 is true?
Small
What are the two degrees of freedom for the reference distribution for ANOVA?
df1 = k - 1 df2 = ntot - k
What does a 5% family error rate mean?
We are 95% confident that the full set of intervals contain the true mean difference
What is assumed for our data when doing ANOVA?
1) Independence of data within and between the groups
2) Equal standard deviations
3) Normally distributed data
How can we check independence of data within and between the groups?
Looking at sampling design
What does the Kruskal Wallis test assume?
- Different groups have the same standard deviation
- Groups with different standard deviations have different distributions
What is heteroscedastic data?
Data with no similar standard deviations for each group
What test should you use if your data is heteroscedastic?
Welch’s ANOVA
What are the two hypotheses for Welch’s ANOVA?
H0: That the median of the groups are the same
H1: At least one median is different from another one
Describe what happens in Welch’s ANOVA
Data are assigned ranks
Smallest score is given rank 1 and the largest is given rank N, which N is the total number of independent observations
Average rank is calculated for each group and assessed using the KW test statistic
Small test statistic suggests differences are expected among random samples
