hypothesis testing

Question 1

nominal value: ⍺

Answer 1

⍺: probability of committing a type 1 error
- usually selected a priori, most common is 0.05

means that the significance level corresponds to the probability of committing a type 1 error

Question 2

1- ⍺

Answer 2

probability of not rejecting H0 when it is true (not committing type 1)

Question 3

which anova assumption violates inflate the type 1 error rate?

Answer 3

violations of independence :(increasing sample size does not solve this problem)
- underestimation of true variability leads to an increased rate of false positives

violations of homogeneity of variance:
- increasing sample size and creating equal groups can alleviate some of the inflation

Question 4

what is 1-β

Answer 4

power - probability of correctly rejecting a false H0 (identifying an effect)

Question 5

what is the relationship between type 1 error rate and power for a statistical test?

Answer 5

higher values of ⍺ = lower values of β

a less conservative test makes it easier to detect an effect (but to also make errors)

Question 6

what is the family wise type 1 error rate?

Answer 6

the probability of making at least one type 1 error rate in a family of tests if the null is true

1-(1-⍺)^c

Question 7

what is the Bonferroni correction for individual statistical tests?

Answer 7

an adjustment made to P values in order to reduce type 1 errors when multiple pair wise tests are performed on a single set of data

creates a more conservative type 1 error rate

done by dividing the critical value P by the number of comparisons being made (statistical power is then calculated based on this value)

Question 8

how do we find the appropriate critical value for a statistical test from the F table?

Answer 8

use significance level ⍺ and dfM and dfR

if F is greater than or equal to the crit val, reject the null

or, if the p value of the F value <= ⍺ then, reject the null

Question 9

what is the null hypothesis for a T test

Answer 9

H0: µ = population
H1: µ ≠ population

Question 10

null hypothesis for one way anova

Answer 10

H0: µ1=µ2=…=µk
H1: not all µ’s are the same

Question 11

null hypothesis for two/three way ANOVA

Answer 11

main effect A:
H0A: µA1=….=µAa (equal row marginal means)
H1A: not all µAg are the same

main effect B:
H0B: µB1=…=µBb (equal column marginal means)
H1B: not all µBj are the same

interaction effect:
H0AxB: all µAgBj are the same/ the interaction between Factor A and Factor B = 0
H1AxB: not all µABj are the same/ the interaction between Factor A and Factor B is not 0

three way ANOVA: more main effects and interaction effects

Question 12

null hypothesis for one way repeated measures ANOVA

Answer 12

H0: µ1=µ2=µ3
H1: not all µg are the same

(between group/effect of treatment)