module 11

Question 1

f-test

Answer 1

• used to evaluate difference in variable between groups
• Fo=s2a/s2b
• observed variance= data1/data2

Question 2

t or f for f tests,
dfA: degrees of freedom for group A is dfA=nA-1 where nA is the number of sampling units in group A.

Answer 2

true

Question 3

how decimal points do you report your p value to when doing a scientific conclusion

Answer 3

3

Question 4

the f test is used to evaluate whether the variances of _______ are different

Answer 4

two group

Question 5

what is ANOVA also known as

Answer 5

analysis of variance

Question 6

what is an ANOVA

Answer 6

method to work with data that has both numerical and categorical variables

Question 7

when to use ANOVA vs two sample t test

Answer 7

t test: two levels in a categorical variable
ANOVA: more than two levels

Question 8

ANOVA test works be separating data into two sources of variation: _____ and ______

Answer 8

• group variation (variation among categorical levels)
• residual variation (variation within a categorical level ie within sampling units)

Question 9

If the means of two groups are the same, then the variation among the groups is ______

Answer 9

0

Question 10

If the means among the groups are quite different, then the variation among the groups is ______

Answer 10

high

Question 11

t or f: the variation among the groups is a direct indicator as to whether the groups have different means

Answer 11

true

Question 12

ANOVA models evaluate _____________ among the categorical levels

Answer 12

whether there is a difference in the means

Question 13

the stats model for ANOVA looks at the ratio of the _______ over the _______

Answer 13

group variation, residual difference

Question 14

If the group variation is about the same size as the residual variation, then the means of the levels are _____________

Answer 14

not overly different

Question 15

If the group variation is much larger than the residual variation, then the groups are _______

Answer 15

different

Question 16

Since ANOVA uses a ratio of variances (group/residual), the statistical model boils down to ________

Answer 16

an F-test

Question 17

what questions are two factor ANOVAs used for

Answer 17

• main effects A (differences among levels of factor A averaging across levels of factor B, compare among full columns/rows)
• main effects B (differences among levels of factor B averaging across levels of factor A, compare among full columns/rows)
• interactions (questions abt differences among levels of one factor within each level of other factors. cell-by cell comparison)

Question 18

additivity

Answer 18

the response to the combination of two levels is simply the sum of the two
(ie two 1 pound weights is two pounds)

Question 19

What is group variation?

Answer 19

The variation between the group means and the overall grand mean.

Question 20

What is residual variation?

Answer 20

The variation between the sampling units and the group means.

Question 21

To calculate the f-score you:

Answer 21

The F-score = group variation divided by residual variation.

Question 22

interaction is defined as any deviation from ______

Answer 22

additivity

Question 23

The null and alternative hypothesis are directional because

Answer 23

Since our interest is in whether the means are different, we are evaluating whether the group variation is larger than the residual variation. As such, the null and alternative hypotheses are directional. HO: F≤1 HA: F>1

Question 24

how are interaction plots set up

Answer 24

• y-axis shows numerical variable (like box plot)
• x-axis shows levels one categorical variable
• lines connect cells across x axis according to levels of other categorical variables

Question 25

dfG vs dfG

Answer 25

dfG: degrees of freedom for the group variation is dfG=k-1 where k is the number of levels in the categorical variable.

dfE: degrees of freedom for the residual variation is dfE=n-k where n is the total number of sampling units in the dataset and k is the number of levels in the categorical variable.

Question 26

if the categorical variables are additive they have ______ interaction

Answer 26

no, parallel lines on an interaction plot

Question 27

Statistical decisions for f-score tests (for the hypothesis)

Answer 27

• Reject the null hypothesis if the observed score is greater than the critical score (i.e., FO>FC) or if the p-value is smaller than the Type I error rate (i.e., p<⍺).
• Fail to reject the null hypothesis if the observed score is less than or equal to the critical score (i.e., FO≤FC) or if the p-value is larger or equal to the Type I error rate (i.e., p≥⍺).

Question 28

t or f: if two categorical variables are not additive (ie they have an interaction) the lines on an interaction plot are parallel

Answer 28

false

Question 29

The scientific conclusions for an ANOVA are:

Answer 29

• Reject the null hypothesis and conclude there is evidence that at least two of the means are different.
• Fail to reject the null hypothesis and conclude there is no evidence that the means are different.

Question 30

main A effects null and alt hypotheses for a two factor ANOVA:

a) Ho: μA1=μA2=…=μAk-1=μAk and Ha: μA1≠μA2≠…≠μAk-1≠μAk
b) Ho: μB1=μB2=…=μBk-1=μBk and Ha: μB1≠μB2≠…≠μBk-1≠μBk
c) Ho: δA1B1=δA1B2=…=δAkBk-1=δAkBk=0 and Ha: δA1B1≠δA1B2≠…≠δAkBk-1≠δAkBk≠0

Answer 30

a)

Question 31

Reporting of an ANOVA should include the following:

Answer 31

1. The mean, standard deviation, and sample size for each group (ideally in a table)
2. The observed F-score (two decimal places)
3. degrees of freedom for the group variation and the residual variation
4. p-value (three decimal places)

Question 32

Rejecting the __(1)__ hypothesis of the ___(2)___ means that at least two of the groups are different. The __(2)__cannot identify how many groups are different, nor identify which ones.

Answer 32

1. Null
2. F-test

Question 33

TukeyHSD test

Answer 33

A type of post hoc test that evaluates all possible contrast statements

Question 34

main B effects null and alt hypotheses for a two factor ANOVA:

a) Ho: μB1=μB2=…=μBk-1=μBk and Ha: μB1≠μB2≠…≠μBk-1≠μBk
b) Ho: μA1=μA2=…=μAk-1=μAk and Ha: μA1≠μA2≠…≠μAk-1≠μAk
c) Ho: δA1B1=δA1B2=…=δAkBk-1=δAkBk=0 and Ha: δA1B1≠δA1B2≠…≠δAkBk-1≠δAkBk≠0

Answer 34

a)

Question 35

main B effects null and alt hypotheses for a two factor ANOVA:

a) Ho: μB1=μB2=…=μBk-1=μBk and Ha: μB1≠μB2≠…≠μBk-1≠μBk
b) Ho: δA1B1=δA1B2=…=δAkBk-1=δAkBk=0 and Ha: δA1B1≠δA1B2≠…≠δAkBk-1≠δAkBk≠0
c) Ho: μA1=μA2=…=μAk-1=μAk and Ha: μA1≠μA2≠…≠μAk-1≠μAk

Answer 35

b)

Question 36

Post hoc tests

Answer 36

Secondary tests uses to evaluate what groups have diffferent means in an ANOVA. The role of a post hoc test is to evaluate whether group means are different while controlling for the Type I error rate for all comparisons among groups.

Question 37

When are you able to use post hoc tests?

Answer 37

They are only used if the ANOVA F-test indicates to reject the null hypothesis.

Question 38

What is the purpose of a contrast statement

Answer 38

To test the difference in means between two groups in an ANOVA

Question 39

Family of contrasts

Answer 39

The set of all contrast statements used for a set of data

Question 40

Family-wise error rate

Answer 40

The Type I error rate for the family of contrasts

Question 41

Contrasts

Answer 41

A test of the difference in means between two groups in an ANOVA

Question 42

If the _____________ is not controlled, increasing the number of contrast statements quickly increases the effective Type I error.

Answer 42

1. family-wise error rate

Question 43

_________ is one type of post hoc test that compares the means of all possible contrasts. It uses a specialized null distribution to adjust for the number of contrasts.

Answer 43

1. TukeyHSD