Midterm Revision 2

Question 1

What kind of variable must the IV for an ANOVA be?

Answer 1

Nominal

Question 2

What kind of variable must the DV for an ANOVA be?

Answer 2

Quasi-continuous

Question 3

How are quasi-continuous variables usually treated?

Answer 3

They are usually treated like continuous variables

Note - they are always all real numbers

Question 4

What is are conditional distributions?

Answer 4

A distribution of YIX. The number of conditional distributions will depend on the sample space of X.

Question 5

If X is a dichotomous IV and Y is a QC DC. How many conditional distributions are there for YIX?

Answer 5

Two - one for when YIX=0 and one for when YIX=1

Question 6

What does relationship ‘type’ refer to?

Answer 6

Type -captures the functional dependencies between two variables, or more specifically, the shape of the conditional mean function E(YIX)

Question 7

What is primary strength?

Answer 7

It captures how closely packed the points [Xi,Yi] are to the conditional mean function

Question 8

The way in which we measure primary strength depends on what?

Answer 8

The quantitative scenario - the type of random variables

Question 9

What is secondary strength?

Answer 9

The slope of the conditional mean function. It captures the sensitivity of Y to X, or the rate of change in Y given X.

Question 10

If it is the case and X and Y are related (in the ANOVA scenario), how to we quantify both the primary and secondary sense of strength?

Answer 10

omega_sq= σ²A/σ²

variance in DV due to IV/total variance in DV

Question 11

Good sentence for leading from the relationship overview into ANOVA

Answer 11

“If we are interested in conducting a formal test under this particular quantitative scenario, we may conduct an inferential test on whether the relationship is flatline or not”

Question 12

What does the hypothesis pair for an ANOVA look like?

Answer 12

H0: μ1=μ2=μ3=…μj

H1: ~(not H0)

Question 13

What is our aim using ANOVA technology?

Answer 13

Our aim using ANOVA technology is to make a binary decision about the relationship between a nominal IV and a QC DV.

Question 14

What is σ²A?

Answer 14

The population variance of Factor A

It quantifies the departure of the conditional means from the grand mean.

Question 15

a

Answer 15

the levels of the treatment Factor A

Question 16

What does a little i usually denote?

Answer 16

The individual

Question 17

What does a little j or k usually denote?

Answer 17

The group

Question 18

Factor A

Answer 18

An IV that is categorical with a certain number of levels

Question 19

What is the conditional mean function E(YIX)

Answer 19

A line connecting the conditional means of each conditional distribution

Question 20

E(YIX)=x

Answer 20

The mean of the conditional distribution of Y given a particular level of the IV (X=x)

Question 21

We employ ANOVA technology in order to partition the total variance in the DV into two portions, what is the formula used to denote this?

Answer 21

〖SS〗_T=〖SS〗A+〖SS〗(U/A)

Question 22

SS_U/A

Answer 22

variance associated with the residual

Question 23

SS_A

Answer 23

variance associated with the factor

Question 24

MSu/A=

Answer 24

MSu/A=(SSu/A) / (∑nj-a)

~ E(MSu/A) expected MS from the chi-square sampling distribution

Question 25

MSA =

Answer 25

MSA = (SSA) / (a-1)

~ E(MSA) expected MS from the chi-square sampling distribution

Question 26

What are the 8 steps in answering an ANOVA question?

Answer 26

1. Define a relationship
2. State the purpose of ANOVA
3. F ratio definition and construction (how this works at pop level)
4. Sample ANOVA decomposition: calculate the sample level variance (sum of squares)
5. Sample ANOVA decomposition: calculate the mean squares
6. Sample ANOVA decomposition: estimate the expected mean squares
7. Sample ANOVA decomposition: construct an If/Then link
8. If we reject H0 then estimate omegaA (effect size)

Question 27

What is the distribution that the ANOVA stat comes from?

Answer 27

F(a-1)(∑nj-a)

Question 28

What is the ANOVA test statistic?

Answer 28

MSA/MSu/A

Question 29

What is the grand mean?

Answer 29

The mean of all observations divided by the total sample size