Midterm Revision 2 Flashcards
What kind of variable must the IV for an ANOVA be?
Nominal
What kind of variable must the DV for an ANOVA be?
Quasi-continuous
How are quasi-continuous variables usually treated?
They are usually treated like continuous variables
Note - they are always all real numbers
What is are conditional distributions?
A distribution of YIX. The number of conditional distributions will depend on the sample space of X.
If X is a dichotomous IV and Y is a QC DC. How many conditional distributions are there for YIX?
Two - one for when YIX=0 and one for when YIX=1
What does relationship ‘type’ refer to?
Type -captures the functional dependencies between two variables, or more specifically, the shape of the conditional mean function E(YIX)
What is primary strength?
It captures how closely packed the points [Xi,Yi] are to the conditional mean function
The way in which we measure primary strength depends on what?
The quantitative scenario - the type of random variables
What is secondary strength?
The slope of the conditional mean function. It captures the sensitivity of Y to X, or the rate of change in Y given X.
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?
omega_sq= σ²A/σ²
variance in DV due to IV/total variance in DV
Good sentence for leading from the relationship overview into ANOVA
“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”
What does the hypothesis pair for an ANOVA look like?
H0: μ1=μ2=μ3=…μj
H1: ~(not H0)
What is our aim using ANOVA technology?
Our aim using ANOVA technology is to make a binary decision about the relationship between a nominal IV and a QC DV.
What is σ²A?
The population variance of Factor A
It quantifies the departure of the conditional means from the grand mean.
a
the levels of the treatment Factor A
What does a little i usually denote?
The individual
What does a little j or k usually denote?
The group
Factor A
An IV that is categorical with a certain number of levels
What is the conditional mean function E(YIX)
A line connecting the conditional means of each conditional distribution
E(YIX)=x
The mean of the conditional distribution of Y given a particular level of the IV (X=x)
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?
〖SS〗_T=〖SS〗A+〖SS〗(U/A)
SS_U/A
variance associated with the residual
SS_A
variance associated with the factor
MSu/A=
MSu/A=(SSu/A) / (∑nj-a)
~ E(MSu/A) expected MS from the chi-square sampling distribution
MSA =
MSA = (SSA) / (a-1)
~ E(MSA) expected MS from the chi-square sampling distribution
What are the 8 steps in answering an ANOVA question?
- Define a relationship
- State the purpose of ANOVA
- F ratio definition and construction (how this works at pop level)
- Sample ANOVA decomposition: calculate the sample level variance (sum of squares)
- Sample ANOVA decomposition: calculate the mean squares
- Sample ANOVA decomposition: estimate the expected mean squares
- Sample ANOVA decomposition: construct an If/Then link
- If we reject H0 then estimate omegaA (effect size)
What is the distribution that the ANOVA stat comes from?
F(a-1)(∑nj-a)
What is the ANOVA test statistic?
MSA/MSu/A
What is the grand mean?
The mean of all observations divided by the total sample size
