Final session 11a

Question 1

what are Two of the most versatile approaches for investigating variable relationships

Answer 1

Correlation analysis Regression analysis

Question 2

Both regression-based methods and ANOVA are subsumed by what

Answer 2

the general linear model

Question 3

Regression-based methods subsume ANOVA, ANCOVA, etc.

This means that what

Answer 3

ANOVA models can be done in a regression analysis framework

The language and notation used to describe ANOVA is just different

Question 4

what are ANOVA-based methods

Answer 4

Categorical independent variables (IVs):
Only interactions among categorical IVs are allowed

Continuous “covariates” can be added as IVs (ANCOVA)

Question 5

explain Regression-based methods

Answer 5

Categorical and/or continuous IVs

Interactions among both types of IVs are possible

Question 6

how many DV are in regression-based and ANOVA-based methods

Answer 6

just 1

Question 7

A scatterplot shows what

Answer 7

the relationship between two quantitative variables measured on the same individuals

Question 8

scatterplots It helps us understand the . . .

Answer 8

Form (linear or nonlinear?) Direction (positive or negative?)
Strength (none, weak, strong?)

of the relationship

Question 9

A scatterplot is a graphical display of the relationship between what

Answer 9

two quantitative variables

The relationship examined by our eyes may not be satisfactory in many cases

Question 10

what often supplement the scatterplot graph

Answer 10

Numerical measures often supplement the graph Example: Correlation

Question 11

The Pearson correlation measures what

Answer 11

the direction and strength of the linear relationship between two quantitative variables
Pearson correlation coefficient (r)

Question 12

The Pearson correlation coefficient is a what

Answer 12

standardized covariance

Question 13

Covariance indicates what

Answer 13

how much X and Y vary together

Question 14

Interpreting Covaraince:

Cov(X, Y ) > 0:

Answer 14

X and Y tend to move in the same direction

If X and Y tend to increase (or decrease) together → positive

Question 15

Interpreting Covaraince:

Cov(X, Y ) < 0:

Answer 15

X and Y tend to move in opposite directions

If X increases when Y decreases → negative

Question 16

Interpreting Covaraince:

Cov(X, Y ) = 0

Answer 16

X and Y are independent
Otherwise, the size of the covariance is difficult to interpret

It depends on the scales (or units, or variances) of X and Y

Question 17

Pearson correlation coefficient (r) Compute from what

Answer 17

covariances and variances

Question 18

is the Correlation coefficient sensitive to the units of X and Y

Answer 18

Not sensitive to the units of X and Y

Rescaling X and Y does not change the correlation between them

Question 19

The Pearson correlation coefficient can be understood as the what

Answer 19

Covariance between z-scores for X and Y :

Question 20

for correlation, explain The closer to −1,

Answer 20

the stronger the negative linear relationship

Question 21

for correlation, explain The closer to 1,

Answer 21

the stronger the positive linear relationship

Question 22

for correlation, explain The closer to 0,

Answer 22

the weaker any linear relationship

Question 23

does correlation indicate causation

Answer 23

Correlation does NOT indicate any causal relationship among variables

Question 24

True of false: A strong correlation between two variables does not mean that changes
in one variable cause changes in the other

Answer 24

true

Question 25

what is the best way to establish causality

Answer 25

Experiments with random assignment to experimental condition are the best way to establish causality

Question 26

give the hypotheses for Statistical test for significance of correlation

Answer 26

H0 : ρ = 0
ρ - Population correlation, “rho”
No linear association between two variables
When the two variables are both normally distributed, they are independent

H1 :ρ̸=0
There is more than one way to do hypothesis testing for correlations
Unlike sample means, r does NOT in general have a normal sampling distribution

Question 27

Traditional approaches assume that the population distributions for the two variables are what

Answer 27

jointly normal (bivariate normality)

Question 28

One way to test for significance in correlation coefficient is what

Answer 28

involves a t-test
IfH0 :ρ=0,at-testwithdf=N−2canbeformed
This is how SPSS does significance testing

Question 29

If we want a confidence interval (CI) in correlation coefficient how to do

Answer 29

Fisher z transformation
r → zr
Form a CI around zr
Transform the lower and upper bounds of zr back to the correlation metric

Question 30

give the steps to find Confidence interval

Answer 30

Fisher z transformation
Compute CI for zr
Transform each CI boundary back to r metric (use boundary in place of zr)

Question 31

do you ned to calculate effect size for correlation coefficient

Answer 31

is already an effect size
Some will use r2, and instead capitalize it, R2
-Proportion of shared variance between X and Y
-Similar effect sizes will be used in regression analysis

Question 32

explain hw correlation treats linear regression

Answer 32

Correlation treats two variables X and Y as equals

There is no distinction between predictor and outcome, IV and DV

Question 33

In many cases we want to predict one variable from another (correlation linear regression) explain

Answer 33

Usually we construct a model in which one variable (X) predicts the other variable (Y)
X - usually the IV or predictor variable
Y - usually the DV or outcome variable

Question 34

Linear Regression describes what

Answer 34

Describes how the DV (Y) changes as a single independent variable (X) changes

If there is only one IV, it is called ‘simple’ linear regression analysis Summarizes the relationship between two variables if the form of the relationship is linear

Question 35

Linear Regression is often used as what

Answer 35

a mathematical model to predict the value of the DV (Y) based on a value of an IV (X)

Question 36

what do we do In linear regression. .

Answer 36

We “fit a straight line” that best describes the linear relationship between X and Y

Question 37

The equation of a line fitted to data gives what

Answer 37

a compact description of the dependency of the DV on the IV

It is a mathematical model for the straight-line relationship Called a regression line

Question 38

what is the equation for slope of line

Answer 38

Straight line relating Y to X has an equation of the form:

Yˆ = b 0 + b 1 X

Question 39

explain the parts to the equation Yˆ = b 0 + b 1 X

Answer 39

b0 = intercept
Where the regression
line crosses the Y-axis (at X=0)
Mean or expected value of DV (Y) when IV (X) is zero

b1 = slope
Change in predicted
value for Y for every one unit increase in X “Rise / run”

Yˆ = “y hat”
Predicted value of Y
Straight line that best explains X and Y relationship