Final session 11a Flashcards

1
Q

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

A

Correlation analysis Regression analysis

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2
Q

Both regression-based methods and ANOVA are subsumed by what

A

the general linear model

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3
Q

Regression-based methods subsume ANOVA, ANCOVA, etc.

This means that what

A

ANOVA models can be done in a regression analysis framework

The language and notation used to describe ANOVA is just different

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4
Q

what are ANOVA-based methods

A

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

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

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5
Q

explain Regression-based methods

A

Categorical and/or continuous IVs

Interactions among both types of IVs are possible

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6
Q

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

A

just 1

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7
Q

A scatterplot shows what

A

the relationship between two quantitative variables measured on the same individuals

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8
Q

scatterplots It helps us understand the . . .

A

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

of the relationship

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9
Q

A scatterplot is a graphical display of the relationship between what

A

two quantitative variables

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

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10
Q

what often supplement the scatterplot graph

A

Numerical measures often supplement the graph Example: Correlation

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11
Q

The Pearson correlation measures what

A

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

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12
Q

The Pearson correlation coefficient is a what

A

standardized covariance

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13
Q

Covariance indicates what

A

how much X and Y vary together

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14
Q

Interpreting Covaraince:

Cov(X, Y ) > 0:

A

X and Y tend to move in the same direction

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

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15
Q

Interpreting Covaraince:

Cov(X, Y ) < 0:

A

X and Y tend to move in opposite directions

If X increases when Y decreases → negative

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16
Q

Interpreting Covaraince:

Cov(X, Y ) = 0

A

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

17
Q

Pearson correlation coefficient (r) Compute from what

A

covariances and variances

18
Q

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

A

Not sensitive to the units of X and Y

Rescaling X and Y does not change the correlation between them

19
Q

The Pearson correlation coefficient can be understood as the what

A

Covariance between z-scores for X and Y :

20
Q

for correlation, explain The closer to −1,

A

the stronger the negative linear relationship

21
Q

for correlation, explain The closer to 1,

A

the stronger the positive linear relationship

22
Q

for correlation, explain The closer to 0,

A

the weaker any linear relationship

23
Q

does correlation indicate causation

A

Correlation does NOT indicate any causal relationship among variables

24
Q

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

25
what is the best way to establish causality
Experiments with random assignment to experimental condition are the best way to establish causality
26
give the hypotheses for Statistical test for significance of correlation
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
27
Traditional approaches assume that the population distributions for the two variables are what
jointly normal (bivariate normality)
28
One way to test for significance in correlation coefficient is what
involves a t-test IfH0 :ρ=0,at-testwithdf=N−2canbeformed This is how SPSS does significance testing
29
If we want a confidence interval (CI) in correlation coefficient how to do
Fisher z transformation r → zr Form a CI around zr Transform the lower and upper bounds of zr back to the correlation metric
30
give the steps to find Confidence interval
Fisher z transformation Compute CI for zr Transform each CI boundary back to r metric (use boundary in place of zr)
31
do you ned to calculate effect size for correlation coefficient
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
32
explain hw correlation treats linear regression
Correlation treats two variables X and Y as equals | There is no distinction between predictor and outcome, IV and DV
33
In many cases we want to predict one variable from another (correlation linear regression) explain
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
34
Linear Regression describes what
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
35
Linear Regression is often used as what
a mathematical model to predict the value of the DV (Y) based on a value of an IV (X)
36
what do we do In linear regression. .
We “fit a straight line” that best describes the linear relationship between X and Y
37
The equation of a line fitted to data gives what
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
38
what is the equation for slope of line
Straight line relating Y to X has an equation of the form: | Yˆ = b 0 + b 1 X
39
explain the parts to the equation Yˆ = b 0 + b 1 X
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