Final session 11a Flashcards
what are Two of the most versatile approaches for investigating variable relationships
Correlation analysis Regression analysis
Both regression-based methods and ANOVA are subsumed by what
the general linear model
Regression-based methods subsume ANOVA, ANCOVA, etc.
This means that what
ANOVA models can be done in a regression analysis framework
The language and notation used to describe ANOVA is just different
what are ANOVA-based methods
Categorical independent variables (IVs):
Only interactions among categorical IVs are allowed
Continuous “covariates” can be added as IVs (ANCOVA)
explain Regression-based methods
Categorical and/or continuous IVs
Interactions among both types of IVs are possible
how many DV are in regression-based and ANOVA-based methods
just 1
A scatterplot shows what
the relationship between two quantitative variables measured on the same individuals
scatterplots It helps us understand the . . .
Form (linear or nonlinear?) Direction (positive or negative?)
Strength (none, weak, strong?)
of the relationship
A scatterplot is a graphical display of the relationship between what
two quantitative variables
The relationship examined by our eyes may not be satisfactory in many cases
what often supplement the scatterplot graph
Numerical measures often supplement the graph Example: Correlation
The Pearson correlation measures what
the direction and strength of the linear relationship between two quantitative variables
Pearson correlation coefficient (r)
The Pearson correlation coefficient is a what
standardized covariance
Covariance indicates what
how much X and Y vary together
Interpreting Covaraince:
Cov(X, Y ) > 0:
X and Y tend to move in the same direction
If X and Y tend to increase (or decrease) together → positive
Interpreting Covaraince:
Cov(X, Y ) < 0:
X and Y tend to move in opposite directions
If X increases when Y decreases → negative
Interpreting Covaraince:
Cov(X, Y ) = 0
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
Pearson correlation coefficient (r) Compute from what
covariances and variances
is the Correlation coefficient sensitive to the units of X and Y
Not sensitive to the units of X and Y
Rescaling X and Y does not change the correlation between them
The Pearson correlation coefficient can be understood as the what
Covariance between z-scores for X and Y :
for correlation, explain The closer to −1,
the stronger the negative linear relationship
for correlation, explain The closer to 1,
the stronger the positive linear relationship
for correlation, explain The closer to 0,
the weaker any linear relationship
does correlation indicate causation
Correlation does NOT indicate any causal relationship among variables
True of false: A strong correlation between two variables does not mean that changes
in one variable cause changes in the other
true
what is the best way to establish causality
Experiments with random assignment to experimental condition are the best way to establish causality
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
Traditional approaches assume that the population distributions for the two variables are what
jointly normal (bivariate normality)
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
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
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)
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
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
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
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
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)
what do we do In linear regression. .
We “fit a straight line” that best describes the linear relationship between X and Y
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
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
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
