Wk 12 - Regression 1

Question 1

How do we assess the association/effect for chi-square? (x1)

Answer 1

By calculating Cramer’s phi

Question 2

Why do we convert the value of r in order to compare correlations for two independent groups? (x2)
(tip - what is the difference between null of r = o, and r = some other number)

Answer 2

Because if the null is that correlations are equal, or that rho = particular number, the sampling distribution becomes skewed
Whereas for significance of r, the null is normal distribution around r = 0 (there is no relationship between variables)

Question 3

What factors affect the magnitude of correlations? (x4)

Answer 3

Nonlinear relationships - eg curvilinear (u-shapes)
Restriction of range - not including full range of possible scores
Presence of extreme scores - big impact of outliers
Heterogenous subsamples - combination of data that could be distinctly separated, eg age-groups

Question 4

What is bivariate regression analysis? (x1)

Answer 4

Predicting the criterion (y) from the predictor (x)

Question 5

What is the least squares criterion? (x2)

Answer 5

Is for the line of best fit/regression line -

So it has minimum squared distance from all data points

Question 6

What is the formula of the regression line? (the regression equation)

Answer 6

Yhat = bx + a

Question 7

What do a, b and y-hat represent?

Answer 7

a = y-intercept
b = slope (rate at which y changes for every unit of x)
y-hat = the predicted value of y for a given x

Question 8

What are the effect-size tests for...
t-tests
ANOVA
Correlation
Chi-square

Answer 8

Cohen’s d
Omega square
r square
Cramer’s phi

Question 9

What is Cramer’s phi? (x1)

Steps for calculating for r by c tables… (x3)

Answer 9

The measure of association for chi-square, that tells us how big the effect is
Divide chi-square by N(k - 1), where k = smaller of r or c
Take the root of that
Interpret according to Cohen’s conventions

Question 10

What are Cohen’s conventions for interpreting Cramer’s phi? (x3)

Answer 10

Small are around .08
Medium are around .23
Larger are around .40

Question 11

What does squaring Cramer’s phi tell us? (x1)

Answer 11

The proportion of variance accounted for in a chi-square test

Question 12

How do we convert the value of r in order to compare correlations for two independent groups? (x1)

Answer 12

By using Fisher’s tables of r’ transformations

Question 13

What are residuals (in terms of regression)? (x1)

And how are they calculated? (x2)

Answer 13

The errors left over from predictions
e = y - y-hat
error for one data point = person’s real score - the predicted

Question 14

What is the standard error of the estimate? (x1)
When is it used? (x1)
And how calculated? (x1)

Answer 14

The average error of the regression line in predicting y from x
After calculating the regression equation
Sy .x formula given in sheet

Question 15

How is a calculated for the regression equation?

Answer 15

a = mean of y - (b times the mean of x)

Question 16

How is b calculated for the regression equation? (x3 methods)
And choice depends on…

Answer 16

Use the sums of products, SPxy, and SSx from data table
Covariance divided by the variance of x
r times the (standard deviation of y over the standard deviation of x)
Whether given raw scores, the covariance and standard deviations, or r and the standard devs