Chapter 6

Question 1

Correlational Study

Answer 1

Examines the relationship between 2 or more measured variables (not manipulated or controlled by experimenter)

Question 2

Correlation

Answer 2

Statistical technique used to measure and describe the relationship between 2 variables

You can correlate any two variables as long as they are numerical (meaning they can be represented by numbers)

Question 3

Why do we use a correlation coefficient?

Answer 3

It is used to make a prediction (if two variables are related, we can use one variable to predict the other; example: SAT scores and college success)
To measure reliability (Test-retest, alternate forms; example: is that dependable friend going to pick you up at 2am at the airport)
To measure validity (Are the two variables really related?; example: SAT and ACT scores related to college grades)

BUT. IT IS NOT A MEASURE OF CAUSALITY

Question 4

All correlations range from? And what does this number mean?

Answer 4

-1.00 to +1.00

This absolute value shows strength of relationship
Higher the absolute number, the stronger the relationship

Question 5

What is perfect correlation?

Answer 5

+/- 1.00 is the strongest possible relationship

The graph of a perfect correlation is just one straight line

Question 6

What does the sign of the correlation tell you?

Answer 6

It tells us the directionality of the relationship of any two variables, X and Y

If the sign is positive: (the variables change in the same direction)
As X is increasing, Y is increasing
As X is decreasing, Y is decreasing

If the sign is negative: (the variables change in opposite directions)
As X is increasing, Y is decreasing
As X is decreasing, Y is increasing

Question 7

What is the correlation coefficient?

Answer 7

r, it is reflected by a spread. The fatter the oval the lower the correlation

Question 8

What kind of line will r have if it equals zero?

Answer 8

It will be horizontal, because there is no correlation

Question 9

Pearson correlation coefficient

Answer 9

r= the Pearson coefficient
r measures the amount that the 2 variables (X&Y) vary together taking into account how much they vary apart
It is a ratio

r= (degree to which X and Y vary together) / (degree to which X and Y vary separately)

Question 10

Sum of Products of Deviations (SP)

Answer 10

Definitional Formula
SP= The sum of (X-X bar)(Y-Y bar)
Computational Formula
SP= The sum of XY - ((sum of x, times the sum of Y) / n)
N is the number of (X,Y) pairs

Question 11

r squared

Answer 11

percentage of variance in Y accounted for by X

This ranges from 0 to 1 (POSITIVE ONLY)
you can not have a negative percentage, because squaring anything is positive

This number is a meaningful proportion (unlike the Pearson’s r)
It has a similar idea to effect size

Question 12

What are the limitations of Pearson’s r?

Answer 12

1. Correlation does not mean causation
2. Strength of the relationship
   (Pearson’s doesn’t give directly interpretable strength of relationship, the r squared (coefficient of determination ))
   3.Outliers (extreme scores)
   (scores with extreme X and/or Y value can drastically effect Pearson’s r)
3. Restriction of range
   (restricted range of measured values can lead to inaccurate conclusions about the data;
   finding no correlation when there really isn’t one
   finding a correlation when there really is one)

Question 13

What is regression?

Answer 13

Fitting a line to the data using an equation in order to describe and predict data

Question 14

Simple regression

Answer 14

Uses just two variables (x and y)

Question 15

Multiple regression

Answer 15

one y and many x’s. You’re still predicting one outcome, but comparing it to multiple causations
Multiple regression has a lot more external validity. Meaning that It is most comparable to the real world.

Question 16

Linear regression

Answer 16

fits data to a straight line

Question 17

Curvilinear regression

Answer 17

involves using geometry AND calculus to come up with a solution

Question 18

From geometry we know:

Answer 18

That we can describe any line by an equation
Slope = change in Y per unit change in x
y intercept = where line crosses the Y axis (when X = 0)
statistics notation : y hat = bX + a,
it is like y = mx + b

Question 19

Y hat

Answer 19

Is the predicted value of Y, given a certain value of X

Question 20

Strong, moderate, weak correlation?

Answer 20

Strong= 0.8
Moderate= 0.4
Weak= 0.2

Question 21

What does r = 0.0 look like?

Answer 21

The best fit line is a horizontal line. And dots are basically everywhere

Question 22

What is the Pearson Correlation Coefficient?

Answer 22

It is r.
It measures the amount that the two variables (X and Y) vary together taking into account how much they vary apart.

r= (degree to which X and Y vary together) / (degree to which X and Y vary separately)

Question 23

Standard Error of the Estimate

Answer 23

It is an estimate of how consistent it would be if we resampled over and over again. The amount of sampling variation there would be for Beta (slope).

Example:

If SE(B) = 0.2 and (B) by itself is 1. Then B is 5 standard errors away from zero. That means B = 1 is pretty far away from zero.