Chapter 6: Correlation and Predicted Variance

Question 1

Relationships in statistics are looked at for what three reasons?

Answer 1

• comparison of different distributions - determining causality - psychometric properties of questionnaires

Question 2

Correlations? (4)

Answer 2

• interested in relationship not magnitude of one over the other.. - one variable carries information about another variable - easy first step in determining causality but there has to be a correlation - Correlations do not = CAUSATION. ever.

Question 3

When constructing a scatter what is being graphed?

Answer 3

X and Y data points….

Question 4

Linear relationships? What the heck are they?

Answer 4

• straight line…what we are interested in!

Question 5

Curve relationship?

Answer 5

• not interested in this - BAD…..they are bias..

Question 6

Describe a positive relationship?

Answer 6

• each variable is increasing together - correlation is evident - direct

Question 7

Describe a negative relationship?

Answer 7

• one variable is increasing while the other is decreasing… -inverse

Question 8

Describe a perfect relationship ? Are they common?

Answer 8

• all data points fall exactly on the line - not very common

Question 9

Describe an imperfect relationship? Are they common?

Answer 9

• all data points do not fall on the line - still linear -very common -line of best fit/ regression line L> basically a mean….points around it = variance…

Question 10

Correlation part 2 yo

Answer 10

• family of statistical tests that quantify the relationship between the variables….

Question 11

Correlation coefficient what the heck is that?

Answer 11

single # that summarizes the relationship of two variables.. ranges from +1.00 to - 1.00 L> signs only indicate direction….both are equally as strong correlations

Question 12

Characteristics of Correlation coefficient? most common correlation coefficient values?

Answer 12

• zero = very weak/ no relationship - + correlation = with every one unit increase there is a proportional increase in another variable..and vise versa - -0.5- + 0.5

Question 13

Describe the Pearson r Correlation Coefficient.. how does it get around the issue of varying units?

Answer 13

• extent that paired scores occupy the same or opposite positions within their distributions…. - convert data into z score…so no unit score issue…

Question 14

What is the raw score Pearson r Formula?? What does each part represent?

Answer 14

Question 15

Variability of Y can be explained by?

Answer 15

• X

Question 16

When r= 0 the best predictor of Y is the _____ of the y scores.. What are the erros associated with this?

Answer 16

• mean, imperfection in prediction…

Question 17

When r does not equal 0 the best predictor of Y is ____. Prediction errors?

Answer 17

• X
• when x is a predictor the error goes down significantly

Question 18

The total deviation of score is divisible into two parts..what are they?

Answer 18

1. the distance from the regression line to the mean line = deviation accounted for by X (A)
2. The distance from the regression line to the point in question….prediction error (B)

A+B= deviation of score

Question 19

The deviation of Y_i

is what??

Answer 19

prediction error + deviation of Yi accounted for by X

Question 20

The total variablilty of Y ?

Answer 20

Variability of prediction errors + variability of Y accounted for by x

Question 21

When correlation goes up the variability of prediction errors goes _____, variability of Y accounted for by Y _____.

Answer 21

-decreases, increases

Question 22

When r= 0 the variability of P.errors = ________. Variability of Y accounted for x =___?

Answer 22

-min variable, none

Question 23

When r= 1.00 Variability of P.errors = _____ and the variability of Y accounted for by x ____.

The greater x is = ___ proportion of Y is accounted for

Answer 23

• none, maximum
• greater

Question 24

Explained variance? Explain it ! (4)

Answer 24

• r= correlation coefficient

L> magnitude and direction of relationship

• r = coefficient of determination

L>proportion of total variability in Y accounted for by x…

Question 25

Describe the Explained Variance table…

Answer 25

r r²

0.10 1

.20 4

0. 30 9
1. 40 16
2. 50 25
3. 60 36
4. 70 49
5. 80 64
6. 90 81
7. 00 100

1, 9 and 16 are the most common in the behavioural sciences

25, 36 are large correlations

49, approx 1/2 variance

64, 81 and 100 are rarely seen ever…more so in psychometrics..

Question 26

Issues with a curve shaped graph?? GO

Answer 26

r values cancel each other out

magnitude of correlation is severly reduced….

ex: performance in anxiety

Question 27

Describe the following coefficients !

Pearson r

Biserial rb

Spearman rank order rho

Phi ro

Answer 27

• 2 interval/ or ratio
• one interval/ratio and one dichotomous
• 1 or both = ordinal
• 2 dichotomous

Question 28

Phi coefficient??

|A|B|

|C|D|

formula?

Answer 28

AD-BC/ >/ (A+B)(C+D)(A+C)(B+D)

>/ = square root

Question 29

With the phi coefficient everything is related to ____

Answer 29

A

Question 30

What are the three issues with correlations?

Answer 30

• restricted ranges : reduces magnitude of correlation…reducing variability
• outliers: increases magnitude
• correlation does not equal causation