Correlation

Question 1

Why would we compute a partial correlation

Answer 1

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Question 2

Why would we compute a semi-partial correlation?

Answer 2

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Question 3

What’s the main difference between semi and partial correlation?

Answer 3

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Question 4

Which correlation is larger or further away from zero, and why?:

Answer 4

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Question 5

What kind of variables is X and Y in correlations?

Answer 5

X and Y variables in correlations is random- beyond the experimenter’s control and subject to sampling error in both.

Question 6

What is the goal of correlations?

Answer 6

To express the degree of relationship between X and Y.

Question 7

Define univariate information.

Provide an example.

Answer 7

Univariate information deals with 1 variable varying with itself. Not looking at the relationship between 2 variables yet.

We use the general sums of squares information (i,e., x vary with x; y vary with y).

Question 8

Explain the direction and strength of correlation.

Answer 8

It is bounded by -1 and +1. Zero indicates no relationship. The relationship gets larger in strength as we go from 0 to +1 or -1.

Question 9

Conceptually define SSCP - what does SSCP tell us?

Answer 9

We are taking the cross product of 2 deviations. It tells us how X and Y varies together.

Question 10

Conceptually define SS

Answer 10

It is the raw measure of variability.

The deviation of x times the deviation of x…

Question 11

Conceptually define covariance

Answer 11

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Question 12

Conceptually define variance and SD

Answer 12

Variance is the SS over df.

SD is the average deviation from the mean.

Question 13

What is the conceptual formula for pearson r?

Answer 13

r = degree to which X and Y vary together/degree of which X and Y vary individually

or

r = covariability of X and Y/variability of X and Y seperately

SSCPxy/sqrt of SSxSSy

Question 14

Why would we assess scatterplots before we access numbers?

Answer 14

Since pearson r doesn’t show curvilinear graphs, we look at scatterplots to show us the trend and outliers.

Question 15

What does pearson correlation measures specifically?

Answer 15

The degree of and direction of Linear Relationships between 2 variables.

Question 16

X is to predictor as Y is to

Answer 16

Y is to outcome

Question 17

Define bivariate

Answer 17

How variables vary with each other rather than separately.

Question 18

Looking at bivariate information, what indicates the positive or negative direction?

Why can’t the denominator of the correlation statistics be negative?

Answer 18

Looking at the bivariate information, the SSCP or (x-xbar)(y-ybar) indicates the + or - direction.

The denominator is always positive due to the square rooting of the SSx and SSy.

Question 19

In a pearson r correlation formula, what indicates the direction?

Answer 19

The SSCP. A positive SSCP = positive correlation, and negative SSCP = negative correlation.

Question 20

Why is correlations considered the standardized relationship?

Answer 20

Because it’s bounded by -1 and +1.

Question 21

Define covariance in regards to correlations.

Answer 21

Covariance is the stepping block to correlations - it is the unstandardized relationship between our 2 variables and also get variance along with relationship.

Question 22

Where in a matrix do we see covariance?

Answer 22

The off-diagonal values will be covariances and the diagonal values are variances.

Question 23

If the scatterplot looks about a football, what might the correlation be?

Answer 23

About .50.

Question 24

If the scatterplot looks like a wider football, what might the correlation be?

Answer 24

About .30… less correlation.

Question 25

What does the correlation effect size indicate? What is the notation? How is it interpreted?

Answer 25

little r squared = tells us the proportion in X that can be explained by Y. Ex: If r squared is .26, we would indicate that 26% of the number of doctor visits can be explained by attitudes of drug use.

Question 26

Correlations are standardized metrics and tells us how 2 variables are related to each other in a standardized way - we can calculate this correlation based on previously standardized information... what is this previously standardized information? And how will we get the scores?

Answer 26

Z-scores. We convert all of our x and y values into z-scores and we can just do covariance of the z-scores (ZxZy or SSCP) over n-1.

Question 27

Why is it important to calculate covariances (like z-scores)?

Answer 27

It is important to calculate a covariance that are unstandardized because in estimations, covariances are used. Just like computing sd, we start with variance and square root it to get the sd...

Question 28

What is the hypothesis testing notation for pearson correlation?

Answer 28

p = 0; no linear relationship p ≠ 0; there is a relationship

Question 29

What is the df for a correlations test? Why is this the case?

Answer 29

The df for r is n-2 because we have 2 means (a mean for x and a mean for y).

Question 30

What is n in a correlations test?

Answer 30

The number of individuals (rows).

Question 31

If the critical value is .632 and our r obtained is .51, do we reject or fail to reject the null?

Answer 31

We fail to reject the null.

Question 32

Why would sample size affect the strength of a correlation?

Answer 32

It could be not powerful enough to detect the correlation. The larger the n, the smaller the critical value number.

Question 33

What is the statistical sentence for pearson correlation if n = 10, df = 8, r = .51, CV = .632.

Answer 33

r (df) = .51, p >.05 r (8) = .51, p >.05 We fail to reject the null

Question 34

In a covariance, does a large number indicate the magnitude of the relationship?

Answer 34

No, it doesn't indicate strength, just the direction (pos. or neg.), because covariances are unbounded (there's nothing to compare the magnitude to).

Question 35

What does a covariance near zero indicate? What does a correlation near zero indicate?

Answer 35

They both indicate there is no linear relationship. However, a correlation near zero doesn't mean there isn't a relationship at all... just no LINEAR relationship.

Question 36

Restricting the range of data (removing extremes) will do what to a correlational scatterplot? In real life application, when would this happen?

Answer 36

The correlation or the degree of relationship gets weaker, smaller. If we restrict age for example, like only getting college kids instead of 25 to 70 y.o.

Question 37

What's wrong with selecting for extremes in a correlation?

Answer 37

Researchers take the mid-point and say anything above or lower is too high or too low and dichotomize continuos variables - artificially inflating the relationship and with the low group and high group on the continuos measure, they attempt to do t-tests that are easier to interpret by the masses... but really, just to get a significant correlation.

Question 38

What happens when a value is extreme on X and extreme on Y?

Answer 38

It is artificially inflated and makes the correlation much stronger (an outlier).

Question 39

What happens when a value is extreme on Y but in the middle of X?

Answer 39

The correlation decreases - reduced the relationship.

Question 40

How does trend of the base model affect the relationship due to an outlier?

Answer 40

If an outlier is near the trend of the base model (i.e., if my base model is headed into a positive direction), and the outlier on x is also in a positive direction relative to the trend, it will barely affect the model in a positive direction. However, if the trend is positive, but the outlier on x is negative, it brings the base model down by a lot. (pg 11).

Question 41

What is the diagonals of correlation matrix?

Answer 41

1s... a variable that is correlated with itself is 1.

Question 42

If I'm asked to compute the variance of x, what will I do?

Answer 42

I am essentially solving for x-xbar squared, so I will need to compute the mean of the observations, then solve for the sum of squares and divide it by n-1.