CORRELATION AND INFERENCE

Question 1

CORRELATION AND INFERENCE

Answer 1

Concept of Correlation

Pearson r

Spearman Rho

Graphic Representations of Correlation

Meta-Analysis

Question 2

a number that provides

us with an index of the strength of the relationship between two things.

Answer 2

coefficient of correlation

Question 3

an expression of the degree and direction of correspondence between
two things.

Answer 3

correlation

Question 4

expresses a linear relationship between two (and only
two) variables,

continuous in nature

reflects the degree of concomitant variation
between variable X and variable Y

numerical index that
expresses this relationship: It tells us the extent to which X and Y are “co-related.”

Answer 4

coefficient of correlation (r)

Question 5

If asked to supply information about its magnitude, it would respond with a
number anywhere at all between

Answer 5

−1 and +1

Question 6

If two variables simultaneously increase or simultaneously

decrease, then those two variables are

Answer 6

positively (or

directly) correlated.

Question 7

occurs

when one variable increases while the other variable decreases

Answer 7

negative (or inverse) correlation

Question 8

absolutely no relationship exists

between the two variables.

Answer 8

correlation is zero

Question 9

third variety of perfect correlation; that

is, a perfect noncorrelation.

Answer 9

“perfectly

no correlation”

Question 10

does not imply causation, but there is an implication of prediction.

Answer 10

correlation

Question 11

if we know that there is a high correlation between X and Y…

Answer 11

able to predict—with various degrees of accuracy, depending on other factors—the value of
one of these variables if we know the value of the other.

Question 12

known as the Pearson correlation coefficient and the Pearson product-moment
coefficient of correlation.

Karl Pearson

Answer 12

Pearson r

Question 13

statistical tool
of choice when the relationship between the variables is linear

when the two variables
being correlated are continuous

Answer 13

r

Question 14

calculate a Pearson r

Answer 14

r = Σ(X − X)(Y− Y)
√[Σ(X − X)2[Σ(Y − Y)2]

convert each raw score to a standard score and then multiply each pair of standard scores

Question 15

simplified Pearson r

Answer 15

r = Σxy

√(Σx2)(Σy2)

Question 16

Another formula for calculating a Pearson r

Answer 16

r = NΣXY -(ΣX)(ΣY)
√NΣX2 - (ΣX)2√NΣY2−(ΣY)2

N - number of paired scores

Σ XY -sum of the product
of the paired X and Y scores

Σ X - sum of the X scores

Σ Y - sum of the Y scores

Σ X2 - sum of the squared X scores

Σ Y2 - sum of the squared Y scores

Question 17

r2

indication of how much variance is shared by the X- and the Y-variables

Answer 17

coefficient of determination

Question 18

calculation

of r2

Answer 18

square the correlation coefficient and multiply by 100;

the result is equal to the percentage of the variance accounted for.

Question 19

moment describes a deviation about a mean of a

distribution

Answer 19

product-moment coefficient of correlation

Question 20

Individual deviations about the mean of a distribution

referred to as the first moments of the distribution

Answer 20

deviates

Question 21

second moments of the

distribution

Answer 21

moments squared

Question 22

third moments of the distribution

Answer 22

moments

cubed, and so forth

Question 23

called a rank-order correlation
coefficient, a rank-difference correlation coefficient

Charles Spearman

Answer 23

Spearman Rho

Question 24

used when the sample size is small (fewer than 30 pairs of measurements)

when both sets of measurements are in ordinal (or rank-order) form.

Answer 24

Spearman’s rho

Question 25

Graphic Representations of Correlation

Answer 25

bivariate distribution

scatter diagram

scattergram

scatterplot.

Question 26

a simple graphing of the coordinate points for values of the X-variable
(horizontal axis) and the Y-variable (
vertical axis)

provide a quick indication of the direction
and magnitude of the relationship, if any, between the two variables.

Figures 3–13 and 3–14

Answer 26

scatterplot

Question 27

distinguish positive from negative correlations, note the direction of the curve.

estimate the strength of magnitude of the correlation, note the degree to which the points
form a straight line.

Answer 27

scatterplot

Question 28

“eyeball gauge” of how curved
a graph is.

graph does not appear to take the form of a straight line, the chances
are good that the relationship is not linear

Figure 3–15

Answer 28

curvilinearity

Question 29

an extremely
atypical point located at a relatively long distance—an outlying distance—from the rest of the
coordinate points in a scatterplot

(Figure 3–16)

Answer 29

outlier

Question 30

a family of techniques used to statistically combine
information across studies to produce single estimates of the data under study.

facilitates
the drawing of conclusions and the making of statements like, “the typical therapy client is
better off than 75% of untreated individuals”

Answer 30

Meta-Analysi

Question 31

typically expressed as a correlation coefficient.

Answer 31

effect size

Question 32

advantages

to meta-analyses

Answer 32

can be replicated

conclusions of meta-analyses
tend to be more reliable and precise than the conclusions from single studies

more
focus on effect size rather than statistical significance alone

promotes
evidence-based practice

Question 33

professional practice that is based on clinical

and research findings

Answer 33

evidence-based practice