CORRELATION AND INFERENCE Flashcards

1
Q

CORRELATION AND INFERENCE

A

Concept of Correlation

Pearson r

Spearman Rho

Graphic Representations of Correlation

Meta-Analysis

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2
Q

a number that provides

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

A

coefficient of correlation

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3
Q

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

A

correlation

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4
Q

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.”

A

coefficient of correlation (r)

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5
Q

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

A

−1 and +1

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6
Q

If two variables simultaneously increase or simultaneously

decrease, then those two variables are

A

positively (or

directly) correlated.

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7
Q

occurs

when one variable increases while the other variable decreases

A

negative (or inverse) correlation

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8
Q

absolutely no relationship exists

between the two variables.

A

correlation is zero

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9
Q

third variety of perfect correlation; that

is, a perfect noncorrelation.

A

“perfectly

no correlation”

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10
Q

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

A

correlation

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11
Q

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

A

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.

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12
Q

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

Karl Pearson

A

Pearson r

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13
Q

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

when the two variables
being correlated are continuous

A

r

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14
Q

calculate a Pearson r

A

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

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15
Q

simplified Pearson r

A

r = Σxy

√(Σx2)(Σy2)

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16
Q

Another formula for calculating a Pearson r

A

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

17
Q

r2

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

A

coefficient of determination

18
Q

calculation

of r2

A

square the correlation coefficient and multiply by 100;

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

19
Q

moment describes a deviation about a mean of a

distribution

A

product-moment coefficient of correlation

20
Q

Individual deviations about the mean of a distribution

referred to as the first moments of the distribution

21
Q

second moments of the

distribution

A

moments squared

22
Q

third moments of the distribution

A

moments

cubed, and so forth

23
Q

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

Charles Spearman

A

Spearman Rho

24
Q

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.

A

Spearman’s rho

25
Graphic Representations of Correlation
bivariate distribution scatter diagram scattergram scatterplot.
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
scatterplot
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.
scatterplot
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
curvilinearity
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)
outlier
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”
Meta-Analysi
31
typically expressed as a correlation coefficient.
effect size
32
advantages | to meta-analyses
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
33
professional practice that is based on clinical | and research findings
evidence-based practice