CORRELATION AND INFERENCE Flashcards
CORRELATION AND INFERENCE
Concept of Correlation
Pearson r
Spearman Rho
Graphic Representations of Correlation
Meta-Analysis
a number that provides
us with an index of the strength of the relationship between two things.
coefficient of correlation
an expression of the degree and direction of correspondence between
two things.
correlation
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.”
coefficient of correlation (r)
If asked to supply information about its magnitude, it would respond with a
number anywhere at all between
−1 and +1
If two variables simultaneously increase or simultaneously
decrease, then those two variables are
positively (or
directly) correlated.
occurs
when one variable increases while the other variable decreases
negative (or inverse) correlation
absolutely no relationship exists
between the two variables.
correlation is zero
third variety of perfect correlation; that
is, a perfect noncorrelation.
“perfectly
no correlation”
does not imply causation, but there is an implication of prediction.
correlation
if we know that there is a high correlation between X and Y…
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.
known as the Pearson correlation coefficient and the Pearson product-moment
coefficient of correlation.
Karl Pearson
Pearson r
statistical tool
of choice when the relationship between the variables is linear
when the two variables
being correlated are continuous
r
calculate a Pearson r
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
simplified Pearson r
r = Σxy
√(Σx2)(Σy2)
Another formula for calculating a Pearson r
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
r2
indication of how much variance is shared by the X- and the Y-variables
coefficient of determination
calculation
of r2
square the correlation coefficient and multiply by 100;
the result is equal to the percentage of the variance accounted for.
moment describes a deviation about a mean of a
distribution
product-moment coefficient of correlation
Individual deviations about the mean of a distribution
referred to as the first moments of the distribution
deviates
second moments of the
distribution
moments squared
third moments of the distribution
moments
cubed, and so forth
called a rank-order correlation
coefficient, a rank-difference correlation coefficient
Charles Spearman
Spearman Rho
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.
Spearman’s rho
Graphic Representations of Correlation
bivariate distribution
scatter diagram
scattergram
scatterplot.
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
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
“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
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
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
typically expressed as a correlation coefficient.
effect size
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
professional practice that is based on clinical
and research findings
evidence-based practice
