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Mathematically, the square root of the reliability of a test
will set the upper limit of
the validity coecient of a test. So if a test has a relatively
low reliability of .64, the
maximum correlation that the test could have with any criteria
is .8. he point is
that while a test can be reliable but not valid for a particular
use, a test cannot be
valid for any use if the scores are very unreliable.
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"ere we illustrate how to determine whether a correlation
coecient is si#ni$cant
%evidence of a true relationship& or not si#ni$cant %no
relationship&. 'et(s say that
we have collected data from )* students. +e have #iven the
students a test of
verbal achievement, and we have correlated students( scores with
their #rades from
a course on creative writin#. he resultin# correlation coecient
is .4.
+e now #o to the table of critical values for -earson
productmoment correlation
coecients in /ppendix 0. he table shows the de#rees of freedom
%df& and alpha
%a& levels for two1tailed and one1tailed tests.
-sycholo#ists usually set their alpha
level at chances out of 2** %p 3 .*& usin# a two1tailed
test, so we use that
standard for our example. ecause we used the data from )*
students in our
sample, we substitute )* for 5 in the formula for de#rees of
freedom %df ! 5 )&.
herefore, df ! )* ) or 28.
+e then #o to the table and $nd 28 in the df column. inally, we
locate the criticalvalue in that row under the .* column. / portion
of the table from /ppendix 0 is
reproduced in the table below showin# the alpha level for a
twotailed test. he
critical value of .4478 %bolded in the table& is the one we
use to test our correlation.
ecause our correlation %.4& is #reater than the critical
value %.4478&, we can infer
that the probability of $ndin# our correlation by chance is less
than chances out of
2**. herefore, we assume that there is a true relationship and
refer to the
correlation coecient as si#ni$cant. 5ote that if we had set our
alpha level at a
more strin#ent standard of .*2 %2 chance out of 2**&, our
correlation coecient
would have been interpreted as not si#ni$cant. ritical 9alues
for -earson -roduct
Moment orrelation oecients : ; S0? rom Statistical ables for
iolo#ical,
/#ricultural and Medical >esearch by >./. isher and .
:ates. opyri#ht [email protected] by -earson 0ducation 'imited.
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D +hen a relationship can be established between a test and
a criterion, the test
scores can be used to predict how well individuals are liEely to
perform on the
criterion.
D 'inear re#ression is used to maEe predictions from scores from
one test.
D he slope b %the expected chan#e in one unit of : for every
chan#e in F& and the
intercept a %the point where the re#ression line crosses the
y1axis& are important for
plottin# a re#ression line.
D Multiple re#ression is used to maEe predictions about a sin#le
criteria from two or
more diGerent tests.
D Cecisions based on test scores have far1reachin# consequences,
and test users
should have evidence of validity to be sure that the test scores
and their predictions
will be accurate.
D +hen test taEers are members of minorities, especially
those who do not speaEstandard 0n#lish as their primary lan#ua#e,
test users must be aware of test bias
and how it aGects test validity
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