Summary of Significance Tests
Ann Porteus
z-tests
Means: One Sample How far is our sample
mean from the
hypothesized population
mean?
Difference in Means:
Two samples - How large
is the difference of our
two sample means from a
null hypothesis of no
difference in the
population
Correlation Coefficients:
How far is our sample r
from a hypothesized
population coefficient ()
of 0
Difference in Correlation
Coefficients: How large
is the difference between
two r's from a null
hpothesis of no
difference in the
population
Population  is known
Ho: m = specific value
(known pop mean)Ho: m
> (or <) specific value
("known" pop mean)
Population  for both
samples is known
Ho: m1- m2= 0
Use Z transformation of
r and  (use Table I for
making transformations)
Ho: r = 0 or some
specified value
Use Z transformation of
r of both samples (Use
Table I for making
transformations)
Ho: r1-r2 = 0
Assumptions:: Scores
are normally distributed
in the population
Yardstick: Standard
error of mean (semean):
Assumptions:: Normal
distribution of scores in
each sample being
Assumptions:
comparedEqual variances IndependenceBivariate
(equal s.d.s)
Normality (at least
normal distribution of
Yardstick:: Standard
each variable)N>=30
error of differences of
Yardstick:: Standard
means (sediffmean):
error of Zr(seZr):
Assumptions:
IndependenceBivariate
Normality (at least
normal distribution of
each variable)N>=30
Yardstick:: Standard
error of Zdiffr (sediffZr):
t-test
Means: One Sample How far is our sample
mean from the
hypothesized population
mean?
Difference in Means:
Two samples - How
large is the difference of
our two sample means
from a null hypothesis of
no difference in the
population
Correlation Coefficients:
How far is our sample r
from a hypothesized
population coefficient
() of 0
Difference in Correlation
Coefficients: How large
is the difference between
two r's from a null
hpothesis of no
difference in the
population
Population  is not
known (use sample s.d.
to calculate standard
error)
Population  for each
sample not known (use
sample s.d.s to calculate
standard error)
Can use when testing
Ho:  = 0
Ser):
Might see t-test, but best
to use z-test (with Z
transformations)
(sediffrr):
Ho: same as above
Assumptions: same as
above
Ho: same as above
Assumptions: same as
above
Yardstick: Standard
error of mean
(semean):
Yardstick: Standard
error of differences of
means (sediffmean):
Ho: same as above
Assumptions: same as
above
Yardstick: Standard
error of r
(serr):
(Can use Table G when
testing a single r, or use
Table H when testing
more than one r)