ztest and onesample ttest: These are used to compare
one sample
mean
to a
population mean
or some other known value.
More common: compare two(or more) sample means to each other.
Two general research strategies: (1) Two completely separate
(independent) samples. (2) Two related (dependent) samples.
chance (sampling error)
Setting the Statistical hypothesis for Independent samples.
Ho
Ho: μ
₁
 μ
₂
= 0
or
Ho: μ
₁
= μ
₂
H1
H
₁
: μ
₁
 μ
₂
≠0
H
₁
: μ
₁
≠ μ
₂
Independent Samples t Ratio
Where
2
1
x
x
s

is the standard error of the mean difference
Two Sample ttest Example
Research Question: Does mental imagery change memory scores?
State Statistical Hypothesis:
Ho: μ rote = μ imagery
H1: μ rote ≠ μ imagery
Set Decision Criteria:
df= (n
₁
 1) + (n
₂
1) = w
 If α=.05 and twotailed test, from ttable,
t(crit)= + or – 2.101
 Reject Ho if t(obtained) > t(crit)
Compute test statistics (t (obtained))
Make Decision: Reject Ho
Mental imagery memory scores are significantly higher compared
to rote scores, t(18) = 3.00 p< .05
Setting Decision Criteria for a Directional Test (onetailed)
Mental imagery improves memory scores.
H0: µ1>
µ2
or
H0: µ1µ2>
0
H1: µ1<µ2
or
H1: µ1µ2<0
Where µ1=Rote Group and µ2=Imagery Group
In this case, set decision criteria: Critical region is in the lower tail of
the distribution.
df=(n11)+(n21)=(101)+(101)=18
If α=.05 and onetailed test, from ttable, tcrit =  1.734
Reject Ho if obtained falls within the critical region.
Setting Decision Criteria for a Directional Test (onetailed)
Mental imagery decreases memory scores.
H0: µ1<
µ2
or
H0: µ1µ2<
0
H1: µ1>µ2
or
H1: µ1µ2>0
Where µ1=Rote Group and µ2=Imagery Group
In this case, set decision criteria: Critical region is in the upper tail of
the distribution.
Assumptions of the Independent Samples ttest
Independent Observations –Normality –Homogeneity of Variance
Effect size. Small d=.2 Medium d=.5 Large d=.8
Dependent Samples ttest
The type of ttest you use is determined by the research design
employed.
(1) Use a one sample ttest
if you wish to compare a single
sample
mean to a hypothesized population mean value. (2) Use a independent
samples ttest
if you have two
independent sample means that you wish
to compare. (3) Use a dependent samples ttest
if you1) measure the
same
participants on a dependent variable at two different times
, or 2)
have two separate groups
of participants that have been matched
based
on some characteristic.
Dependent Sample t Ratio
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Winter '08
 Ard
 Statistics, Null hypothesis, Statistical hypothesis testing, decision criteria

Click to edit the document details