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
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 Winter '08
 Ard
 Statistics, Null hypothesis, Statistical hypothesis testing, decision criteria

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