Review of Statistics
Group Results
Which type of statistics?
When comparing two group scores-Use
the t-test.
When comparing more than two scores:
Use the Analysis of Variance (ANOVA),
which is an F-test
Both the t and the F tests are ratios.
T-Test
t=
group difference
within group variability
Therefore the numerator is the difference
between the means of the two groups, and
the denominator is the variability between
each individual score and the group mean.
Examples
Group One
25
15
20
40
Mean of Group One is 25
Mean of Group Two ( not shown) is 65
Variability within group.
Compare each score to the group mean in absolute
value:
25-25 = 0
15-25 = 10
20-25= 5
40-25 = 15
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Add together and the variability of group one is 30
Group Two ( not shown) variability is 10
Total within group variability is 40
T-test example
t = 65 ( mean of group Two) -25( mean of
group one)
Divided by the within group variability -40
t = 40
40
t ratio = 1.00
T-Ratio
The value of t increases as the difference
between your group means increases
Within group variability- want this number to be
small as it indicates your groups were relatively
equal on the measure.
A large amount of variability would increase the
denominator and decrease the size of the tstatistic, thus decreasing the chance your study
worked.
Critical Value
The critical value is a number which has been
calculated to represent the smallest number you
must obtain with the t-ratio to obtain significance.
This number depends on your number of
participants and number of conditions.
Each critical value represents a normal
distribution for that number of participants and
groups and the critical value is the mean.
To find your critical value, you must calculate
your degrees of freedom.
Degrees of Freedom
The degrees of freedom are the number of
scores free to “vary” given the stated
mean.
The t-statistic has only one number for
degrees of freedom.
Where N= total number of participants and
n= total number of groups: df = ( N-n)
N=60 participants, n= 2 groups, df=58
T-test critical value
t(58)=1.0
Critical Value = 1.671
p-value: this is the probability that your
actual findings are incorrect. Science
recognizes nothing above a p< .05
Did this experiment work? At what
probability level?
One-tailed vs. Two Tailed test
When comparing scores to critical values, one
must look at the hypothesis. Did the hypothesis
predict one group would perform better than
another? One tailed test.
Or…did the hypothesis predict one group would
differ from the other.
This makes a difference in the critical value as it
is an area under the normal curve.
A one tailed test is less conservative than a two:
One tail t(58)=1.67 critical value
Two tail t(58) =2.00 critical value
Analysis of Variance (ANOVA)
Used when there is more than one group.
Is an extension of the t-test F=t squared.
Tells us there is an over-all difference
between the three or more groups.
Analysis of Variance
F = Systematic variance
Error Variance
Systematic Variance is the deviation of the
group means from the Grand means.
The grand mean is the mean of the means.
Systematic Variance
Group 1 M= 35, Group 2 M= 25, Group 3
M=30.
Grand Mean: 35 +25 + 30 = 90/3 =30
Systematic Variance
35-30 = 5
25-30 = 5
30-30 = 0
Systematic variance is 10
Error Variance
Is the same as Within group variability.
Compare the mean of group one to the
individual scores of the group as well as
group two, and group 3.
Add together to obtain the within group
variability (error variance)
Error variance among this group = 2 ( very
Low! What does this mean)