Mini 10_ Effect Size, Power, Signa Detection Theory
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Mini #10 Effect Size & Power & Signal Detection Theory
1.
The Secretary of Labor wants to know if productivity increases when you give employees
2 vacations a year instead of one. Employees who receive 1 and 2 vacations a year are
selected at random from nearby companies to fill out a survey which rates their
productivity as an index on a scale 1-10. The table below provides the productivity Mean
and Standard Deviation, and Sample Size for both groups of employees with 1 Vacation
per year and those with 2 Vacations per year.
Mean1Vac
6
Mean2Vac
8.2
S
1Vac
1.3
S
2Vac
1.2
N1Vac
16
N2Vac
9
IV: Type of Employee
DV: Productivity rating
Ho: Mean Productivity rating 2 Vacation = Mean Productivity 1 Vacation
H1: Mean Productivity rating 2 Vacation ≠ Mean Productivity 1 Vacation
pooled var: 1.603043
sdiff var: 0.278306
sdiff: 0.527547
t-test: -4.17024
Since the difference in productivity index means between employees who take one annual
vacation and those who take two exceeds what we would expect from pure chance, we
reject the null hypothesis. Our sample size is 25, yielding a t-value of -4.17 with 23 degrees
of freedom, indicating significance at p<.05.
a.
Using the information provided conduct all steps for the appropriate hypothesis
test.
b.
If appropriate, calculate and interpret (small medium, large) the effect size using
Cohen’s
d
, and calculate and interpret the explained variance,
r
2
.
d
= 1.7376 and
r
2
= .430565
c.
Without repeating all the steps for hypothesis testing, change
S
1Vac
= 1.6 and
S
2Vac
=1.5. What is the new t-statistic?
-3.3718
d.
Would it be appropriate to calculate the effect size? If so, please calculate and
interpret the new Cohen’s
d
and the explained variance,
r
2
.
yes the results are
statistically significant
e.
What happened to the power as a result of increasing the variability (you do not
need to calculate power to answer this)?
Alpha did not change while the power
did. In other words, while the likelihood of rejecting the null hypothesis when
it was false has reduced, the likelihood of rejecting the null hypothesis when
it was true has remained unchanged.
f.
In terms of Signal Detection Theory, what does the change in Power mean in
terms of Hits and in terms of False Alarms?
While the likelihood of committing
a False Alarm has not altered, the likelihood of committing a Hit has.
2.
A professor wants to know if students perform better solo or in groups. He compares grades on
the final project of the class where there was an option to do the project solo or with a group.
The table below provides the Mean, Standard Deviation of final project grades and Sample Size
for the number of recorded grades of the randomly selected solo projects and group projects
(only one grade was picked from each randomly selected group projects).
IV: Solo and Group (Project Type)
DV: Grades
Ho: MeanGradeSolo = MeanGradeGroup
H1: MeanGradeSolo ≠ MeanGradeGroup
pooled var: 58.5
sdiffvar: 7.8
sdiff: 2.792848
t-test: -429669
We reject the Null Hypothesis, indicating that there is a significant difference
between the average performance of students working individually and those
working in groups. With a sample size of 30, the calculated t-value of -4.29669
demonstrates this distinction, with a p-value of less than .05
a.
Using the information provided conduct all steps for the appropriate hypothesis
test.
b.
If appropriate, calculate and interpret (small medium, large) the effect size using
Cohen’s
d
, and calculate and interpret the explained variance,
r
2
.
1.623996
c.
Without repeating all the steps for hypothesis testing, change
Nsolo = 10
and
NGroup = 10.
What is the new t-statistic?
-3.5082
d.
Would it be appropriate to calculate the effect size? If so, please calculate and
interpret the new Cohen’s
d
and the explained variance,
r
2
.
Yes, the results are
statistically significant, so it is appropriate to report the effect size.
MeanSolo
70
MeanGroup
82
S
Solo
9
S
Group
6
N
Solo
15
N
Group
15
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