1. How big is my sample going to be?
Sample Power
How big is my sample going to be?

2. Sample Power - introduction
Null Hypothesis is true: No difference
Null Hypothesis is false: There is difference
Null Hypothesis is accepted
Correct Decision
95% probability
Wrong Decision
Null Hypothesis is rejected
5% probability
Type I error

3. Sample Power
Probability that a sample of given size will allow us to correctly reject the null hypothesis.
Null Hypothesis is true: No difference
Null Hypothesis is false: There is difference
Wrong Decision
Null Hypothesis is accepted
Type II error
20% probability
Null Hypothesis is rejected
Correct decision
Sample Power
80% probability

4. Example: Probability of rejecting a null hypothesis
We have a sample:
Mean 104, SD=15
N=50
Is this sample is coming from a Population A:
Mean 100, SD=15
Null Hypothesis????
Alternative Hypothesis????
Solution ????
Conclusions ?????
Actually, the sample is coming from population B
Mean 105

5. If Population A was generating 1000 samples of 50
Population mean
5% rejection area
mean = 104, p=.03
Population mean = 100, SD = 15, n=50, 1,000 samples were drawn.

6. Sample is actually coming from Population B: Null hypothesis is false
Samples from population A
Samples from population B
Power
Type II error
Population mean
Population A mean = 100, SD = 15, n=50, 1,000 samples were drawn.
Population B mean = 105, SD = 15, n=50, 1,000 samples were drawn.

7. If Population A was generating 1000 samples of 20
Population mean
5% rejection area
mean = 104, p=.06
Population mean = 100, SD = 15, n=20, 1,000 samples were drawn.

8. Sample is actually coming from Population B: Null hypothesis is false
Samples from population A
Samples from population B
Power
Type II error
Population mean
Population A mean = 100, SD = 15, n=20, 1,000 samples were drawn.
Population B mean = 105, SD = 15, n=20, 1,000 samples were drawn.

9. Summary
Power is the probability of correctly rejecting the null hypothesis
Power is related to the mean of the population that the sample is actually coming from
Power is related to the SEM (SD & sample size)
larger the sample size, greater the power
Power is related to the chosen level of significance

10. IMPLICATION Given: WE CAN COMPUTE THE REQUIRED SAMPLE SIZE
DESIRED POWER,
POPULATION MEAN,
POPULATION SD, AND
LEVEL OF SIGNIFICANCE,
WE CAN COMPUTE THE REQUIRED SAMPLE SIZE

11. Summary
Power is the probability of correctly rejecting the null hypothesis
Power is related to the mean of the population that the sample is actually coming from
Power is related to the SEM (SD & sample size)
larger the sample size, greater the power
Power is related to the chosen level of significance (usually p=.05)

12. Example sample size calculation
I have two groups that I wish to compare.
The mean of group 1 is 50.
The mean of group 2 is 55.
SD of both groups is 10.
What should be my sample size so that I can conclude that the difference is statistically significant?
Probability of correctly detecting this difference should be high (usually 80%)
SOLUTION:

13. Power Analysis Example
Exercise 1: I wish to estimate the behavior problem scores of children age who had school disciplinary problems. This mean is estimated to be I wish to be able to say that this sample of children could not have been generated by a normative population (mean = 100, SD = 15).
What should my sample size be?

14. Using effect size: Exercise 2
Hypothesis: Children who experienced highly authoritarian parenting are expected to be less empathetic in their dating relationships than children who did not experience high levels of authoritarian parenting because ….
What should be your sample size????
What is the IV and what is the DV?
What would be your expectation about the size of the effect? Small, medium, or large?
How does that translate to the difference between two groups?

15. Effect Size 0.2 or less: Small effect 0.3-0.4: Moderate effect
: Large effect
0.7 or greater: Very large effect (almost impossible in Social Sciences)

16. Power Analysis Example
Exercise 3: I wish to compare the mean behavior problems scores of children age who have intact or disrupted families. I expect the score in disrupted families to be higher and to me, this score should be at least 0.3 SD higher than the intact families to be meaningful. What should my sample size be?

17. Power Analysis Example
Exercise 4
I would like to test if students with high self esteem give more autonomous decisions in choosing their colleges than students with low self esteem. I expect that the difference between low and high self esteem groups will be small (0.2 SD). What should my sample size be, so that I can detect this small difference with statistical significance at p=0.05 level with 85% power?

18. Power Analysis Example
Exercise 5
I would like to estimate the effects of authoritarian parenting on the level of religious prejudice of adolescents. I expect that this correlation will be about What should my sample size be, so that I can detect this modest correlation with statistical significance at p=0.05 level with 85% power?

19. Power Analysis FINAL Example
Exercise 6
[YOUR PARAGRAPH ON SAMPLE POWER] This research is about the effects of interparental violence on the level of intimacy in the dating relationships of college students. It is expected that there is a moderate negative correlation between the level of overt interparental conflict and ability of the college students to maintain intimacy in their dating relationships. Previous studies found this correlation to be around (Smith, 1999; Miller, 2001).
What should the sample size be, so that this correlation can be detected with statistical significance at p=0.05 level with 80% power?

20. Should we try to get as big a sample as we can?
A sample of 10 (or 80, or 250) ELC students has a mean duration of completing the reading assignment in 47 minutes. The estimate of the population SD is 22 minutes. What is the estimated mean duration for this reading assignment for the population of all ELC students?

21. Review our findings

22. Review our findings

23. If it costs 10TLs to have 1 unit of observation

24. How much does it cost per increased point of precision?

25. How big should my sample be?
Optimum size will depend on the purpose of the study, the precision required, and the costs of increased precision

26. How precise should this be?
Sample Power
How precise should this be?
Sample mean
Population mean