1. STATISTICAL
POWER
HUSNUL & NUR

2. Introduction
Hypothesis Testing 𝐻0 VS 𝐻 𝑎
4 possible outcomes
True in Real Life
There is no
effect
There is an effect
Conclusion
reached by
the
researcher
There
is no
effect
Correct
Conclusion
(p = 1 – α)
Type II error
(p = β)
There
is an
effect
Type I error
(p = α)
Correct Conclusion
(p = 1 – β)

3. WHAT does a value of Statistical
Power mean?
𝜶
Ho is rejected
Before
treatment
Expected
𝜷
𝟏 − 𝜷
Statistic Power
𝑧 𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙
Ideally, power should be set around 0.80
(Cohen, 1988)

4. WHYshould we consider
statisticalpower?
Underpowered Overpowered
The research becomes useless
Might be unethical
Could be wasteful
Common question associated with statistical power
How big a sample size do I need for my research?

5. WHAT could affect statistical
power?
1. Effect size
2. Sample size
3. Alpha significance criterion (α)
4. Error rate (β)
𝜶
Ho is rejected
Before
treatment
Expected
𝜷
𝟏 − 𝜷
Statistic Power

6. STEPS to determine the Statistical Power
Suppose we are going to study how a training could improve the writing
score of 30 participants. We also knew that their current score in average is
5 with deviation standard 0.5.
We expect that the score could increase to 6.5 with deviation standard 0.5.
We also had chosen 𝛼 = 0.05 (for 2-tailed test)
1. Find the critical values in a
probability distribution (see table)
Here, we take 𝛼 = 0.05 for two tailed z-test, which
leads to 𝑧 = 1.96
𝑥 = 𝜇 𝑛𝑢𝑙𝑙 + 𝑧. 𝜎 = 5 + 1.96 × 0.5 = 5.98
Since 𝜇 𝑎𝑙𝑡 = 6.5, thus 𝐻0 is rejected
5 5.98 6.5

7. STEPS to determine the Statistical Power
2. Standardize the critical value on the
alternative probability distribution
5 5.98 6.5
𝒛 =
𝟓. 𝟗𝟖 − 𝟔. 𝟓
𝟎. 𝟓
= −𝟏. 𝟎𝟒
3. Find the power from the table
Power (1 – β) = P (X > -1.04) = 1 – 0.1492 = 0.8508
Since the power is 0.8508 which is around 0.80, so it is considered
powerful enough

8. ANY QUESTIONS?