1. Statistical Decision Making

2. History of the Student’s t Distribution and the t Test
Guinness and statistics

3. Hypothesis Testing State the null hypothesis
State the alternate hypothesis
Select the level of significance
Collect and summarize the sample data
Refer to the criterion for evaluating the sample evidence
Make a decision to discard/retain the null hypothesis

4. Type I and Type II Errors
Reality
Null is true
Null is false
Accept null
No error
Type II error
Reject null
Type I error

5. Possible Causes of Error
Type I
Measurement error
Lack of random sample
p value too liberal
(p = .10)
Investigator bias
Improper use of one-tailed test
Type II
Measurement error
Lack of sufficient power
(N too small)
P value too conservative
(p = .01)
Treatment effect not properly applied

6. The Alpha and p Levels
p value - probability with which the difference in means could occur by chance
Alpha () level - p value set prior to the experiment
Indication of risk willing to take in making a wrong decision to reject the null hypothesis
Smaller p values do not indicate greater importance of findings
Only indicates a smaller probability that the findings occurred by chance

7. Two-Tailed Test
When direction of outcome is uncertain we use the null hypothesis
Ho is tested with a two-tailed test
If t does not reach p = .05, we know sample mean falls within the normal curve that includes 95% of all possible differences
Accept Ho with a 5% chance of being wrong
5% rejection area divided between the 2 tails of the curve
Each area is 2.5% of the area under the curve

8. One-Tailed Test Use when direction of difference is know
Not sure what the size of difference is
Most likely trying to test H1
Difference to be tested is always positive
Only use positive side of normal curve

9. Why Use Statistical Decision Making?
Make decisions about differences between groups
Not necessarily that the 2 groups are different from each other
Did the two groups come from different populations?

10. The t Test Used when standard deviation of the population is not known
Need to calculate the standard error of the mean estimated from a sample
Using SEM we can determine odds that a sample is representative of the population it is drawn from

11. The Independent t Test Method comparing independent samples
Comparing means of 2 samples
Need to determine the standard error of the difference (SED) from the SEM of each sample
t Test becomes

12. Independent t Test Software packages Calculate t value and p value
p typically = .05 as standard for rejecting null hypothesis
5 times in 100

13. Assumptions for the t Test
t Test produces reasonably reliable results
Robust measure
4 assumptions
Population from which sample are drawn is normally distributed
Sample or samples are randomly selected from the population
Homogeneity of variance
Variance of one group should not be more than twice as large as the variance of the other
Data must be parametric
Interval or ratio measurement scale

14. The Correlated t Test
Standard formulas for calculating t assume no correlation between groups
Dependent samples assume relationship (correlation) between scores from same group of subjects
Posttest is partially dependent on pretest score

15. Correction for Correlated Samples
Need to make adjustment to denominator
T Test becomes

16. Reading the Statistical Output
Figure 12-2
Independent t Test
Figure 12-3
Dependent t Test
Paired samples

17. Statistical Power
Power - Ability of a test to correctly reject a false null hypothesis
Since critical t values are lower for one-tailed test, it is considered more powerful at a given p value
1- is area of power

18. Power Power is dependent on 4 factors
Z level set by researcher
The difference between the 2 means being compared
The standard deviation of the 2 groups
Determines the spread of the curve
The sample size (N) of the 2 groups
Only N and Z are under your control

19. Calculating Power
Power is calculated by determining Z, converting it to a percentile, and adding this percent to the 50% of the curve to the right of the experimental curve
t = Z + Z
Z = t - Z
Use table A to determine percentile for Z add that value to 50%
= 1-

20. Sample Size The only factor easily manipulated in power is N
How large does N need to be to produce a given power?
Complicated calculation
This is the last step

21. Statistical vs. Clinical Significance
Which one is important?
Effect size holds the answer

22. Effect Size .30 is low .50 is moderate .80 is high Example from book
Should be obvious to clinician
Example from book
ES = 2.68/5.01
ES = 0.53