1. CHAPT 7 Hypothesis Testing Applied to Means Part B
pp # 6 t-Static
CHAPT 7 Hypothesis Testing Applied to Means Part B

3. t-Static
3. Related Samples t-test or Repeated Measures Experiment AKA Within Subject Designs or, Paired (SPSS) Sample t-Test.

4. Repeated Measure Experiment, or Related/Paired Sample t-test Within Subject Experiment Design
A single sample of individuals is measured more than once on the same dependent variable. The same subjects are used in all of the treatment conditions.

5. Null Hypothesis
t-Statistics:
If the Population mean or µ is unknown the statistic of choice will be t-Statistic
Repeated Measure Experiment, or Related/Paired Sample t-test
If non-directional/two tailed test, then
Step. 1
H0 : µD = 0
H1 : µD ≠ 0

6. t-Statistics: Null Hypothesis If directional or one tailed tests
Step. 1
H0 : µD ≤ 0
H1 : µD > 0
or, Step. 1
H0 : µD ≥ 0
H1 : µD < 0

7. Step 2 None-directional Hypothesis Test

8. Calculations for t-test Step 3: Computations/ Calculations or Collect Data and Compute Sample Statistics
t= MD-μD
SMD
SMD = S/√n or
SMD= MD-μD t
MD= t.SMD + μD
μD = MD – SMD . t
SMD= estimated standard error of the mean difference

9. Calculations for t-test Step 3: Computations/ Calculations or Collect Data and Compute Sample Statistics
df = n-1
Difference Score D= X2-X1
MD = ΣD n

10. FYI Variability SS, Standard Deviations and Variances
X σ² = ss/N Pop
σ = √ss/N 2
s = √ss/df
s² = ss/n-1 or ss/df Sample
SS=Σx²-(Σx)²/n new SS  SS=ΣD²-(ΣD)²/n
SS=Σ( x-μ)²
Sum of Squared Deviation from Mean

11. Cohen's d and Effect Size
d=Effect Size/Cohn’ d
Cohen's d and Effect Size
A statistically significant result does not mean that the result is practically significant (treatment effect). To correct this problem, it is recommended that whenever researchers report a statistically significant effect, they also provide a report of the effect size (see the guidelines presented by L. Wilkinson and the APA Task Force on Statistical Inferences, 1999). Therefore for different hypothesis test (test statistics) there are different options for measuring and reporting effect size.

12. Use Phi Coefficient and Cramer,s V for Chi Square
d=Effect Size/Cohn’ d
The “effect size” gives an indication of whether something is practically significant. There are different ways of calculating an effect size. r which is the correlation coefficient or R² which is the coefficient of determination Use Eta squared ή² for ANOVA Use Cohen’s d for t-test
Use Phi Coefficient and Cramer,s V for Chi Square

13. Evaluating effect size with Cohen’s d
Magnitude of d
Evaluation of effect size
d= 0.2
Small effect (mean difference around 0.20 standard deviation)
d= 0.5
Medium effect (mean difference around 0.5 standard deviation)
d= 0.8
Large effect (mean difference around 0.8 standard deviation)

14. percentage of Variance accounted for by the Treatment
Percentage of Variance Explained
r²=  Small Effect
r²=  Medium Effect
r²=  Large Effect

15. Cohn’s d=Effect Size for t Use S instead of σ for t-test
d = MD/s
S= MD/d
MD= d . S

16. Percentage of Variance Accounted for by the Treatment (similar to Cohen’s d) Also known as ω² Omega Squared

17. Problem 1
Research indicates that the color red increases men’s attraction to women (Elliot & Niesta, 2008). In the original study, men were shown women’s photographs presented on either white or red background. Photographs presented on red were rated significantly more attractive than the same photographs mounted on white.

18. Problem 1
In a similar study, a researcher prepares a set of 30 women’s photographs, with 15 mounted on a white background and 15 mounted on red. One picture is identified as the test photograph, and appears twice in the set, once on white and once on red.

19. Problem 1
Each male participant looks through the entire set of photographs and rated the attractiveness of each woman on a 12-point scale. The data in the next slide summarizes the responses for a sample of n=9 men.
Set the level of significance at α=.01
for two tailed.
Do the data indicate the color red increases men’s attraction to women ?

20. Problem 1
Participants White background X1 Red Background X2 D=X2-X D² A B C D E F G H I
ΣD = ΣD²=99
MD = For SPSS enter X2 values first then X1

21. Null Hypothesis Step. 1 H0 : µD = 0 H1 : µD ≠ 0
For Non-Directional or two tailed tests
Step. 1
H0 : µD = 0
H1 : µD ≠ 0

25. Problem 2
One technique to help people deal with phobia is to have them counteract the feared objects by using imagination to move themselves to a place of safety. In an experiment test of this technique, patients sit in front of a screen and are instructed to relax. Then they are shown a slide of the feared object for example, a picture of a spider, (arachnophobia). The patient signals the researcher as soon as feelings of anxiety begin to arise, and the researcher records the amount of time that the patient was able to endure looking at the slide.

27. Problem 2
The patient then spends two minutes imagining a “safe scene” such as a tropical beach (next slide) before the slide is presented again. If patients can tolerate the feared object longer after the imagination exercise, it is viewed as a reduction in the phobia. The data in next slide summarize the items recorded from a sample of n=7 patients. Do the data indicate the imagination technique effectively alters phobia? Set the level of significance at α=.05 for one tailed test.

29. Problem2
Participant Before X After X2 Imagination D=X2-X D² A B C D E F G
MD = ΣD =56 ΣD²=502

30. For Directional or one tailed tests
Null Hypothesis
For Directional or one tailed tests
Step. 1
H0 : µD ≤ 0 (The amount of time is not increased.)
H1 : µD > 0 (The amount of time is increased.)

31. df = n-1 MD = ΣD n SS=ΣD²-[(ΣD)²/n] s² = ss/n-1 or ss/df
Difference Score D= X2-X1
MD = ΣD n
SS=ΣD²-[(ΣD)²/n]
s² = ss/n-1 or ss/df

32. Calculations for t-test Step 3: Computations/ Calculations or Collect Data and Compute Sample Statistics
t= MD-μD
SMD
SMD = S/√n or
SMD= MD-μD t
SMD= estimated standard error of the mean difference

33. Please read Power-point # 7 Chapter 8 Power