2. Practice
10.15
Did the type of signal effect response time?

3. t crit (15) = +/- 2.447 t obs = -2.24 Fail to reject Ho
The type of signal does not have a significant effect on response time.

5. New Step Should add a new page Determine if One-sample t-test
Two-sample t-test
If it is a dependent samples design
If it is a independent samples with equal N
If it is a independent samples with unequal N

6. Thus, there are 4 different kinds of designs
Each design uses slightly different formulas
You should probably make up ONE cook book page (with all 7 steps) for each type of design
Will help keep you from getting confused on a test

8. Practice Does drinking milkshakes affect (alpha = .05) your weight?
To see if milkshakes affect a persons weight you collected data from 5 sets of twins. You randomly had one twin drink water and the other twin drank milkshakes. After 3 months you weighed them.

9. Results Water Twin A 186 Twin B 200 Twin C 190 Twin D 162 Twin E 175
Milkshakes
195
202
196
165
183

10. Hypothesis Two-tailed
Alternative hypothesis
H1: water = milkshake
Null hypothesis
H0: water = milkshake

11. Step 2: Calculate the Critical t
N = Number of pairs
df = N - 1
5 - 1 = 4
 = .05
t critical = 2.776

12. Step 3: Draw Critical Region
tcrit =
tcrit = 2.776

13. Step 4: Calculate t observed
tobs = (X - Y) / SD

14. (D) -9 -2 -6 -3 -8
D = -28
D2 =194
N = 6
-28
3.04 =
194 5
5 - 1

15. Step 4: Calculate t observed
tobs = (X - Y) / SD
1.36=3.04 / 5
N = number of pairs

16. Step 4: Calculate t observed
-4.11 = (182.6 – 188.2) / 1.36
X = 182.6
Y = 188.2
SD = 1.36

17. Step 5: See if tobs falls in the critical region
tcrit =
tcrit = 2.776
tobs = -4.11

18. Step 6: Decision If tobs falls in the critical region:
Reject H0, and accept H1
If tobs does not fall in the critical region:
Fail to reject H0

19. Step 7: Put answer into words
Reject H0, and accept H1
Milkshakes significantly ( = .05) affect a persons weight.

21. What if. . .
You were asked to determine if psychology and sociology majors have significantly different class attendance (i.e., the number of days a person misses class)
You would simply do a two-sample t-test
two-tailed
Easy!

22. But, what if. . .
You were asked to determine if psychology, sociology, and biology majors have significantly different class attendance
You can’t do a two-sample t-test
You have three samples
No such thing as a three sample t-test!

23. One-Way ANOVA ANOVA = Analysis of Variance
This is a technique used to analyze the results of an experiment when you have more than two groups

24. Example
You measure the number of days 7 psychology majors, 7 sociology majors, and 7 biology majors are absent from class
You wonder if the average number of days each of these three groups was absent is significantly different from one another

25. Hypothesis Alternative hypothesis (H1)
H1: The three population means are not all equal

26. Hypothesis
Alternative hypothesis (H1)
socio = bio

27. Hypothesis
Alternative hypothesis (H1)
socio = psych

28. Hypothesis
Alternative hypothesis (H1)
psych = bio

29. Hypothesis
Alternative hypothesis (H1)
psych = bio =  soc

30. Hypothesis Alternative hypothesis (H1)
Notice: It does not say where this difference is at!!

31. Hypothesis Null hypothesis (H0) psych = socio = bio
In other words, all three means are equal to one another (i.e., no difference between the means)

32. Results
X = 3.00
X = 2.00
X = 1.00

33. Logic Is the same as t-tests
1) calculate a variance ratio (called an F; like t-observed)
2) Find a critical value
3) See if the the F value falls in the critical area

34. Between and Within Group Variability
Two types of variability
Between
the differences between the mean scores of the three groups
The more different these means are, the more variability!

35. Results
X = 3.00
X = 2.00
X = 1.00

36. Between Variability
S2 = .66
X = 3.00
X = 2.00
X = 1.00

37. Between Variability
+ 5
X = 3.00
X = 2.00
X = 1.00

38. Between Variability
X = 8.00
X = 2.00
X = 1.00

39. Between Variability
S2 = 9.55
X = 8.00
X = 2.00
X = 1.00

40. Between Group Variability
What causes this variability to increase?
1) Effect of the variable (college major)
2) Sampling error

41. Between and Within Group Variability
Two types of variability
Within
the variability of the scores within each group

42. Results
X = 3.00
X = 2.00
X = 1.00

43. Within Variability
S2 =.57
X = 3.00
X = 2.00
X = 1.00

44. Within Variability
S2 =.57
S2 =1.43
S2 =.57
X = 3.00
X = 2.00
X = 1.00

45. Within Group Variability
What causes this variability to increase?
1) Sampling error

46. Between and Within Group Variability
Between-group variability
Within-group variability

47. Between and Within Group Variability
sampling error + effect of variable
sampling error

48. Between and Within Group Variability
sampling error + effect of variable
sampling error
Thus, if null hypothesis was true this would result in a value of 1.00

49. Between and Within Group Variability
sampling error + effect of variable
sampling error
Thus, if null hypothesis was not true this value would be greater than 1.00