1. Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2018 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays.
Welcome
3/28/18

2. Lecturer’s desk Projection Booth Screen Screen Harvill 150 renumbered
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Harvill 150
renumbered
table 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
Projection Booth
Left handed desk

4. Before next exam (April 6th)
Schedule of readings
Before next exam (April 6th)
Please read chapters in OpenStax textbook
Please read Chapters 2, 3, and 4 in Plous
Chapter 2: Cognitive Dissonance
Chapter 3: Memory and Hindsight Bias
Chapter 4: Context Dependence

5. Labs continue this week Project 3
Lab sessions
Labs continue this week Project 3

6. Project 3: Analysis of Variance (ANOVA)

8. Writing Assignment – ANOVA – Another Example
1. Write formula for standard deviation of sample
2. Write formula for variance of sample
3. Re-write formula for variance of sample using the nicknames
for the numerator and denominator SS df
= MS
ANOVA table
4. Complete this ANOVA table
Source SS df MS F
5. Given a critical F(4,45) = 2.58
Write a summary statement
of findings (all three parts)
Between 32 ? ? ?
Within
450 ? ?
Total
482 ?

9. Writing Assignment – ANOVA – Another Example
1. Write formula for standard deviation of sample
2. Write formula for variance of sample
3. Re-write formula for variance of sample using the nicknames
for the numerator and denominator SS df
= MS
ANOVA table
4. Complete this ANOVA table
Source SS df MS F
5. Given a critical F(4,45) = 2.58
Write a summary statement
of findings (all three parts)
Between 32 4 8
0.80
Within
450 45 10
Total
482 49

10. Make decision whether or not to reject null hypothesis
Observed F(4,45) = 0.80
Critical F(4,45) = 2.58
0.80 is not larger than our critical of 2.58
so, we do not reject the null hypothesis
Observed F(4,45) = 0.80
Conclusion: There appears to be no main effect of type of
major on number of units taken in school
The average number of units taken by Geography, Sociology,
Nutrition, Communication and Criminal Justice majors are 11.6,
11.1, 9.3, 11.3 and 11 respectively. An ANOVA was conducted and
there appears to be no main effect of the number of units taken
as a result of the different majors. F(4,45) = 0.80; n.s.

11. Hand in your writing assignment

12. Let’s do same problem Using MS Excel
A girlscout troop leader wondered whether providing an
incentive to whomever sold the most girlscout cookies would
have an effect on the number cookies sold. She provided
a big incentive to one troop (trip to Hawaii), a lesser
incentive to a second troop (bicycle), and no incentive to
a third group, and then looked to see who sold more cookies.
Troop 1
(Nada) 10 8 12 7 13
Troop 2
(bicycle) 12 14 10 11 13
Troop 3
(Hawaii) 14 9 19 13 15
n = 5
x = 10
n = 5
x = 12
n = 5
x = 14

13. Let’s do one Replication of study (new data)

14. Let’s do same problem Using MS Excel

15. Let’s do same problem Using MS Excel

16. SSbetween
dfbetween 40 2
=20
“Sum of Squares”
MSbetween
MSwithin
# groups - 1 20
7.33
=2.73
3-1=2 88 12
=7.33
# scores - # of groups
SSwithin
dfwithin
15-3=12
# scores - 1
15- 1=14

17. No, so it is not significant Do not reject null
F critical (is observed F greater than critical F?)
P-value (is it less than .05?)
“Sum of Squares”

18. Make decision whether or not to reject null hypothesis
Observed F = 2.73
Critical F(2,12) = 3.89
2.7 is not farther out on the curve than 3.89
so, we do not reject the null hypothesis
Also p-value is not smaller than 0.05
so we do not reject the null hypothesis
Step 6: Conclusion: There appears to be no effect of type of
incentive on number of girl scout cookies sold

19. Make decision whether or not to reject null hypothesis
Observed F =
F(2,12) = 2.73; n.s.
Critical F(2,12) =
2.7 is not farther out on the curve than 3.89
so, we do not reject the null hypothesis
Conclusion: There appears to be no effect of type of
incentive on number of girl scout cookies sold
The average number of cookies sold for three different incentives
were compared. The mean number of cookie boxes sold for the
“Hawaii” incentive was 14 , the mean number of cookies boxes sold
for the “Bicycle” incentive was 12, and the mean number of cookies
sold for the “No” incentive was 10. An ANOVA was conducted and
there appears to be no significant difference in the number of
cookies sold as a result of the different levels of incentive
F(2, 12) = 2.73; n.s.

20. incentive then the means are significantly different from each other
Main effect of incentive: Will offering an incentive result in more girl scout cookies being sold?
If we have a “effect” of
incentive then the means
are significantly different
from each other
we reject the null
we have a significant F
p < 0.05
To get an effect we want:
Large “F” - big effect and small variability
Small “p” - less than 0.05 (whatever our alpha is)
We don’t know which means are different from which …. just that they are not all the same 20

21. Homework

24. Type of major in school
4 (accounting, finance, hr, marketing)
Grade Point Average
0.05
2.83
3.02
3.24
3.37

25. # scores - number of groups3 24
0.3937
If observed F is bigger than critical F: Reject null & Significant!
If observed F is bigger than critical F: Reject null & Significant!
0.1119
/ = 3.517
3.517
3.009
If p value is less than 0.05: Reject null & Significant!
4 – 1 = 3
# groups - 1
# scores - number of groups
28 – 4 = 24
# scores - 1
28 – 1 = 27

26. Yes
F (3, 24)
= 3.517;
p < 0.05
The GPA for four majors was compared. The average GPA was 2.83 for accounting, 3.02 for finance, 3.24 for HR, and 3.37 for marketing. An ANOVA was conducted and there is a significant difference in GPA for these four groups (F(3,24) = 3.52; p < 0.05).

27. Average for each group (We REALLY care about this one)
Number of observations in each group

28. Number of groups minus one (k – 1)  4-1=3
“SS” = “Sum of Squares” - will be given for exams
Number of people minus number of groups (n – k)  28-4=24

29. SS between
df between
MS between
MS within
SS within
df within

32. Type of executive
3 (banking, retail, insurance)
Hours spent at computer
0.05
10.8 8
8.4

33. 2 12
11.46 2
If observed F is bigger than critical F: Reject null & Significant!
If observed F is bigger than critical F: Reject null & Significant!
11.46 / 2 = 5.733
5.733
3.88
If p value is less than 0.05: Reject null & Significant!
0.0179

34. Yes
F (2, 12)
= 5.73;
p < 0.05
The number of hours spent at the computer was compared for three types of executives. The average hours spent was 10.8 for banking executives, 8 for retail executives, and 8.4 for insurance executives. An ANOVA was conducted and we found a significant difference in the average number of hours spent at the computer for these three groups , (F(2,12) = 5.73; p < 0.05).

35. Number of observations in each group
Average for each group
Number of observations in each group
Just add up all scores

36. Number of groups minus one (k – 1)  3-1=2
“SS” = “Sum of Squares” - will be given for exams
Number of people minus number of groups (n – k)  15-3=12

37. MS between
MS within
SS between
df between
SS within
df within

39. Thank you!
See you next time!!