1. Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Fall 2017 Room 150 Harvill Building 10: :50 Mondays, Wednesdays & Fridays.
Welcome

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. A note on doodling

5. Lab sessions Continue Project 3 This Week
Everyone will want to be enrolled
in one of the lab sessions
Continue
Project 3 This Week

7. Schedule of readings Before next exam (November 17th)
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

8. Question: Using nicknames…. what is formula for SAMPLE variance?
Sum of Squares
Degrees of freedom SS df
“SS” = “Sum of Squares”
“SS” = “Sum of Squares”
“df” = degrees of freedom
“SS” = “Sum of Squares”
We lose one degree of freedom for every parameter we estimate
Remember, you should know
these four formulas by heart

9. This is our sample variance…
what is formula for
SAMPLE variance? SS df
ANOVA table
Source df MS F SS
Between 40 ? ? ?
Within 88 ? ?
Total
128 ?

10. Re-dux Writing Assignment - ANOVA
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
4. Complete this ANOVA table
ANOVA table
5. Given a critical F(2,12) = 3.89
Write a summary statement
of findings (all three parts)
Source SS df MS F
Between 40 ? ? ?
Within 88 ? ?
Total
128 ?
Re-dux

11. Re-dux ANOVA table Source df MS F SS Between 40 ? ? 2 ? ? Within 88 ?
“SS” = “Sum of Squares” - will be given for exams
ANOVA table
Source df MS F SS
Between 40 ? ? 2
# groups - 1 ? ?
3-1=2
15-3=12
Within 88 ? 12 ? ?
# scores - number of groups
Total
128 ? ? 14
# scores - 1
15- 1=14
Re-dux

12. “SS” = “Sum of Squares” - will be given for exams
ANOVA table
SSbetween
dfbetween
“SS” = “Sum of Squares” - will be given for exams 40 2 40 2
=20
MSbetween
MSwithin
ANOVA table
Source df MS F SS 20
7.33
=2.73
Between 40 2 ? 20 ?
2.73
Within 88 12
7.33 ?
Total
128 14
SSwithin
dfwithin 88 12
=7.33 88 12
Re-dux

13. Re-dux Make decision whether or not to reject null hypothesis
Observed F = 2.73
Critical F(2,12) = 3.89
2.73 is not farther out on the curve than 3.89
so, we do not reject the null hypothesis
F(2,12) = 2.73; n.s.
Conclusion: There appears to be no main 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 main effect of the number of cookies sold
as a result of the different levels of incentive F(2, 12) = 2.73; n.s.
Re-dux

14. Hand in your writing assignment

15. 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 15

16. 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

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

18. Let’s do same problem Using MS Excel

19. Let’s do same problem Using MS Excel

20. ANOVA table SSbetween “Sum of Squares” 40 =20 dfbetween 2 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

21. 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”

22. 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

23. 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.

24. Homework

25. Homework

26. Homework

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

28. # scores - number of groups
0.3937
0.1119
If observed F is bigger than critical F: Reject null & Significant!
If observed F is bigger than critical F: Reject null & Significant!
/ = 3.517
Homework
3.517
3.009
If p value is less than 0.05: Reject null & Significant! 3 24
0.03
4-1=3
# groups - 1
# scores - number of groups
28 - 4=24
# scores - 1
28 - 1=27

29. Yes
Homework
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).

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

31. 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

32. SS between
df between
MS between
MS within
SS within
df within

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

36. 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! 2 12
0.0179

37. 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).

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

39. 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

40. MS between
MS within
SS between
df between
SS within
df within

42. “Between Groups” Variability Difference between means .
“Between Groups” Variability
Difference between means
Difference between means
Difference between means
“Within Groups” Variability
Variability of curve(s)
Variability of curve(s)
Variability of curve(s)

43. One way analysis of variance Variance is divided
Remember, one-way = one IV
Total variability
Between
group
variability
(only one factor)
Within
group
variability
(error variance)
Remember, 1 factor = 1 independent variable (this will be our numerator – like difference between means)
Remember, error variance = random error (this will be our denominator – like within group variability

44. F = MSBetween MSWithin Five steps to hypothesis testing
Step 1: Identify the research problem (hypothesis)
Describe the null and alternative hypotheses
Step 2: Decision rule
Alpha level? (α = .05 or .01)?
Still, difference between means
Critical statistic (e.g. z or t or F or r) value?
Step 3: Calculations
MSWithin
MSBetween
F =
Still, variability of curve(s)
Step 4: Make decision whether or not to reject null hypothesis
If observed t (or F) is bigger then critical t (or F) then
reject null
Step 5: Conclusion - tie findings back in to research problem

45. The sum of squared deviations of some set of scores about their mean
Sum of squares (SS):
The sum of squared deviations of some set of scores about their mean
Mean squares (MS):
The sum of squares divided by its degrees of freedom
Mean square between groups:
sum of squares between groups
divided by its degrees of freedom
Mean square total: sum of squares total
divided by its degrees of freedom
MSWithin
MSBetween
F =
Mean square within groups:
sum of squares within groups
divided by its degrees of freedom 45

46. F = ANOVA Variability between groups Variability within groups
“Between” variability bigger than “within” variability so should get a big (significant) F
Variability Within Groups
Variability Within Groups
Variability Between Groups
Variability Within Groups
“Between” variability getting smaller “within” variability staying same so, should get a smaller F
Variability Between Groups
“Between” variability getting very small “within” variability staying same so, should get a very small F
Variability Within Groups

47. ANOVA Variability between groups F = Variability within groups
“Between” variability bigger than “within” variability so should get a big (significant) F
Variability Within Groups
Variability Within Groups
Variability Between Groups
“Between” variability getting smaller “within” variability staying same so, should get a smaller F
Variability Within Groups
“Between” variability getting very small “within” variability staying same so, should get a very small F (equal to 1)

48. In a one-way ANOVA we have three types of variability.
Let’s try one
In a one-way ANOVA we have three types of variability.
Which picture best depicts the random error variability (also known as the within variability)?
a. Figure 1
b. Figure 2
c. Figure 3
d. All of the above 1.
correct 2. 3.

49. In a one-way ANOVA we have three types of variability.
Let’s try one
In a one-way ANOVA we have three types of variability.
Which picture best depicts the between group variability?
a. Figure 1
b. Figure 2
c. Figure 3
d. All of the above
correct 1. 2. 3.

50. Questions?

51. Thank you!
See you next time!!