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
3/26/18

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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. Remember this?

9. One-way ANOVA Review One-way ANOVAs test only one independent variable
Number of
cookies sold
One-way ANOVA
None
Bike
Hawaii trip
Incentives
One-way ANOVAs test only one independent variable
- although there may be many levels
“Factor” = one independent variable
“Level” = levels of the independent variable
treatment
condition
groups
“Main Effect” of independent variable = difference between levels
Note: doesn’t tell you which specific levels (means) differ from each other
A multi-factor experiment would be a multi-independent
variables experiment
Review

10. Comparing ANOVAs with t-tests
Similarities still include:
Using distributions to make decisions about
common and rare events
Using distributions to make inferences about
whether to reject the null hypothesis or not
The same 5 steps for testing an hypothesis
Tells us generally about number of participants / observations
Tells us generally about number of groups / levels of IV
The three primary differences between t-tests and ANOVAS are:
1. ANOVAs can test more than two means
2. We are comparing sample means indirectly by
comparing sample variances
3. We now will have two types of degrees of freedom
t(16) = 3.0; p < F(2, 15) = 3.0; p < 0.05
Tells us generally about number of participants / observations
Review

11. Review A girl scout troop leader wondered whether providing an
incentive to whomever sold the most girl scout 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.
How many levels of the Independent Variable?
What is Independent Variable?
Troop 1
(nada) 10 8 12 7 13
Troop 2
(bicycle) 12 14 10 11 13
Troop 3
(Hawaii) 14 9 19 13 15
What is
Dependent Variable?
How many groups?
n = 5
x = 10
n = 5
x = 12
n = 5
x = 14
Review

12. Hypothesis testing: Review Step 1: Identify the research problem
Is there a significant difference in the number of
cookie boxes sold between the girlscout troops that were
given the different levels of incentive?
Describe the null and alternative hypotheses
Null hypotheses:
No difference between the groups (e.g. group means)
Alternative hypotheses:
There is a difference between the means
Review

13. Hypothesis testing: Review Decision rule = .05
Degrees of freedom (between) = number of groups - 1
= = 2
Degrees of freedom (within) = # of scores - # of groups
= (15 - 3) = 12*
*or = (5-1) + (5-1) + (5-1) = 12.
Critical F (2,12) =
3.98
Review

14. α= .05 Appendix B.4 (pg.518) F (2,12) Critical F(2,12) = 3.8914

15. number of scores – number of groups
“SS” = “Sum of Squares” - will be given for exams - you can think of this as the numerator in a standard deviation formula
ANOVA table
Source df MS F SS
df between =
number of groups minus 1
Between 40 ? ? ? ?
Within 88 ? ? ?
df within =
number of scores – number of groups
Total
128 ? ?
Critical F(2,12)
= 3.89

16. 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
Source SS df MS F
Between 40 ? ? ?
Within 88 ? ?
Total
128 ?
4. Decide whether to reject the null
5. Write your conclusion

17. ANOVA table Source df MS F SS Between 40 ? 2 ? ? ? Within ? 88 12 ? ?
“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

18. “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

19. 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 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. Thank you!
See you next time!!