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
3/21/18

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. Comparing more than two means
One-way Analysis of Variance (ANOVA)
Prep
Project 3

8. Review of the homework assignment

9. 6 – 5 = 4.0 .25 Two tailed test 1.96 (α = .05) 1 1 = = .25 16 4 √ 4.0
z- score : because we know the population standard deviation
Ho: µ = 5
Bags of potatoes from that plant are not different from other plants
Ha: µ ≠ 5
Bags of potatoes from that plant are different from other plants
Two tailed test
1.96
(α = .05) 1 1 =
= .25
6 – 5 4 √ 16
= 4.0
.25
4.0
-1.96
1.96

10. Because the observed z (4.0 ) is bigger than critical z (1.96)
These three will always match
Yes
Yes
Probability of Type I error is always equal to alpha
Yes
.05
1.64 No
Because observed z (4.0) is still bigger than critical z (1.64)
2.58 No
Because observed z (4.0) is still bigger than critical z(2.58)
there is a difference
there is not
there is no difference
there is
1.96
2.58

11. 89 - 85 Two tailed test (α = .05) n – 1 =16 – 1 = 15
-2.13
2.13
t- score : because we don’t know the population standard deviation
Two tailed test
(α = .05)
n – 1 =16 – 1 = 15
Critical t(15) = 2.131
2.667 6 √ 16

12. Because the observed z (2.67) is bigger than critical z (2.13)
These three will always match
Yes
Yes
Probability of Type I error is always equal to alpha
Yes
.05
1.753 No
Because observed t (2.67) is still bigger than critical t (1.753)
2.947
Yes
Because observed t (2.67) is not bigger than critical t(2.947) No
These three will always match No No
consultant did improve morale
she did not
consultant did not improve morale
she did
2.131
2.947

13. Value of observed statistic
Finish with statistical summary z = 4.0; p < 0.05
Or if it *were not* significant:
z = 1.2 ; n.s.
Start summary with two means (based on DV) for two levels of the IV
Describe type of test (z-test versus t-test) with brief overview of results
n.s. = “not significant”
p<0.05 = “significant”
The average weight of bags of potatoes from this particular plant
is 6 pounds, while the average weight for population is 5 pounds.
A z-test was completed and this difference was found to be
statistically significant. We should fix the plant. (z = 4.0; p<0.05)
Value of observed statistic

14. Value of observed statistic
Finish with statistical summary t(15) = 2.67; p < 0.05
Or if it *were not* significant:
t(15) = 1.07; n.s.
Start summary with two means (based on DV) for two levels of the IV
Describe type of test (z-test versus t-test) with brief overview of results
n.s. = “not significant”
p<0.05 = “significant”
The average job-satisfaction score was 89 for the employees who went
On the retreat, while the average score for population is 85. A t-test
was completed and this difference was found to be statistically
significant. We should hire the consultant. (t(15) = 2.67; p<0.05)
Value of observed statistic df

15. Homework .

16. Homework .

17. This is significant with alpha of 0.05
Homework
Type of instruction
Exam score 50 40
2-tail
0.05
CAUTION
This is significant with alpha of 0.05
BUT NOT WITH
alpha of 0.01
2.66
2.02 38
p =
yes
The average exam score for those with instruction was 50, while the average exam score for those with no instruction was 40. A t-test was conducted and found that instruction significantly improved exam scores, t(38) = 2.66; p < 0.05

18. Homework .
Type of Staff
Travel Expenses
142.5
130.29
2-tail
0.05
2.2 11
p = 0.153 no
The average expenses for sales staff is 142.5, while the average expenses for the audit staff was A t-test was conducted and no significant difference was found, t(11) = 1.54; n.s.

19. If the observed t is less than one it will never be significant.
Homework
Location of lot
Number of cars
86.24
92.04
2-tail
0.05
-0.88
2.01 51
p = 0.38 no
Fun fact:
If the observed t is less than one it will never be significant
The average number of cars in the Ocean Drive Lot was 86.24, while the average number of cars in Rio Rancho Lot was A t-test was conducted and no significant difference between the number of cars parked in these two lots, t(51) = -.88; n.s.

20. What happened? We ran more subjects: Increased n
So, we decreased variability
Easier to find effect significant
even though effect size didn’t change
This is the sample size
This is the sample size
Small sample
Big sample 20

21. What happened? We ran more subjects: Increased n
So, we decreased variability
Easier to find effect significant
even though effect size didn’t change
This is variance for each sample
(Remember, variance is just standard deviation squared)
This is variance for each sample
(Remember, variance is just standard deviation squared)
Small sample
Big sample 21

22. Review Study Type 2: t-test
We are looking to compare two means
Study Type 2: t-test
Study Type 3: One-way Analysis of Variance (ANOVA)
Comparing more than two means
Review

23. Review Study Type 3: One-way ANOVA
Single Independent Variable comparing more than two groups
Single Dependent Variable (numerical/continuous)
Used to test the effect of the IV on the DV
Ian was interested in the effect of incentives for girl scouts on the number
of cookies sold. He randomly assigned girl scouts into one of three groups.
The three groups were given one of three incentives and looked to see who
sold more cookies. The 3 incentives were 1) Trip to Hawaii, 2) New Bike
or 3) Nothing. This is an example of a true experiment
Dependent
variable is always quantitative
Sales per
Girl scout
Sales per
Girl scout
None
New
Bike
Trip
Hawaii
None
New
Bike
Trip
Hawaii
In an ANOVA, independent variable is qualitative
(& more than two groups)
Review

24. One-way ANOVA versus Chi Square
Be careful you are not designing a Chi Square
If this is just frequency you may have a problem
This is a
Chi Square
Total Number
of Boxes Sold
Sales per
Girl scout
This is an ANOVA
None
New
Bike
Trip
Hawaii
None
New
Bike
Trip
Hawaii
These are just frequencies
These are just frequencies
These are just frequencies
These are means
These are means
These are means

25. One-way ANOVA 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

26. 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

27. 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

28. Hypothesis testing: 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

29. Thank you!
See you next time!!