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G9, H3, M17
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2. Screen Stage Social Sciences 100 Lecturer’s desk broken desk
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Projection Booth

3. MGMT 276: Statistical Inference in Management Fall, 2014
Welcome
Green sheets

4. Reminder A note on doodling
Talking or whispering to your neighbor can be a problem for us – please consider writing short notes.

6. It went really well! Exam 3 Thanks for your patience and cooperation
Grades have been posted

7. Frequency Score on Exam Remember… In a negatively skewed distribution:
mean < median < mode
90 = mode = tallest point
85 = median = middle score
81 = mean = balance point
Frequency
Note:
Always “frequency”
Score on Exam
Mode
Mean
Median
Note:
Label and Numbers

8. Schedule of readings Before our next exam (December 4th)
Lind (10 – 12)
Chapter 13: Linear Regression and Correlation
Chapter 14: Multiple Regression
Chapter 15: Chi-Square
Plous (2, 3, & 4)
Chapter 17: Social Influences
Chapter 18: Group Judgments and Decisions

9. Exam 4 – Optional Times for Final
Two options for completing Exam 4
Thursday (12/4/14) – The regularly scheduled time
Tuesday (12/9/14) – The optional later time
Must sign up to take Exam 4 on Tuesday (12/2)
Only need to take one exam – these are two optional times

10. Homework due – Tuesday (November 18th)
On class website:
Please print and complete homework worksheet #18
Hypothesis Testing with ANOVAs

11. By the end of lecture today 11/13/14
Use this as your
study guide
By the end of lecture today 11/13/14
Logic of hypothesis testing
Steps for hypothesis testing
Hypothesis testing with analysis of variance (ANOVA)
Interpreting excel output of hypothesis tests
Constructing brief, complete summary statements

12. 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
How could we
make this a
quasi-experiment?
Independent Variable: Type of incentive
Levels of Independent Variable: None, Bike, Trip to Hawaii
Dependent Variable: Number of cookies sold
Levels of Dependent Variable: 1, 2, 3 up to max sold
Between participant design
Causal relationship: Incentive had an effect – it increased sales

13. 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)

14. 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 an
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

16. z scores Review Difference between means
z score: A score that indicates how many standard deviations
an observation is above or below the mean of the distribution
z score = raw score - mean
standard deviation
Variability of curve(s)
Review

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

18. 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

19. 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

20. 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

21. What if we want to compare 3 means?
One independent variable with 3 means
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
(Hawaii) 14 9 19 13 15
Troop 2
(bicycle) 12 14 10 11 13
Troop 3
(nada) 10 8 12 7 13
x = 10
x = 14
x = 12
Note: 5 girls in each troop

22. 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

23. 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 23

24. 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

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

26. Appendix
B.4 (pg.518)
F (2,12)
α= .05
Critical F(2,12)
= 3.89 26

27. ANOVA table Source df MS F SS Between ? ? ? ? Within ? ? ? Total ? ?
“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
Between ? ? ? ?
Within ? ? ?
Total ? ?

28. # 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
3-1=2
Between 40 ? ? 2
# groups - 1 ? ?
15-3=12
Within 88 ? 12 ?
# scores - number of groups ?
Total
128 ? ? 14
# scores - 1
15- 1=14

29. ANOVA table SSbetween dfbetween 40 2 40 2 =20 MSbetween MSwithin
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

30. 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.

31. 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

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

33. Let’s do same problem Using MS Excel

34. Let’s do same problem Using MS Excel

35. # scores - number of groups
SSbetween
dfbetween 40 2 40 2
=20
3-1=2
# groups - 1
MSbetween
MSwithin
# scores - number of groups
15-3=12
SSwithin
dfwithin 88 12
=7.33 20
7.33
=2.73 88 12
# scores - 1
15- 1=14

36. 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?)

37. 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

38. 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.

39. 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

40. Three different types of variance
Between groups
Within groups
Total
Between Groups Variability
Total Variability
Variability between groups
F =
Within Groups Variability
Variability within groups 40

41. 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

42. 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)

43. Effect size is considered relative to variability of distributions.
Effect size is considered relative to variability of distributions
Treatment
Effect x
Variability between groups
Treatment
Effect x
Variability within groups

44. 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.

45. Which figure would depict the largest F ratio a. Figure 1 b. Figure 2
Variability between groups
F =
Let’s try one
Variability within groups
“F ratio” is referring
to "observed F”
Which figure would depict the largest F ratio
a. Figure 1
b. Figure 2
c. Figure 3
d. All of the above
correct 1. 2. 3.

46. Winnie found an observed z of .74, what should she conclude?
If your observed z is within
one standard deviation of the mean,
you will never reject the null
Let’s try one
Winnie found an observed z of .74, what should she conclude?
(Hint: notice that .74 is less than 1)
a. Reject the null hypothesis
b. Do not reject the null hypothesis
c. Not enough info is given
correct x x
small observed z score
small observed z score

47. Winnie found an observed t of .04, what should she conclude?
Let’s try one
Winnie found an observed t of .04, what should she conclude?
(Hint: notice that .04 is less than 1)
a. Reject the null hypothesis
b. Do not reject the null hypothesis
c. Not enough info is given
correct x
small observed t score

48. Let’s try one
Winnie found an observed F ratio of .9, what should she conclude?
a. Reject the null hypothesis
b. Do not reject the null hypothesis
c. Not enough info is given
correct 1. 2. 3.

49. F(4, 25) = 3.12; p < 0.05 Let’s try one
How many
observations within
each group?
Let’s try one
An ANOVA was conducted comparing different types of solar cells and there appears to be a significant difference in output of each (watts) F(4, 25) = 3.12; p < In this study there were __ types of solar cells and __ total observations in the whole study?
a. 4; 25
b. 5; 30
c. 4; 30
d. 5; 25
F(4, 25) = 3.12; p < 0.05
correct
# groups - 1
# scores - # of groups
# scores - 1

50. F(4, 25) = 3.12; p < 0.05 Let’s try one
An ANOVA was conducted comparing different types of solar cells and there appears to be significant difference in output of each (watts) F(4, 25) = 3.12; p < In this study ___
a. we rejected the null hypothesis
b. we did not reject the null hypothesis
correct
F(4, 25) = 3.12; p < 0.05
Observed F
bigger than
Critical F
p < .05

51. F(4, 25) = 3.12; p < 0.05 Let’s try one
An ANOVA was conducted comparing different types of solar cells. The analysis was completed using an alpha of But Julia now wants to know if she can reject the null with an alpha of at In this study ___
a. we rejected the null hypothesis
b. we did not reject the null hypothesis
correct
F(4, 25) = 3.12; p < 0.05
Comparison of the Observed F and Critical F
Is no longer are helpful because
the critical F is no longer correct.
We must use the p value
p < .05
p > .01

52. Let’s try one
An ANOVA was conducted comparing home prices in four neighborhoods (Southpark, Northpark, Westpark, Eastpark) .
For each neighborhood we measured the price of four homes. Please complete this ANOVA table. Degrees of freedom between is _____; degrees of freedom within is ____
a. 16; 4
b. 4; 16
c. 12; 3
d. 3; 12
correct .

53. Let’s try one
An ANOVA was conducted comparing home prices in four neighborhoods (Southpark, Northpark, Westpark, Eastpark) .
For each neighborhood we measured the price of four homes. Please complete this ANOVA table. Mean Square between is _____; Mean Square within is ____
a. 300, 300
b. 100, 100
c. 100, 25
d. 25, 100
correct .

54. Let’s try one
An ANOVA was conducted comparing home prices in four neighborhoods (Southpark, Northpark, Westpark, Eastpark) .
For each neighborhood we measured the price of four homes. Please complete this ANOVA table. The F ratio is:
a. .25
b. 1
c. 4
d. 25
correct .

55. a. reject the null hypothesis b. not reject the null hypothesis
Let’s try one
An ANOVA was conducted comparing home prices in four neighborhoods (Southpark, Northpark, Westpark, Eastpark) .
For each neighborhood we measured the price of four homes. Please complete this ANOVA table. We should:
a. reject the null hypothesis
b. not reject the null hypothesis
correct
Observed F
bigger than
Critical F
p < .05

56. Let’s try one
An ANOVA was conducted comparing home prices in four neighborhoods (Southpark, Northpark, Westpark, Eastpark) .
For each neighborhood we measured the price of four homes. The most expensive neighborhood was the ____ neighborhood
a. Southpark
b. Northpark
c. Westpark
d. Eastpark
correct

57. An ANOVA was conducted comparing home prices in four neighborhoods (Southpark, Northpark, Westpark, Eastpark) .
For each neighborhood we measured the price of four homes. Please complete this ANOVA table. The best summary statement is:
a. F(3, 12) = 4.0; n.s.
b. F(3, 12) = 4.0; p < 0.05
c. F(3, 12) = 3.49; n.s.
d. F(3, 12) = 3.49; p < 0.05
correct

58. Let’s try one
An ANOVA was conducted and there appears to be a significant difference in the number of cookies sold as a result of the different levels of incentive F(2, 27) = ___; p < 0.05.
Please fill in the blank a b c d
correct

59. An ANOVA was conducted and we found the following results: F(3,12) = 3
An ANOVA was conducted and we found the following results: F(3,12) = 3.73 ____. Which is the best summary
a. The critical F is 3.89; we should reject the null
b. The critical F is 3.89; we should not reject the null
c. The critical F is 3.49; we should reject the null
d. The critical F is 3.49; we should not reject the null
correct
Let’s try one

60. Thank you!
See you next time!!