1. INTEGRATED LEARNING CENTER
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Lecturer’s desk
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Computer Storage Cabinet 4 3
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INTEGRATED LEARNING CENTER
ILC 120
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2. BNAD 276: Statistical Inference in Management Spring 2016
Welcome
Green sheets

4. Schedule of readings Before our next exam (April 7th)
OpenStax Chapters 1 – 12
Plous (2, 3, & 4)
Chapter 2: Cognitive Dissonance
Chapter 3: Memory and Hindsight Bias
Chapter 4: Context Dependence

5. By the end of lecture today 3/24/16
Analysis of Variance (ANOVA)
Constructing brief, complete summary statements

6. “df” = degrees of freedom
Remember, you should know these two formulas by heart
“SS” = “Sum of Squares”
“SS” = “Sum of Squares”
= s2 =
Sample
Variance
Sample
Standard Deviation
= s =
“SS” = “Sum of Squares”
“df” = degrees of freedom

7. Study Type 3: One-way Analysis of Variance (ANOVA)
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

8. 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 8

9. 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

10. 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

11. “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)

12. 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 12

13. 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

14. 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)

15. Homework

16. Homework

17. Homework

18. 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

19. # 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

20. 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).

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

22. 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

23. SS between
df between
MS between
MS within
SS within
df within

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

27. 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

28. 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).

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

30. 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

31. MS between
MS within
SS between
df between
SS within
df within

33. Questions?

34. Writing Assignment - Quiz
1. When do you use a t-test and when do you use an ANOVA
2. What is the formula for degrees of freedom in a two-sample t-test
3. What is the formula for degrees of freedom “between groups” in ANOVA
4. What is the formula for degrees of freedom “within groups” in ANOVA
5. How are “levels”, “groups”, “conditions” “treatments” related?
6. How are “significant difference”, “p< 0.05”, “main effect” and “we reject the null” related?
7. Draw and match each with proper label
Within Group
Variability
Total Variability
Between Group Variability

35. Writing Assignment - Quiz
8. Daphne compared running speed for three types of running
shoes. She asked 10 people to run as fast as they could
wearing one type of shoe. So, there were 30 people altogether
What is the independent variable?
What is the dependent variable?
How many factors do we have (what are they)?
How many treatments do we have (what are they)?
9. Complete this ANOVA table
10. Find the critical F value from the table
11. Is there a main effect of type of running shoe?
Is “p< 0.05”?

36. Writing Assignment - Quiz
n -1 per group
or n-2 or
Total n - # of groups
1. When do you use a t-test and when do you use an ANOVA
t-tests compare two means
ANOVA compares more than two means
2. What is the formula for degrees of freedom in a two-sample t-test
3. What is the formula for degrees of freedom “between groups” in ANOVA
# of groups - 1
4. What is the formula for degrees of freedom “within groups” in ANOVA
n -1 per group or
Total n - # of groups
5. How are “levels”, “groups”, “conditions” “treatments” related?
6. How are “significant difference”, “p< 0.05”, “main effect” and “we reject the null” related?
They all mean the same thing
They all mean the same thing
7. Draw and match each with proper label
Within Group
Variability
Total Variability
Between Group Variability

37. Writing Assignment - Quiz
8. Daphne compared running speed for three types of running
shoes. She asked 10 people to run as fast as they could
wearing one type of shoe. So, there were 30 people altogether
What is the independent variable?
What is the dependent variable?
How many factors do we have (what are they)?
How many treatments do we have (what are they)?
Type of running shoe
Running
Speed
Type 1
Type 2
Type 3
3 groups
1 Factor
9. Complete this ANOVA table
SSB
dfB
# groups - 1
n - # groups
MSB
MSW
SSW
dfW
n - 1
Yes
F(2,27)=4.00; p< 0.05
10. Find the critical F value from the table
3.37
11. Is there a main effect of type of running shoe?
Is “p< 0.05”?

38. 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.

39. 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.

40. 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.

41. Winnie found an observed F ratio of .9, what should she conclude?
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.

42. 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

43. 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

44. 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

45. 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

46. 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

47. 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 .

48. 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 .

49. 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 .

50. 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, alpha = We should:
a. reject the null hypothesis
b. not reject the null hypothesis
correct
Observed F
bigger than
Critical F
p < .05

51. Thank you!
See you next time!!