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INTEGRATED LEARNING CENTER
ILC 120
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desk

2. BNAD 276: Statistical Inference in Management Spring 2016
Welcome
Green sheets

3. By the end of lecture today 2/4/16
Use this as your
study guide
By the end of lecture today 2/4/16
Peer review and the iterative approach in design
Questionnaire design and evaluation
Frequency Distributions
Normal Curve
Measures of Central Tendency
Mean, Median, Mode
Measures of Variability

5. Optional Homework Due Tuesday, February 9th
Students are invited to rework Homework Assignment 3 & 4 based on feedback provided in class
We will provide feedback today on this assignment

6. Schedule of readings Before next exam: February 18th Please read
Chapters in OpenStax
Supplemental reading (Appendix D)
Supplemental reading (Appendix E)
Supplemental reading (Appendix F)
Please read Chapters 1, 5, 6 and 13 in Plous
Chapter 1: Selective Perception
Chapter 5: Plasticity
Chapter 6: Effects of Question Wording and Framing
Chapter 13: Anchoring and Adjustment

7. Must be complete and must be stapled
Preview of Questionnaire Homework
There are five parts:
Statement of Objectives
Questionnaire itself (which is the operational definitions of the objectives)
Data collection and creation of database
Creation of graphs representing results
Generate a formal memorandum describing results
Must be complete and must be stapled

8. Iterative design process
Peer review is an important skill in nearly all areas of business and science. Please strive to provide productive, useful and kind feedback as you complete your peer review

9. Iterative design process
Peer review is an important skill in nearly all areas of business and science. Please strive to provide productive, useful and kind feedback as you complete your peer review
If you do not have a hard copy of your formal memorandum you may not participate. There is alternative worksheet, please ask for one.
You have
10 minutes

10. Hand in the peer review with the questionnaire *Hand them in together*
Preview of Questionnaire Homework
There are five parts:
Statement of Objectives
Questionnaire itself (which is the operational definitions of the objectives)
Data collection and creation of database
Creation of graphs representing results
Generate a formal memorandum describing results
Hand in the peer review with the questionnaire
*Hand them in together*
Also hand in Correlation Worksheet

11. Homework Assignment #5 & 6 (Has 2 parts)
Act as consultant for Hospital Administrator
How to report findings in a formal memorandum
Example of formal memorandum for homework assignments 3 & 4
Due: Tuesday, February 9th (both handed in together)

12. Overview Frequency distributions
The normal curve
Challenge yourself as we work through characteristics of distributions to try to categorize each concept as a measure of
1) central tendency
2) dispersion or 3) shape
Mean, Median,
Mode, Trimmed Mean
Skewed right, skewed left
unimodal, bimodal, symmetric

13. A little more about frequency distributions
An example of a normal distribution

14. A little more about frequency distributions
An example of a normal distribution

15. A little more about frequency distributions
An example of a normal distribution

16. A little more about frequency distributions
An example of a normal distribution

17. A little more about frequency distributions
An example of a normal distribution

18. Measure of central tendency: describes how scores tend to
Measure of central tendency: describes how scores tend to cluster toward the center of the distribution
Normal distribution
In all distributions:
mode = tallest point
median = middle score
mean = balance point
In a normal distribution:
mode = mean = median

19. Positively skewed distribution
Measure of central tendency: describes how scores tend to cluster toward the center of the distribution
Positively skewed distribution
In all distributions:
mode = tallest point
median = middle score
mean = balance point
In a positively skewed distribution:
mode < median < mean
Note: mean is most affected by outliers or skewed distributions
With Bill Gates our Average Income would be $38 million a year

20. Measure of central tendency: describes how scores tend to
Measure of central tendency: describes how scores tend to cluster toward the center of the distribution
Negatively skewed distribution
In all distributions:
mode = tallest point
median = middle score
mean = balance point
In a negatively skewed distribution:
mean < median < mode
Note: mean is most affected by outliers or skewed distributions

21. Mode: The value of the most frequent observation
Bimodal distribution: Distribution with two most
frequent observations (2 peaks)
Example: Ian coaches two boys baseball teams. One team is made up of 10-year-olds and the other is made up of 16-year-olds. When he measured the height of all of his players he found a bimodal distribution

22. Overview Frequency distributions
The normal curve
Mean, Median,
Mode, Trimmed Mean
Standard deviation,
Variance, Range
Mean Absolute Deviation
Skewed right, skewed left
unimodal, bimodal, symmetric

23. Frequency distributions
The normal curve

24. Some distributions are more
Variability
What might this be?
Some distributions are more
variable than others
Let’s say this is our distribution of heights of men on U of A baseball team 5’
5’6” 6’
6’6” 7’ 5’
5’6” 6’
6’6” 7’
Mean is 6 feet tall
What might this be? 5’
5’6” 6’
6’6” 7’

25. Dispersion: Variability
Some distributions are more variable
than others 6’ 7’ 5’
5’6”
6’6” A
The larger the variability
the wider the curve tends to be
The smaller the variability
the narrower the curve tends to be B
Range: The difference between
the largest and smallest
observations C
Range for distribution A?
Range for distribution B?
Range for distribution C?

26. 84” – 70” = 14” Wildcats Basketball team:
Tallest player = 84” (same as 7’0”) (Kaleb Tarczewski and Dusan Ristic)
Shortest player = 70” (same as 5’10”)
(Parker Jackson-Cartwritght)
Fun fact:
Mean is 78
Range:
The difference
between the largest
and smallest scores
84” – 70” = 14”
xmax - xmin = Range
Range is 14”

27. No reference is made to numbers between the min and max
Baseball
Fun fact:
Mean is 72
Wildcats Baseball team:
Tallest player = 77” (same as 6’5”)
(Austin Schnabel)
Shortest player = 69” (same as 5’9”)
(Justin Behnke and Ernie DeLaTrinidad )
Range:
The difference between the largest and smallest score
77” – 69” = 8”
xmax - xmin = Range
Range is 8” (77” – 69” )
Please note:
No reference is made to numbers between the min and max

28. 84” – 70” = 14” Wildcats Basketball team:
Tallest player = 84” (same as 7’0”) (Kaleb Tarczewski and Dusan Ristic)
Shortest player = 70” (same as 5’10”)
(Parker Jackson-Cartwritght)
Fun fact:
Mean is 78
Range:
The difference
between the largest
and smallest scores
84” – 70” = 14”
xmax - xmin = Range
Range is 14”

29. No reference is made to numbers between the min and max
Baseball
Fun fact:
Mean is 72
Wildcats Baseball team:
Tallest player = 77” (same as 6’5”)
(Austin Schnabel)
Shortest player = 69” (same as 5’9”)
(Justin Behnke and Ernie DeLaTrinidad )
Range:
The difference between the largest and smallest score
77” – 69” = 8”
xmax - xmin = Range
Range is 8” (77” – 69” )
Please note:
No reference is made to numbers between the min and max

30. Generally, (on average) how far away is each score from the mean?
Variability
Standard deviation: The average amount by which observations deviate on either side of their mean
Generally, (on average) how far away is each score from the mean?
Mean is 6’

31. Let’s build it up again… U of A Baseball team
Deviation scores
Let’s build it up again… U of A Baseball team
Diallo is 0”
Diallo is 6’0”
Diallo’s deviation score is 0
6’0” – 6’0” = 0
Diallo
5’8” 5’10” 6’0” 6’2” 6’4”

32. Let’s build it up again… U of A Baseball team
Deviation scores
Diallo is 0”
Let’s build it up again… U of A Baseball team
Preston is 2”
Diallo is 6’0”
Diallo’s deviation score is 0
Preston is 6’2”
Preston
Preston’s deviation score is 2”
6’2” – 6’0” = 2
5’8” 5’10” 6’0” 6’2” 6’4”

33. Let’s build it up again… U of A Baseball team
Deviation scores
Diallo is 0”
Let’s build it up again… U of A Baseball team
Preston is 2”
Mike is -4”
Hunter is -2
Diallo is 6’0”
Diallo’s deviation score is 0
Hunter
Preston is 6’2”
Mike
Preston’s deviation score is 2”
Mike is 5’8”
Mike’s deviation score is -4”
5’8” – 6’0” = -4
5’8” 5’10” 6’0” 6’2” 6’4”
Hunter is 5’10”
Hunter’s deviation score is -2”
5’10” – 6’0” = -2

34. Let’s build it up again… U of A Baseball team
Deviation scores
Diallo is 0”
Let’s build it up again… U of A Baseball team
Preston is 2”
Mike is -4”
Hunter is -2
Shea is 4
David is 0”
Diallo’s deviation score is 0
David
Preston’s deviation score is 2”
Mike’s deviation score is -4”
Shea
Hunter’s deviation score is -2”
Shea is 6’4”
Shea’s deviation score is 4”
5’8” 5’10” 6’0” 6’2” 6’4”
6’4” – 6’0” = 4
David is 6’ 0”
David’s deviation score is 0
6’ 0” – 6’0” = 0

35. Let’s build it up again… U of A Baseball team
Deviation scores
Diallo is 0”
Let’s build it up again… U of A Baseball team
Preston is 2”
Mike is -4”
Hunter is -2
Shea is 4
David is 0”
Diallo’s deviation score is 0
David
Preston’s deviation score is 2”
Mike’s deviation score is -4”
Shea
Hunter’s deviation score is -2”
Shea’s deviation score is 4”
David’s deviation score is 0”
5’8” 5’10” 6’0” 6’2” 6’4”

36. Let’s build it up again… U of A Baseball team
Deviation scores
Diallo is 0”
Let’s build it up again… U of A Baseball team
Preston is 2”
Mike is -4”
Hunter is -2
Shea is 4
David is 0”
5’8” 5’10” 6’0” 6’2” 6’4”

37. Standard deviation: The average amount
Deviation scores
Standard deviation: The average amount
by which observations deviate on either side
of their mean
Diallo is 0”
Preston is 2”
Mike is -4”
Hunter is -2
Shea is 4
David is 0”
5’8” 5’10” 6’0” 6’2” 6’4”

38. Standard deviation: The average amount
Deviation scores
Standard deviation: The average amount
by which observations deviate on either side
of their mean
Diallo is 0”
Preston is 2”
Mike is -4”
Hunter is -2
Shea is 4
David is 0”
5’8” 5’10” 6’0” 6’2” 6’4”

39. Standard deviation: The average amount
Deviation scores
Standard deviation: The average amount
by which observations deviate on either side
of their mean
Diallo is 0”
Preston is 2”
Mike is -4”
Hunter is -2
Shea is 4
David is 0”
5’8” 5’10” 6’0” 6’2” 6’4”

40. How far away is each score from the mean?
Diallo is 0”
Mike is -4”
Hunter is -2
Shea is 4
David is 0”
Preston is 2”
Deviation scores
(x - µ)
Deviation scores: The amount by which observations
deviate on either side of their mean
(x - µ)
How far away is each score from the mean?
Mean
Diallo
Deviation
score
Mike
Preston
Shea
(x - µ) = ?
Hunter
Mike
5’8” ’0” = - 4”
5’9” ’0” = - 3”
5’10’ - 6’0” = - 2”
5’11” - 6’0” = - 1”
6’0” ’0 = 0
6’1” ’0” = + 1”
6’2” ’0” = + 2”
6’3” ’0” = + 3”
6’4” ’0” = + 4”
Diallo
How do we find each deviation score?
(x - µ)
Preston
Hunter
Diallo
Mike
Preston
Find distance of each person from the mean (subtract their score from mean)

41. How far away is each score from the mean?
Diallo is 0”
Mike is -4”
Hunter is -2
Shea is 4
David is 0”
Preston is 2”
Deviation scores
(x - µ)
Deviation scores: The amount by which observations
deviate on either side of their mean
(x - µ)
How far away is each score from the mean?
Mean
Diallo
Deviation
score
Preston
Shea
(x - µ) = ?
Mike
5’8” ’0” = - 4”
5’9” ’0” = - 3”
5’10’ - 6’0” = - 2”
5’11” - 6’0” = - 1”
6’0” ’0 = 0
6’1” ’0” = + 1”
6’2” ’0” = + 2”
6’3” ’0” = + 3”
6’4” ’0” = + 4”
Remember
It’s relative
to the mean
Based on difference from the mean

42. How far away is each score from the mean?
Standard deviation: The average amount by which
observations deviate on either side of their mean
Deviation scores
(x - µ)
Diallo is 0”
Preston is 2”
How far away is each score from the mean?
Mike is -4”
Hunter is -2
Shea is 4
Mean
David is 0”
Add up
Deviation scores
Diallo
Preston
Σ (x - µ) = ?
Shea
Mike
5’8” ’0” = - 4”
5’9” ’0” = - 3”
5’10’ - 6’0” = - 2”
5’11” - 6’0” = - 1”
6’0” ’0 = 0
6’1” ’0” = + 1”
6’2” ’0” = + 2”
6’3” ’0” = + 3”
6’4” ’0” = + 4”
How do we find the average height? N Σx
= average height
How do we find the average spread?
Σ(x - x) = 0
Σ(x - µ) N
= average deviation
Σ(x - µ) = 0

43. How far away is each score from the mean?
Standard deviation: The average amount by which
observations deviate on either side of their mean
Deviation scores
(x - µ)
Diallo is 0”
Preston is 2”
How far away is each score from the mean?
Mike is -4”
Hunter is -2
Shea is 4
Mean
David is 0”
Diallo
Preston
Σ (x - µ) = ?
Shea
Mike
5’8” ’0” = - 4”
5’9” ’0” = - 3”
5’10’ - 6’0” = - 2”
5’11” - 6’0” = - 1”
6’0” ’0 = 0
6’1” ’0” = + 1”
6’2” ’0” = + 2”
6’3” ’0” = + 3”
6’4” ’0” = + 4”
Square the deviations
Big problem
Σ(x - x) 2 2
Σ(x - x) = 0
Σ(x - µ) N
Σ(x - µ) 2
Σ(x - µ) = 0

44. These would be helpful to know by heart – please memorize
Standard deviation: The average amount by which
observations deviate on either side of their mean
These would be helpful to know by heart – please memorize
these formula

45. What do these two formula have in common?
Standard deviation: The average amount by which observations
deviate on either side of their mean
What do these two formula have in common?

46. What do these two formula have in common?
Standard deviation: The average amount by which observations
deviate on either side of their mean
What do these two formula have in common?

47. How do these formula differ?
Standard deviation: The average amount by which observations
deviate on either side of their mean
“n-1” is
Degrees of Freedom”
How do these formula differ?

48. “Sum of Squares” “Sum of Squares” “Sum of Squares” “Sum of Squares”
Standard deviation: The average amount by
which observations deviate on either side of their mean
“Sum of Squares”
“Sum of Squares”
“Sum of Squares”
“Sum of Squares”
Diallo is 0”
Mike is -4”
Hunter is -2
Shea is 4
David 0”
Preston is 2”
Deviation scores
Remember, it’s relative to the mean
“n-1” is
“Degrees of Freedom”
“n-1” is
“Degrees of Freedom”
Generally, (on average) how far away is each score from the mean?
Based on difference from the mean
Mean
Remember, We are thinking in terms of “deviations”
Diallo
Please memorize these
Preston
Shea
Mike

49. Standard deviation (definitional formula) - Let’s do one
This numerator is called “sum of squares”
Each of these are deviation scores
_ X - µ _
1 - 5 = - 4
2 - 5 = - 3
3 - 5 = - 2
4 - 5 = - 1
5 - 5 = 0
6 - 5 = 1
7 - 5 = 2
8 - 5 = 3
9 - 5 = 4
(X - µ)2 16 9 4 1 60
Step 1: Find the mean
_ X_ 1 2 3 4 5 6 7 8 9 45
ΣX = 45
ΣX / N = 45/9 = 5
Step 2: Subtract the mean from
each score
Step 3: Square the deviations
Step 4: Find standard deviation
This is the Variance!
a) 60 / 9 =
b) square root of =
Σ(x - µ) = 0
This is the standard deviation!

50. Another example: How many kids in your family?3 4 2 1 4 2 2 3 1 8

51. Standard deviation - Let’s do one
Definitional formula
How many kids?
Step 1: Find the mean
X - µ_
3 - 3 = 0
2 - 3 = -1
1 - 3 = -2
4 - 3 = 1
8 - 3 = 5
(X - µ)2 1 4 25
_ X_ 3 2 1 4 8
= 30
= 30/10 = 3
Step 2: Subtract the mean from
each score (deviations)
Step 3: Square the deviations
Step 4: Add up the squared deviations
Step 5: Find standard deviation
Σ(x - µ) = 0
Σx = 30
Σ(x - µ)2 = 38
This is the Variance!
a) 38 / 10 = 3.8
b) square root of 3.8 = 1.95
This is the standard deviation!

52. Thank you!
See you next time!!