1. BNAD 276: Statistical Inference in Management Winter, 2015
Welcome
Syllabi
Green sheet
Seating Chart

2. Daily group portfolios
Beginning of each lecture (first 5 minutes)
Meet in groups of 3 or 4
Quiz one another on class material
Discuss the questions and determine the correct answer for each question
Five copies (one for each group member – and typed) multiple choice questions based on lecture
Include 4 options (a, b, c, and d)
Include a name and describe a person in a certain situation
Margaret was interested in taking a Statistics course.
It is likely she was interested in studying which of the following? a. economic theories of communism
b. theological perspectives of life after death
c. musical compositions of the 12th century
d. statistical techniques and inference
They can be funny or serious, and must be clear and have only one correct answer.

3. Please start
portfolios

4. . Homework Assignment Go to D2L - Click on “Content”
Click on “Interactive Online Homework Assignments”
Complete the module:
Seven Prototypical Designs

5. Height of Daughters (inches)
Height of Mothers (in)
This shows the strong positive (r = +0.8) relationship between the heights of daughters (in inches) with heights of their mothers (in inches).
Variable name is listed clearly
Description includes:
Both variables
Strength (weak,moderate,strong)
Direction (positive, negative)
Estimated value (actual number)
Both axes have real numbers listed
Both axes and values are labeled
Variable name is listed clearly
1. Describe one positive correlation
Draw a scatterplot (label axes)
2. Describe one negative correlation
Draw a scatterplot (label axes)
Hand in Correlation
worksheet
3. Describe one zero correlation
Draw a scatterplot (label axes)
4. Describe one perfect correlation (positive or negative)
Draw a scatterplot (label axes)
5. Describe curvilinear relationship
Draw a scatterplot (label axes)

6. 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
Standard deviation,
Variance, Range
Mean Absolute Deviation
Skewed right, skewed left
unimodal, bimodal, symmetric

7. Another example: How many kids in your family?
Number of kids in family
1 4
3 2
1 8
4 2
2 14 14 4 2 1 4 2 2 3 1 8

8. Mean: The balance point of a distribution. Found
Measures of Central Tendency (Measures of location) The mean, median and mode
Mean: The balance point of a distribution. Found
by adding up all observations and then dividing
by the number of observations
Mean for a sample:
Σx / n = mean = x
Mean for a population:
ΣX / N = mean = µ (mu)
Measures of “location”
Where on the number line the scores tend to cluster
Note: Σ = add up
x or X = scores
n or N = number of scores

9. Number of kids in family
Measures of Central Tendency (Measures of location) The mean, median and mode
Mean: The balance point of a distribution. Found
by adding up all observations and then dividing
by the number of observations
Mean for a sample:
Σx / n = mean = x
41/ 10 = mean = 4.1
Number of kids in family
1 4
3 2
1 8
4 2
2 14
Note: Σ = add up
x or X = scores
n or N = number of scores

10. How many kids are in your family? What is the most common family size?
Number of kids in family
1 3
1 4
2 4
2 8
2 14
How many kids are in your family?
What is the most common family size?
Median: The middle value when observations are
ordered from least to most (or most to least)

11. Number of kids in family
1 4
3 2
1 8
4 2
2 14
How many kids are in your family?
What is the most common family size?
Median: The middle value when observations are
ordered from least to most (or most to least)
1, 3, 1, 4, 2, 4, 2, 8, 2, 14 1, 1, 2, 2, 2, 3, 4, 4, 8, 14

12. Number of kids in family
1 3
1 4
2 4
2 8
2 14
Number of kids in family
1 4
3 2
1 8
4 2
2 14
How many kids are in your family?
What is the most common family size?
Median: The middle value when observations are
ordered from least to most (or most to least)
1, 3, 1, 4, 2, 4, 2, 8, 2, 14 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 8, 8, 14 14
2.5
µ=2.5
If there appears to be two medians, take the mean of the two
Median always has a percentile rank of 50% regardless of shape of distribution
Median also called the 2nd Quartile

13. Number of kids in family
1 4
3 2
1 8
4 2
2 14
Number of kids in family
1 3
1 4
2 4
2 8
2 14
How many kids are in your family?
What is the most common family size?
Median: The middle value when observations are
ordered from least to most (or most to least) 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 8, 14
Lower half
Upper half
2.5
2nd Quartile Middle number of all scores
(Median) 1, 1, 1, 1, 2, 2, 2, 3, 8, 14 2, 2, 3, 4, 4, 4, 2, 4, 4, 8, 14
1st Quartile
Middle number of lower half of scores
3rd Quartile
Middle number of upper half of scores

14. Number of kids in family
Mode: The value of the most frequent observation
Score f .
1 2
2 3
3 1
4 2
5 0
6 0
7 0
8 1
9 0
10 0
11 0
12 0
13 0
14 1
Number of kids in family
1 3
1 4
2 4
2 8
2 14
Please note:
The mode is “2” because it is the most frequently occurring score. It occurs “3” times. “3” is not the mode, it is just the frequency for the value that is the mode
Bimodal distribution:
If there are two most
frequent observations

15. What about central tendency for qualitative data?
Mode is good for nominal or ordinal data
Median can be used with ordinal data
Mean can be used with interval or ratio data

16. 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

17. 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

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

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

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

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

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

23. 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

24. 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

25. 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

26. 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

27. 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

28. Frequency distributions
The normal curve

29. 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’

30. 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?

31. 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”

32. 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

33. 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’

34. 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”

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”
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”

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
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

37. 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

38. 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”

39. 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”

40. 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”

41. 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”

42. 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”

43. 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)

44. 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

45. 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

46. 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

47. 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

48. 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?

49. 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?

50. 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?

51. “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

52. 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!

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

54. 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!

55. These would be helpful to know by heart – please memorize areas
1 sd above and below mean
68%
2 sd above and below mean
95%
3 sd above and below mean
99.7%
These would be helpful to know by heart – please memorize areas

56. Raw scores, z scores & probabilities
Please note spatially where 1 standard deviation falls on the curve
68%
95%
99.7%

57. Raw scores, z scores & probabilities
Please note spatially where 1 standard deviation falls on the curve

58. Raw scores, z scores & probabilities
1 sd above and below mean
68%
z = +1
z = -1
Mean = 50
S = 10
(Note S = standard deviation)
If we go up one standard deviation
z score = +1.0 and raw score = 60
If we go down one standard deviation
z score = -1.0 and raw score = 40

59. Raw scores, z scores & probabilities
2 sd above and below mean
95%
z = -2
z = +2
Mean = 50
S = 10
(Note S = standard deviation)
If we go up two standard deviations
z score = +2.0 and raw score = 70
If we go down two standard deviations
z score = -2.0 and raw score = 30

60. Raw scores, z scores & probabilities
3 sd above and below mean
99.7%
z = +3
z = -3
Mean = 50
S = 10
(Note S = standard deviation)
If we go up three standard deviations
z score = +3.0 and raw score = 80
If we go down three standard deviations
z score = -3.0 and raw score = 20

61. z score = raw score - mean standard deviation
If we go up one standard deviation
z score = +1.0 and raw score = 105
z = -1
z = +1
68%
If we go down one standard deviation
z score = -1.0 and raw score = 95
If we go up two standard deviations
z score = +2.0 and raw score = 110
z = -2
95%
z = +2
If we go down two standard deviations
z score = -2.0 and raw score = 90
If we go up three standard deviations
z score = +3.0 and raw score = 115
99.7%
z = -3
z = +3
If we go down three standard deviations
z score = -3.0 and raw score = 85
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

62. Writing Assignment – Pop Quiz
1. What is a “deviation score”
2. Preston has a deviation score of 2: What does that tell us about Preston?
Is he taller or shorter than the mean? And by how much?
Are most people in the group taller or shorter than Preston
Mike has a deviation score of -4: What does that tell us about Mike?
Are most people in the group taller or shorter than Mike
Diallo has a deviation score of 0: What does that tell us about Diallo?
Are most people in the group taller or shorter than Diallo?
Please write the formula for the standard deviation of a population
Please draw 3 curves showing 1, 2 & 3 standard deviations from mean

63. Writing Assignment – Pop Quiz
7. What does this symbol refer to?
What is it called?
What does it mean?
Is it referring to a sample or population?
8. What does this symbol refer to?
What is it called?
What does it mean?
Is it referring to a sample or population?
9. What does this symbol refer to?
What is it called?
What does it mean?
Is it referring to a sample or population?
10. What does this symbol refer to?
What is it called?
What does it mean?
Is it referring to a sample or population?
11. What does this symbol refer to?

64. Writing Assignment – Pop Quiz
12. What does this refer to?
What are they called?
What do they refer to?
How are they different
13. What does this refer to?
What are they called?
How are they different
14. What do these two refer to?
What are they called?
How are they different
15. What does this refer to?
What is it called?
Use it for sample data or population?

65. Writing Assignment – Pop Quiz
16. What does this refer to?
What are they called?
What do they refer to?
How are they different
17. What does this refer to?
What are they called?
What do they refer to?
How are they different

66. Writing Assignment – Pop Quiz 1. What is a “deviation score”
2. Preston has a deviation score of 2: What does that tell us about Preston?
Is he taller or shorter than the mean? And by how much?
Are most people in the group taller or shorter than Preston
Mike has a deviation score of -4: What does that tell us about Mike?
Are most people in the group taller or shorter than Mike
Diallo has a deviation score of 0: What does that tell us about Diallo?
Are most people in the group taller or shorter than Diallo?
Please write the formula for the standard deviation of a population
Please draw 3 curves showing 1, 2 & 3 standard deviations from mean
How far away is each score from the mean?
Preston is 2” taller than the mean (taller than most)
Mike is 4” shorter than the mean (shorter than most)
Diallo is exactly same height as mean (half taller half shorter)

67. Writing Assignment – Pop Quiz
The standard deviation
(population)
7. What does this symbol refer to?
What is it called?
What does it mean?
Is it referring to a sample or population?
sigma
population
The mean
(population)
8. What does this symbol refer to? mu
What is it called?
What does it mean?
Is it referring to a sample or population?
population
The mean
(sample)
9. What does this symbol refer to?
x-bar
What is it called?
What does it mean?
Is it referring to a sample or population?
sample
The standard deviation
(sample)
10. What does this symbol refer to? s
What is it called?
What does it mean?
Is it referring to a sample or population?
sample
11. What does this symbol refer to?
Each individual score

68. Variance Writing Assignment – Pop Quiz 12. What does this refer to?
population
sample
12. What does this refer to?
Variance
What are they called?
What do they refer to?
How are they different
S squared
Sigma squared
13. What does this refer to?
population
sample
What are they called?
How are they different
Deviation scores
14. What do these two refer to?
sample
population
What are they called?
How are they different
Sum of squares
15. What does this refer to?
Degrees of freedom
What is it called?
Use it for sample data or population?

69. Writing Assignment – Pop Quiz
Standard
Deviation
Writing Assignment – Pop Quiz
16. What does this refer to?
What are they called?
What do they refer to?
How are they different
sample
population
Variance
17. What does this refer to?
What are they called?
What do they refer to?
How are they different
sample
population

70. Connecting intentions of studies with Experimental Methodologies
Appropriate statistical analyses
Appropriate graphs
Today I want to present some “typical designs”. We will spend the next couple weeks filling in the details.
We’ll come back to these distinctions over and over again, and build on them for the rest of the semester.
Let’s get this overview well!
Not worry about calculation
details for now

71. Create example of each type Identify IV (one or two)
Identify DV (one or two)
Draw possible graph for each
Homework Assignment
Think about this as we work through each type of study
Study Type 1: Confidence Intervals
Study Type 2: t-test
Study Type 3: One-way Analysis of Variance (ANOVA)
Study Type 4: Two-way Analysis of Variance (ANOVA)
Study Type 5: Correlation
Study Type 6: Simple and Multiple regression
Study Type 7: Chi Square
We’ll come back to these distinctions over and over again, and build on them for the rest of the class.
Let’s get this overview well!
Not worry about calculation
details for now

72. Study Type 1: Confidence Intervals
Remember, this is just introduction to the idea
Not worry about calculation
details for now, we will get to those soon
Study Type 1: Confidence Intervals
On average newborns weigh 7 pounds, and are 20 inches long. My sister just had a baby
- guess how much it weighs?
Makes sense, right?!? Guess the mean.
On average you would be right most often if you always guessed the mean
Point estimate versus confidence interval:
Guessing a single number versus a range of numbers
What if you really needed to be right?!!? You could guess a range with smallest and largest possible scores.
(how wide a range to be completely sure?
Confidence interval:
Guessing a range (max and min)
and assigning a level of confidence
that the score falls in that range

73. Study Type 1: Confidence Intervals
Remember, this is just introduction to the idea
Not worry about calculation
details for now, we will get to those soon
Study Type 1: Confidence Intervals
Confidence Intervals: A range of values
that, with a known degree of certainty,
includes an unknown population characteristic, such as a population mean
100% Confidence Interval: We can be 100% confident that our population mean falls between these two scores
(Guess absurdly large and small values)
99% Confidence Interval: We can be 99% confident that our population mean falls between these two scores
95% Confidence Interval: We can be 95% confident that our population mean falls between these two scores
Which has a wider interval
relative to raw scores 95% or 99%?

74. Study Type 1: Confidence Intervals
Remember, this is just introduction to the idea
Not worry about calculation
details for now, we will get to those soon
Study Type 1: Confidence Intervals
Confidence Intervals: A range of values
that, with a known degree of certainty,
includes an unknown population characteristic, such as a population mean
This sample of 10,000 newborns
a mean weight is 7 pounds.
What do you think the minimum and maximum
weights would be to capture 95% of all newborns?
This sample of 1000 flights, the mean number of empty seats is 12.
What do you think the minimum and maximum number of empty seats
are likely to be in the flights today with a 95% level of certainty?
You can use a mean of a sample
to guess the
mean of population
mean of a smaller sample
most likely score for an individual
This sample of 500 households produced
a mean income of $35,000 a year.
What do you think the minimum and maximum income levels are
so that we are 95% confident that we captured Mabel’s?

75. We are looking to compare two means
Study Type 1: Confidence Intervals
Study Type 2: t-test
Comparing Two Means?
Use a t-test
We are looking to compare two means

76. Study Type 2: t-test analysis
Single Independent Variable (categorical) comparing two groups
Single Dependent Variable (numeric)
Used to test the effect of the IV on the DV
Andrea was interested in the effect of vacation time on productivity of the
workers in her department. She randomly assigned workers into two
groups, she allowed one group to go on vacation while the other
group had no vacation. After the vacation she measured productivity
for the two groups.
Independent Variable
Dependent Variable
Between or within
Quasi or true
Causal relationship?
Productivity
Yes
Vacation No
Vacation

77. workers in her department. She randomly assigned workers into two
Andrea was interested in the effect of vacation time on productivity of the
workers in her department. She randomly assigned workers into two
groups, she allowed one group to go on vacation while the other
group had no vacation. After the vacation she measured productivity
for the two groups. This is an example of a true experiment.
Dependent
variable is always quantitative
If “true” experiment
(randomly assigned to groups)
we can conclude that vacation
had an effect - it increased productivity
In t-test, independent variable is qualitative (with two groups)
If “quasi” experiment (not randomly assigned to groups), we can
conclude only that data suggest that vacation may have had an
effect; productivity increased for those who went on vacation,
but we can’t rule out other explanations.

78. p < 0.05 is most common value
Study Type 2: t-test analysis
Single Independent Variable (categorical) comparing two groups
Single Dependent Variable (numerical/continuous)
Comparing two means
(2 bars on graph)
Used to test the effect of the IV on the DV
Please note: a t-test allows us to compare two means
If the means are statistically different
- we say that there is “real” difference that is not just due to chance
- we say there is a statistically significant difference p < 0.05
p < 0.05 is most common value
– the “p value” can vary
(p < 0.01, or p < 0.001)

79. Comparing more than two means
Study Type 1: Confidence Intervals
Study Type 2: t-test
Study Type 3: One-way Analysis of Variance (ANOVA)
Comparing more than two means

80. 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

81. 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
Sales
None
New
Bike
Trip
Hawaii
None
New
Bike
Trip
Hawaii
In an ANOVA, independent variable is qualitative
(& more than two groups)

82. Comparing two independent variables
Study Type 1: Confidence Intervals
Study Type 2: t-test
Study Type 3: One-way Analysis of Variance (ANOVA)
Study Type 4: Two-way Analysis of Variance (ANOVA)
Comparing two independent variables
Each one has
multiple levels

83. Study Type 4: Two-way ANOVA
“Two-way” = “Two IVs”
Study Type 4: Two-way ANOVA
Ian was interested in the effect of incentives (and age) 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 he looked
to see who sold more cookies. The 3 incentives were: 1) Trip to Hawaii,
2) New Bike or 3) Nothing. He also measured the scouts’ ages.
Independent Variable #1
Independent Variable #2
Dependent Variable

84. Study Type 4: Two-way ANOVA
Multiple Independent Variables (categorical), each variable comparing
two or more groups
Single Dependent Variable (numerical/continuous)
Used to test the effect of two IV on the DV
Independent Variable #1: Type of incentive
Levels of Independent Variable: None, Bike, Trip to Hawaii
Independent Variable #2: Age
Levels of Independent Variable: Elementary girls versus college
Dependent Variable: Number of cookies sold
Levels of Dependent Variable: 1, 2, 3 up to max sold
Between participant design
Results: Incentive had an effect – it increased sales
Data suggest age had an effect – older girls sold more

85. Study Type 4: Two-way ANOVA
Two Independent Variables (categorical)
Single Dependent Variable (numerical/continuous)
Used to test the effect of two IV on the DV
Dependent
variable is always quantitative
College
College
Elementary
Sales
Sales
Elementary
None
New
Bike
Trip
Hawaii
None
New
Bike
Trip
Hawaii
In an ANOVA, both
independent variables are qualitative
(with more than two groups)

86. Study Type 1: Confidence Intervals
Study Type 2: t-test
Study Type 3: One-way Analysis of Variance (ANOVA)
Study Type 4: Two-way Analysis of Variance (ANOVA)
Study Type 5: Correlation

87. Study Type 5: Correlation plots relationship between two
Pretty much all correlations are “quasi-experimental”
Study Type 5: Correlation plots relationship between two
continuous / quantitative variables
Neutral relative to causality – but especially useful for predictions
Relationship between amount of money spent
on advertising and amount of money made in sales
Dependent
variable is always quantitative
Dollars spent
on Advertising
Positive
Correlation
In correlation, both variables
are quantitative
Dollars in Sales
Describe strength and direction of correlation
– in this case positive/strong
Graphing correlations use scatterplots (not bar graphs)

88. Study Type 1: Confidence Intervals
Study Type 2: t-test
Study Type 3: One-way Analysis of Variance (ANOVA)
Study Type 4: Two-way Analysis of Variance (ANOVA)
Study Type 5: Correlation
Study Type 6: Simple and Multiple regression

89. You probably make this much
Study Type 6: Regression: Using the correlation to predict
the value of one variable based on its relationship
with the other variable
You probably make this much
The predicted variable goes on the
“Y” axis and is called the dependent
variable.
The predictor variable goes on the
“X” axis and is called the independent
variable
Expenses per year
Yearly Income
If you spend this much

90. Dustin spends $12 for his own Birthday
Angelina Jolie Buys Brad Pitt a $24 million
Heart-Shaped Island for his 50th Birthday
You probably make this much
Expenses per year
Yearly Income
You probably make this much
If you spend this much
If you spend this much
Dustin spends $12
for his own Birthday

91. Study Type 6: Regression: Using the correlation to predict
the value of one variable based on its relationship
with the other variable
You probably make this much
The predicted variable goes on the
“Y” axis and is called the dependent
variable.
The predictor variable goes on the
“X” axis and is called the independent
variable
Expenses per year
Yearly Income
You probably make this much
Dependent Variable
(Predicted)
If you spend this much
If you save this much
Multiple regression will use multiple independent variables to predict the dependent variable
Independent
Variable 1
(Predictor)
If you spend this much
Independent
Variable 2
(Predictor)

92. Study Type 1: Confidence Intervals
Study Type 2: t-test
Study Type 3: One-way Analysis of Variance (ANOVA)
Study Type 4: Two-way Analysis of Variance (ANOVA)
Study Type 5: Correlation
Study Type 6: Simple and Multiple regression
Study Type 7: Chi Square

93. Study Type 7: Chi-squared is used to evaluate whether the differences found in your sample match what you would expect to find. It is used with nominal or ordinal data when we simply count how many participants fall into each category. We are comparing frequencies, not means.
or objects
or events
What is your favorite type of restaurant? (Do university students show the same results as the general population?)
What is your political affiliation? (Do the proportions change when the country is at war or otherwise stressed?
What is the most popular ride at Disneyland? (Are all the rides at Disneyland equally popular?)
Do more children, teens or adults play video games?
What is the most popular ride at Disneyland?
Just count how many people ride each one.
a. Dumbo b. Small World c. Space Mountain d. Splash Mountain
We could gather this data using clickers

94. Study Type 5: Correlation Study Type 1: Confidence Intervals
Connecting intentions of studies with
Experimental Methodologies
Appropriate statistical analyses
Appropriate graphs
Study Type 5:
Correlation
Study Type 1:
Confidence Intervals
Study Type 6:
Regression
Study Type 2:
t-test
Study Type 3:
One-way ANOVA
Study Type 7:
Chi-squared
Study Type 4:
Two-way ANOVA
Remember when p < 0.05 we say: - results are statistically significant
there is “real” difference
(not just due to chance)

95. What type of analysis is this?
Marietta is a manager of a movie theater. She wanted to know whether
there is a difference in concession sales for afternoon (matinee) movies
vs. evening movies. She took a random sample of 25 purchases from
the matinee movie (mean of $7.50) and 25 purchases from the evening
show (mean of $10.50). She compared these two means. This is an
example of a _____.
a. correlation
b. t-test
c. one-way ANOVA
d. two-way ANOVA
t-test
Let’s try another one
Let’s try one
This is an example of a
a. between participant design
b. within participant design
c. mixed participant design
Between

96. What type of analysis is this?
Marietta is a manager of a movie theater. She wanted to know whether there is a difference in concession sales for people of all ages. She simply measured their age and how much they spent on treats.
This is an example of a _____.
a. correlation
b. t-test
c. one-way ANOVA
d. two-way ANOVA
Correlation
Let’s try one

97. What type of analysis is this?
Marietta is a manager of a movie theater. She wanted to know whether
there is a difference in concession sales for afternoon (matinee) movies
and evening movies. She took a random sample of 25 purchases from
the matinee movie (mean of $7.50) and 25 purchases from the evening
show (mean of $10.50). Which of the following would be the appropriate
graph for these data
Matinee
Evening
Concession purchase a. c.
Concession purchase
Movie Times
Two means
t-test
Movie Times
Concession purchase d.
Movie Time
Concession b.
Let’s try one

98. What type of analysis is this?
Gabriella is a manager of a movie theater. She wanted to know whether
there is a difference in concession sales between teenage couples and
middle-aged couples. She also wanted to know whether time of day
makes a difference (matinee versus evening shows). She gathered
the data for a sample of 25 purchases from each pairing.
a. correlation
b. t-test
c. one-way ANOVA
d. two-way ANOVA
Two-way ANOVA
What are the two IV?
What are the levels of each?
Let’s try one

99. What type of analysis is this?
Gabriella is a manager of a movie theater. She wanted to know whether
there is a difference in concession sales between teenage couples and
middle-aged couples. She also wanted to know whether time of day
makes a difference (matinee versus evening shows). She gathered
the means for a sample of 25 purchases from each pairing.
Matinee
Older couples
Evening
Teenagers
Concession purchase a. c.
Concession purchase
Matinee
Older couples
Evening
Teenagers
Movie Times
Concession purchase d.
Older couples
Teenagers
Movie Time
Old / young b.
Matinee
Evening
Four means
Let’s try one

100. What type of analysis is this?
Pharmaceutical firm tested whether fish-oil capsules taken daily
decrease cholesterol. They measured cholesterol levels for 30 male
subjects and then had them take the fish-oil daily for 2 months and
tested their cholesterol levels again. Then they compared the mean
cholesterol before and after taking the capsules. This is an example
of a _____.
a. correlation
b. t-test
c. one-way ANOVA
d. two-way ANOVA
t-test
Let’s try another one
Let’s try one
This is an example of a
a. between participant design
b. within participant design
c. mixed participant design
Within

101. What type of analysis is this?
Elaina was interested in the relationship between the grade point
average and starting salary. She recorded for GPA and starting
salary for 100 students and looked to see if there was a relationship.
This is an example of a _____.
a. correlation
b. t-test
c. one-way ANOVA
d. two-way ANOVA
correlation
GPA
Starting
Salary
Relationship between
GPA and Starting salary
Let’s try one

102. What type of analysis is this?
An automotive firm tested whether driving styles can affect gas efficiency
in their cars. They observed 100 drivers and found there were four
general driving styles. They recruited a sample of 100 drivers all of
whom drove with one of these 4 driving styles. Then they asked all 100
drivers to use the same model car for a month and recorded their gas
mileage. Then they compared the mean mpg for each driving style.
This is an example of a _____.
a. correlation
b. t-test
c. one-way ANOVA
d. two-way ANOVA
Let’s try one
One-way ANOVA
Let’s try another one
Between
Let’s try another one
Quasi-experiment
This is an example of a
a. between participant design
b. within participant design
c. mixed participant design
This is an example of a
a. true experimental design
b. quasi-experimental design
c. mixed design

104. Thank you!
See you next time!!