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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. By the end of lecture today 2/2/16
Use this as your
study guide
By the end of lecture today 2/2/16
Revisit data collection using questionnaires
Correlation is called an “r”
Positive or Negative
Strong, Moderate or Weak (ranges from 0 – 1)
Measures of Central Tendency Mean, median and mode

5. writing assignment forms notebook and clickers to each lecture
Remember bring your
writing assignment forms
notebook and clickers to each lecture
A note on doodling
Remember to register
your clicker soon

7. Homework Assignment #3 & 4 (Has 2 parts)
Questionnaire construction using Likert scales instructions
Important additional materials to help with homework assignments 3 & 4
How to report findings in a formal memorandum
Example of formal memorandum for homework assignments 3 & 4
Rubric for homework assignments 3 & 4
Due: Thursday February 4th (both handed in together)

8. 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

9. 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

10. 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

11. Designed our study / observation / questionnaire
Collected our data
Organize and present our results

12. Scatterplot displays relationships between two continuous variables
Correlation: Measure of how two variables co-occur and
also can be used for prediction
Range between -1 and +1
The closer to zero the weaker the relationship
and the worse the prediction
Positive or negative

13. Correlation
Range between -1 and +1
+1.00 perfect relationship = perfect predictor
+0.80 strong relationship = good predictor
+0.20 weak relationship = poor predictor
0 no relationship = very poor predictor
-0.20 weak relationship = poor predictor
-0.80 strong relationship = good predictor
-1.00 perfect relationship = perfect predictor

14. Positive correlation: as values on one variable go up, so do values
Positive correlation: as values on one variable go up, so do values for the other variable
Negative correlation: as values on one variable go up, the values for the other variable go down
Height of Mothers
by Height of Daughters
Height of Mothers
Positive
Correlation
Height of
Daughters

15. Positive correlation: as values on one variable go up, so do values
Positive correlation: as values on one variable go up, so do values for the other variable
Negative correlation: as values on one variable go up, the values for the other variable go down
Brushing teeth
by number cavities
Brushing Teeth
Negative
Correlation
Number Cavities

16. Perfect correlation = +1.00 or -1.00
One variable perfectly predicts the other
Height in inches
and height in feet
Speed (mph)
and time to finish race
Positive
correlation
Negative
correlation

17. Correlation
The more closely the dots approximate a straight line, (the less spread out they are) the stronger the relationship is.
Perfect correlation = or -1.00
One variable perfectly predicts the other
No variability in the scatterplot
The dots approximate a straight line

18. Correlation

19. Correlation does not imply causation
Is it possible that they are causally related?
Yes, but the correlational analysis does not answer that question
What if it’s a perfect correlation – isn’t that causal?
No, it feels more compelling, but is neutral about causality
Number of
Birthdays
Number of
Birthday Cakes

20. Positive correlation: as values on one variable go up,
so do values for other variable
Negative correlation: as values on one variable go up,
the values for other variable go down
Number of bathrooms in a city and number of crimes committed
Positive correlation
Positive correlation

21. Linear vs curvilinear relationship
Linear relationship is a relationship
that can be described best with a straight line
Curvilinear relationship is a relationship that can be described best with a curved line

22. Correlation - How do numerical values change?
Correlation - How do numerical values change?
Let’s estimate the correlation coefficient for each of the following
r = +.80
r = +1.0
r = -1.0
r = -.50
r = 0.0

23. This shows a strong positive relationship (r = 0
This shows a strong positive relationship (r = 0.97) between the price of the house and its eventual sales price
r = +0.97
Description includes:
Both variables
Strength (weak,moderate,strong)
Direction (positive, negative)
Estimated value (actual number)

24. r = +0.97
r = -0.48
This shows a moderate negative relationship (r = -0.48) between the amount of pectin in orange juice and its sweetness
Description includes:
Both variables
Strength (weak,moderate,strong)
Direction (positive, negative)
Estimated value (actual number)

25. r = -0.91 Description includes: Both variables
Strength (weak,moderate,strong)
Direction (positive, negative)
Estimated value (actual number)
This shows a strong negative relationship (r = -0.91) between the distance that a golf ball is hit and the accuracy of the drive
r = -0.91

26. r = -0.91 r = 0.61 Description includes: Both variables
Strength (weak,moderate,strong)
Direction (positive, negative)
Estimated value (actual number)
This shows a moderate positive relationship (r = 0.61) between the price of the length of stay in a hospital and the number of services provided
r = -0.91
r = 0.61

27. r = +0.97
r = -0.48
r = -0.91
r = 0.61

28. 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

29. 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

30. 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

31. 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

32. 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

33. Use examples that are different from those is lecture
Break into groups of 2 or 3
Each person hand in own worksheet. Be sure to list your name and names of all others in your group
Use examples that are different from those is lecture
1. Describe one positive correlation
Draw a scatterplot (label axes)
You have
12 minutes
(approximately 2 minutes per example)
2. Describe one negative correlation
Draw a scatterplot (label axes)
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)

34. 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)

35. 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

36. 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

37. 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

38. 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

39. 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)

40. 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

41. 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

42. 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

43. 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

44. 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

45. Thank you!
See you next time!!