BUS 208 Week 3
grupy1
bus308week_3.docxBUS308: Statistics for Managers week 3
Ashford 4: - Week 3 (May 05 - May 11)
Overview
|
Assignment |
Due Date |
Format |
Grading Percent |
|
ANOVA |
Day 3 (1st post) |
Discussion |
3 |
|
Effect Size |
Day 3 (1st post) |
Discussion |
3 |
|
Problem Set Week Three |
Day 7 |
Assignment |
8 |
Note: The online classroom is designed to time students out after 90 minutes of inactivity. Because of this, we strongly suggest that you compose your work in a word processing program and copy and paste it into the discussion post when you are ready to submit it.
Learning Outcomes This week students will:
1. Identify multiple group differences in ANOVA testing.
2. Determine a statistical interaction.
Introduction
For Week Three, the focus will be on studying data within groups. In any analysis involving groups of subjects, individuals within the same group may respond to the same stimulus differently. Those differences constitute error variance, which is compounded in independent group tests where the individuals are different for each group. No matter how carefully a researcher randomly selects the groups to be used in a study, there are going to be differences in the ways people in the same group respond to whatever is measured.
Required Resources Required Text
1. Read the following chapters from Statistics for Managers:
a. Chapter 5- ANOVA: Analyzing Differences in Multiple Groups
b. Chapter 6- Factorial ANOVA: More than One Independent Variable
c. Chapter 7- Repeated Measures and Group Interdependence
Recommended Resources Multimedia
1. Rubenstein, B. (Producer) & Reich, J. M. (Director). (2000). Measures of variability and relative standing [Video File]. Available from the Films On Demand database.
2. Rubenstein, B. (Producer) & Reich, J. M. (Director). (2000). Probability distributions for continuous random variables [Video File]. Retrieved from the Films On Demand database.
3. TED (Producer). (2006). TedTalks: Hans Rosling—Debunking third-world myths with the best stats you've ever seen [Video File]. Retrieved from the Films On Demand database.
4. Khan Academy. (Producer). Regression [Video files]. Retrieved from https://www.khanacademy.org/math/probability/regression.
Discussions To participate in the following discussions, go to this week's Discussion link in the left navigation.
1. Anova In many ways, comparing multiple sample means is simply an extension of what we covered last week. Just as we had 3 versions of the t-test (1 sample, 2 sample (with and without equal variance), and paired; we have several versions of ANOVA – single factor, factorial (called 2-factor with replication in Excel), and within-subjects (2-factor without replication in Excel). What examples (professional, personal, social) can you provide on when we might use each type? What would be the appropriate hypotheses statements for each example? Guided Response: Review several of your classmates’ posts. Respond to at least two classmates by commenting on why you agree or disagree with the statistical test that your peers have described as appropriate in this scenario.
2. Effect Size Several statistical tests have a way to measure effect size. What is this, and when might you want to use it in looking at results from these tests on job related data? Guided Response: Review several of your classmates’ posts. Respond to at least two of your classmates.
Assignment To complete the following assignment, go to this week's Assignment link in the left navigation.
Problem Set Week Three Complete the problems included in the resources below and submit your work in an Excel document. Be sure to show all of your work and clearly label all calculations. All statistical calculations will use the Employee Salary Data Set and the Week 3 assignment sheet.
Carefully review the Grading Rubric for the criteria that will be used to evaluate your assignment.
Ashford 4: - Week 3 - Instructor Guidance
Weekly Overview
The F Distribution
It was named to honor Sir Ronald Fisher, one of the founders of modern-day statistics.
It is
– used to test whether two samples are from populations having equal variances
– applied when we want to compare several population means simultaneously. The simultaneous comparison of several population means is called analysis of variance(ANOVA).
– In both of these situations, the populations must follow a normal distribution, and the data must be at least interval-scale.
Characteristics of F Distribution
There is a “family” of F Distributions. A particular member of the family is determined by two parameters: the degrees of freedom in the numerator and the degrees of freedom in the denominator.
The F distribution is continuous
F cannot be negative.
The F distribution is positively skewed.
It is asymptotic. As F the curve approaches the X-axis but never touches it.
Examples:
Two Barth shearing machines are set to produce steel bars of the same length. The bars, therefore, should have the same mean length. We want to ensure that in addition to having the same mean length they also have similar variation.
The mean rate of return on two types of common stock may be the same, but there may be more variation in the rate of return in one than the other. A sample of 10 technology and 10 utility stocks shows the same mean rate of return, but there is likely more variation in the Internet stocks.
A study by the marketing department for a large newspaper found that men and women spent about the same amount of time per day reading the paper. However, the same report indicated there was nearly twice as much variation in time spent per day among the men than the women.
ANOVA Test
Related Populations---The Paired Difference Test
This is a procedure for analyzing the difference between the means of two populations when you collect sample data from populations that are related. That is , when the results of the first population are not independent of the results of the second population.
There are two situations that involve relate data between populations. Either you take repeated measurements from the same set of items or individuals or you match items or individuals according to some characteristic. In either situation, you are interested in the difference between the two related values rather than the individual values themselves.
The formula for the test statistics are in chapter 7.1.
Discussion one
Please review the theories and examples in chapter 5 and 6 before answering this discussion.
Assignment
1. A similar example is on p141of the text (chapter 5.3)
Data entry: You need to enter performance rating for each grade
I entered the first row of the data; you should continue the effort for your assignment:
|
A |
B |
C |
D |
E |
F |
|
90 |
80 |
100 |
90 |
85 |
70 |
Your Anova test result should look like the following
|
SUMMARY |
|
|
|
|
|
|
|
Groups |
Count |
Sum |
Average |
Variance |
|
|
|
A |
15 |
1265 |
84.33333 |
153.095 |
|
|
|
B |
7 |
570 |
81.42857 |
72.619 |
|
|
|
C |
5 |
450 |
90 |
100 |
|
|
|
D |
5 |
415 |
83 |
157.5 |
|
|
|
E |
12 |
1045 |
87.08333 |
152.083 |
|
|
|
F |
6 |
550 |
91.66667 |
116.667 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
ANOVA |
|
|
|
|
|
|
|
Source of Variation |
SS |
df |
MS |
F |
P-value |
F crit |
|
Between Groups |
519.202 |
5 |
103.8405 |
0.77899 |
0.5702155 |
2.42704 |
|
Within Groups |
5865.3 |
44 |
133.3022 |
|
|
|
|
|
|
|
|
|
|
|
|
Total |
6384.5 |
49 |
|
|
|
|
2. A similar example is on p152, the Excel part is on p161(chapter 6.2)
Data entry: You need to enter salary for each grade (I entered the first row, you need to continue…)
|
A |
B |
C |
D |
E |
F |
|
23 |
27 |
41 |
47 |
58 |
76 |
3. Test results are given; you need to interpret these results.
4. This is a paired t test
The null hypothesis is: average salary=> average midpoint salary
The alternative hypothesis is: average salary < average midpoint salary
You need to get averages and midpoints listed in column. I entered the first row of the data; you should continue the effort for your assignment:
|
Salary |
Midpoint |
|
23 |
23 |
Additional Resource
The given resources are enough for the course. However, if you would like an additional resource, I recommend video series: Against All Odds. We use the series for face to face Business Statistics classes.
Ashford 4: - Week 3 - Discussion 1
Your initial discussion thread is due on Day 3 (Thursday) and you have until Day 7 (Monday) to respond to your classmates. Your grade will reflect both the quality of your initial post and the depth of your responses. Reference the Discussion Forum Grading Rubric for guidance on how your discussion will be evaluated.
|
|
|
ANOVA |
In many ways, comparing multiple sample means is simply an extension of what we covered last week. Just as we had 3 versions of the t-test (1 sample, 2 sample (with and without equal variance), and paired; we have several versions of ANOVA – single factor, factorial (called 2-factor with replication in Excel), and within-subjects (2-factor without replication in Excel). What examples (professional, personal, social) can you provide on when we might use each type? What would be the appropriate hypotheses statements for each example?
Guided Response: Review several of your classmates’ posts. Respond to at least two classmates by commenting on why you agree or disagree with the statistical test that your peers have described as appropriate in this scenario.
Ashford 4: - Week 3 - Discussion 2
Your initial discussion thread is due on Day 3 (Thursday) and you have until Day 7 (Monday) to respond to your classmates. Your grade will reflect both the quality of your initial post and the depth of your responses. Reference the Discussion Forum Grading Rubric for guidance on how your discussion will be evaluated.
|
|
|
Effect Size |
Several statistical tests have a way to measure effect size. What is this, and when might you want to use it in looking at results from these tests on job related data? Guided Response: Review several of your classmates’ posts. Respond to at least two of your classmates.
Ashford 4: - Week 3 - Assignment
Problem Set Week Three Complete the problems included in the resources below and submit your work in an Excel document. Be sure to show all of your work and clearly label all calculations. All statistical calculations will use the Employee Salary Data Set and the Week 3 assignment sheet.
Carefully review the Grading Rubric for the criteria that will be used to evaluate your assignment.
