Using Descriptive Statistics
Using Descriptive Statistics
Descriptive Statistics: In six sentences or more, explain how you would use the descriptive statistical procedure(s) at work or in your personal life.
Misuse of Statistics: As we will see in the next 12 weeks, statistics when used correctly can be a very powerful tool in managerial decision making.
Statistical techniques are used extensively by marketing, accounting, quality control, consumers, professional sports people, hospital administrators, educators, politicians, physicians, etc…
As such a strong tool, statistics is often misused. Everyone has heard the joke (?) about the statistician who drowned in a river with an average depth of 3 feet or the person who boarded a plane with a bomb because “the odds of two bombs on the same plane are lower than one in one millionth”.
Can you find examples in the popular press of misuse of statistics?
How to Display Data Badly : Read the article “How to Display Data Badly” by Howard Wainer. It is attached here: How to Display Data Badly and also posted under the Content tab (after you choose the Content tab, choose Course Content and Session 1 from the list on the left).
Next read, Chart Junk Considered Useful after All, by Robert Kosara, https://eagereyes.org/criticism/chart-junk-considered-useful-after-all
In your own words, describe “Chart Junk”.
When should Chart Junk be avoided. When is it useful?
Include an image or link to an example of the worst data display you have seen at work or in the media (not in Wainer’s article).
Wainer gives rules for how to make bad charts & graphs. Which of Wainer’s rules describes what’s so bad about your example?
Discussion: Simpson’s Paradox : A family member can go to one of two local hospitals for heart surgery.
Checking the history for the past year, you find that each of the two hospitals has performed cardiac surgery on 1000 patients. In hospital A 710 patients survived (71%). In hospital B 540 (54%) survived.
Based on the numbers presented, which hospital do you think is superior in cardiac surgery?
Surely hospital A is better, right?
Now, let’s look at more data. The below chart summarizes three categories of patients (those entering in fair, serious and critical condition) and the survival rate from surgery (in percent) for the two local hospitals.
Patient Entering Condition
Hospital A
Hospital B
Survivors from A (# and percent)
Survivors from B (# and percent)
Fair
700
100
600 or 86%
90 or 90%
Serious
200
200
100 or 50%
150 or 75%
Critical
100
700
10 or 10%
300 or 43%
Total
1000
1000
710 or 71%
540 or 54%
Looking at the data broken down in this way, we see that Hospital B has a higher success rate in all three categories of patients but when averaged all together, Hospital A has the higher overall survival rate. Based on the numbers presented, which hospital do you think is superior in cardiac surgery?
MGMT650 Statistics for Managerial Decision Making
Week 4 Discussion
Probability Puzzles
For the probability problems below, please select one question to work on, share your computations, and provide your answer with an explanation. Respond to at least two others within the discussion thread as well. They do not have to be from the same question that you answered.
The Birthday Problem – There are 23 people in this class. What is the probability that at least 2 of the people in the class share the same birthday?
The Game Show Paradox – Let’s say you are a contestant on a game show. The host of the show presents you with a choice of three doors, which we will call doors 1, 2, and 3. You do not know what is behind each door, but you do know that behind two of the doors are beat up 1987 Hyundai Excels, and behind one of the doors is a brand new Cadillac Escalade. The cars were placed randomly behind the doors before the show, and the host knows which car is where. The way the game is played out is as follows. The host lets you choose a door. Assume you choose door #1. Before he opens door #1 to let you see what you have chosen, he opens one of the remaining doors, say door #3, to reveal a Hyundai Excel (he will always open one of the remaining doors that has the booby prize), and asks you whether or not you want to change your choice to door #2. What do you tell him?
Flipping Coins – If you flip a coin 3 times, the probability of getting any sequence is identical (1/8).
There are 8 possible sequences: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT
Let’s make this situation a little more interesting. Suppose two players are playing each other. Each player chooses a sequence, and then they start flipping a coin until they get one of the two sequences.
We have a long sequence that looks something like this: HHTTHTTHTHTTHHTHT…. We continue until one of the two wins.
Do you think this is a fair game, and that under these rules each sequence has an equal chance to appear first?
Think again! If you chose HHH and I chose THH, I have a much higher chance that you do!
The only way that you win is if the first three tosses are HHH. In any other event, I win.
Agree? Do you see why?
For the sequence HHH to appear anywhere except the first three flips, it must come after a T, right? So, the actual sequence for you to win is THHH.
But if there is a sequence of THHH then I already won before that sequence is over (because my sequence was THH).
So, THH will win 7 times out of 8. HHH will only win if the first three are HHH (a one in eight chance).
Suppose you are going to flip a coin until you get the sequence HTH. Say this takes you x flips. Then, suppose you are going to flip the coin until you get the sequence HTT. Say this takes you z flips. On average, how will x compare to z? Will it be bigger, smaller, or equal?
Disease Testing and False Positives – Assume that the test for some disease is 99% accurate. If somebody tests positive for that disease, is there a 99% chance that they have the disease?
A Girl Named Florida – Here’s a three-part puzzler:
Your friend has two children. What is the probability that both are girls?
Your friend has two children. You know for a fact that at least one of them is a girl. What is the probability that the other one is a girl?
Your friend has two children. One is a girl named Florida. What is the probability that the other child is a girl?
The Value of Variance – More often than not, when we are presented with statistics we are given only a measure of central tendency (such as a mean). However, lots of useful information can be gleaned about a dataset if we examine the variance, skew, and the kurtosis of the data as well. Choose a statistic that recently came across your desk where you were just given a mean. If you can’t think of one, come up with an example you might encounter in your life. How would knowing the variance, the skew, and/or the kurtosis of the data give you a better idea of the data? What could you do with that information?
Example: Say you are an executive in an automobile manufacturer, and you are told that, for a particular model of new car that you sell, buyers have on average 2.2 warranty claims over the first three years of owning the car. What would additional information on the shape of your data tell you? If the variance was low, you’d know that just about every car had 2 or 3 warranty claims, while if it was high you’d know that you have a lot of cars with no warranty claims and a lot with more than 2.2. The skew would provide similar information; with a high level of right skew, you’d know that the average is being brought up by a few lemons; with left skew you’d know that very few of the cars have no warranty claims. The kurtosis (thickness of the tails) would help you get an idea as to just how prevalent the lemon problem is. If you have high kurtosis, it means you have a whole bunch of lemons and a whole bunch of perfect cars. If you have low kurtosis, it means that you have few lemons but few perfect cars.
Probability Rules
Web site:
https://stattrek.com/probability/probability-rules.aspx
Select and discuss one of the following probability rules:
Addition rule
Multiplication rule
Subtraction rule
Independence rule
In 6-sentences or more, explain how the rule applies at the workplace or personal life experience.
MGMT650 Statistics for Managerial Decision Making
Week 7 Discussion
Employing the Normal Distribution
1. Normal Distribution: Operations and production managers often use the normal distribution as a probability model to forecast demand in order to determine inventory levels, manage the supply chain, control production and service processes, and perform quality assurance checks on products and services. The information gained from such statistical analyses help managers optimize resource allocation and reduce process time, which in turn often improves profit margins and customer satisfaction.
Based on your understanding of the characteristics of the normal distribution, examine the chart below. Process A standard deviation is .9, Process B standard deviation is 1.4, and the mean of both processes is 12. Contribute to our discussion by posting a response to ONE of the questions below.
Do either of the processes fit a normal distribution? Why or why not?
Which of the processes shows more variation? What does this mean practically?
If the product specification quality limits were 12 +/- 3, which of the processes more consistently meets specification? Explain why.
If the product specification quality limits were changed to 12 +/- 6, is quality loosening or tightening? Which process would benefit the most from this change?
Are there processes at your place of employ that you believe follow a normal distribution? If so, describe one. Why do you believe it is normal?
2. Hang Up and Drive : Check out this snippet from Family Circle magazine (January, 2009, Liz Plosser):
Motorists who talk on a cell phone while driving are 9% slower to hit the brakes, 19% slower to resume normal speed after braking and four times more likely to crash.
Interesting, eh? Need more information? Sorry, that’s all the information this article provided. So, what can we conclude? How reliable are these results? Can you believe what the author tells you? Why or why not?
Pretend you’re a manager for one of the major cell phone service providers in the U.S. You’ve been asked by a major news magazine to speak to these “accusations.” What would you say? Use your knowledge of “statistics for managers” to level some well-founded criticisms of the conclusions above.
Careful! We cannot use personal opinions to battle statistics like these! Instead, you must explain why the numbers reported in Family Circle may, or may not, accurately represent the population of U.S. drivers. There are 100 possible answers to this conference topic.
You need only provide a single idea, to get the conversation rolling. Leave some material for others to contribute. Be sure that your contribution explicitly references what we’ve read and practiced in the class so far. It is your classmates’ job to support or refute what you’ve said.
3. Confidence Intervals at the Workplace
Web site:
https://www.mathsisfun.com/data/confidence-interval.html
https://mathbitsnotebook.com/Algebra2/Statistics/STmarginError.html
Case scenario.
At the workplace, you are the research team leader.
The Boss wants your team to collect data to establish a confidence interval for a situation at work.
In 6-sentences or more, explain how confidence interval procedure can be applied at the workplace for the situation.
MGMT650 Statistics for Managerial Decision Making
Week 9 Discussion
Type I and Type II errors
Balancing the Risks of Errors in Hypothesis Testing
The U.S. FDA is responsible for approving new drugs. Many consumer groups feel that the approval process is too easy and, therefore, too many drugs are approved that are later found to be unsafe. On the other hand, a number of industry lobbyists have pushed for a more lenient approval process so that pharmaceutical companies can get new drugs approved more easily and quickly. This is from an article in the Wall Street Journal. Consider a null hypothesis that a new, unapproved drug is unsafe and an alternative hypothesis that a new, unapproved drug is safe.
a) Explain the risks of committing a Type 1 or Type 2 error.
b) Which type of error is the consumer group trying to avoid?
c) Which type of error is the industry lobbyists trying to avoid?
d) How would it be possible to lower the chances of both Type 1 and 2 errors?
Think about the recent vaccinations developed for Covid in record time. Do you recall reading about the items above and are they important?
MGMT650 Statistics for Managerial Decision Making
Week 11 Discussion
Coaching for standardized exam
Test-preparation organizations like Kaplan, Princeton Review, etc. often advertise their services by claiming that students gain an average of 100 or more points on the Scholastic Achievement Test (SAT). Do you think that taking one of those classes would give a test taker 100 extra points? Why might an average of 100 points be a biased estimate?
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