# Statistics Discussion

1. Descriptive Statistics: In six sentences or more, explain how you would use the descriptive statistical procedure(s) at work or in your personal life.
2. 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?

3. 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).

4. 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?

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# Statistics Discussion

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, TTTLet’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?

1. 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?

1. 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

1. Select and discuss one of the following probability rules:

Multiplication rule

1. Subtraction rule

Independence rule

In 6-sentences or more, explain how the rule applies at the workplace or personal life experience.

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# statistics discussion

I need support with this Statistics question so I can learn better.

An important part of using statistics is being able to explain your results to decision makers. Imagine that you have conducted a two-sample test and determined that the difference was not statistically significant. While one mean was 4.3 and the other was 3.9, the p level for the t test was p=.07. Your management team says, “Well, the difference may not be statistically significant, but the difference is there! Discuss how you would respond and how you would explain the purpose of the t test and significance in this case.

Hello, In response to Week 5 Discussion

The meaning of the phrase “statistically significant” in statistics, means that the result of the analysis or experiment is unlikely due to chance, and a decision has been made to reject the null hypothesis, meaning something is different.

So, if we say something is not statistically significant, we are saying that the result may be likely due to chance. We accept the null hypothesis, that declares that there is no difference between what we expect and what was determined in the analysis-

In business, the word significant is sometimes likely to imply “important”, or a large amount or degree”. So, just because a result is not statistically significant, does not mean that it is not a significant business result.

The phrase “Substantive result” is when the result or outcome of a statistical study produces results that are important to the decision makers. The result in this case are Substantive, but not significant, by statistician terms. We need to be aware of the differences between the statistically significant and Substantive results.

In this case we used a t-test in the statistical study, which means we did not know the population standard deviation, so we had to use the sample standard deviation as an estimate of it. We assume the population is normally distributed. If the alpha = .05 for a 95 percent confidence, and the p-value is determined to be .07, since the p-value is greater than the alpha, we say that there is not enough evidence found in the sample to reject the null hypothesis, so this supports us saying that there is no difference and the result is not statistically significant.

AND

Class,

As illustrated in chapter 10, the approach as to whether to use a z statistic or a t statistic for analyzing the differences in two sample means is the same as that used in chapters 8 and 9. When the population variances are known, the z statistic can be used. However, if the population variances are unknown and sample variances are being used, then the t test is the appropriate statistic for the analysis. It is always an assumption underlying the use of the t statistic that the populations are normally distributed. If sample sizes are small and the population variances are known, the z statistic can be used if the populations are normally distributed.

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