Statistics

Ashford 2: - Week 1 - Instructor Guidance

Week Overview:

The following video series: Against All Odds Inside Statistics is helpful if you would like to watch it.

http://www.learner.org/resources/series65.html?pop=yes&pid=3138

For this week, we’ll learn that statistics is the science of collecting, organizing, presenting, analyzing, and interpreting numerical data to assist in making more effective decisions.

In today’s world, numerical information is everywhere. Statistical techniques are used to make decisions that affect our daily lives. The knowledge of statistical methods will help you understand how decisions are made and give you a better understanding of how they affect you. No matter what line of work you select, you will find yourself faced with decisions where an understanding of data analysis is helpful.

The concepts introduced this week include levels of measurement, measurements of center, variations, etc. Normal distribution and calculations are introduced in this week.

Measurements

You should be able to distinguish among the nominal, ordinal, interval, and ratio levels of measurement.

Nominal level - data that is classified into categories and cannot be arranged in any particular order.

EXAMPLES: eye color, gender, religious affiliation.

Ordinal level – data arranged in some order, but the differences between data values cannot be determined or are meaningless.

EXAMPLE: During a taste test of 4 soft drinks, Mellow Yellow was ranked number 1, Sprite number 2, Seven-up number 3, and Orange Crush number 4.

Interval level - similar to the ordinal level, with the additional property that meaningful amounts of differences between data values can be determined. There is no natural zero point.

EXAMPLE: Temperature on the Fahrenheit scale.

Ratio level - the interval level with an inherent zero starting point. Differences and ratios are meaningful for this level of measurement.

EXAMPLES: Monthly income of surgeons, or distance traveled by manufacturer’s representatives per month.

Why do you need to know the level of measurement of a data? This is because the level of measurement of the data dictates the calculations that can be done to summarize and present the data. It also determines the statistical tests that should be performed on the data.

Probability

PROBABILITY is a value between zero and one, inclusive, describing the relative possibility (chance or likelihood) an event will occur.

There are three ways of assigning probability:

1. Classical Probability

This is based on the assumption that the outcomes of an experiment are equally likely.

2. Empirical Probability

The probability of an event happening is the fraction of the time similar events happened in the past.

Example: On February 1, 2003, the Space Shuttle Columbia exploded. This was the second disaster in 113 space missions for NASA. On the basis of this information, what is the probability that a future mission is successfully completed?

Probability of successful flight = 111/113 = 0.98

3. Subjective Concept Of Probability

The likelihood (probability) of a particular event happening that is assigned by an individual based on whatever information is available.

Discussion

To prepare for this week’s discussion, you need to familiar with the statistics such as mean, median, mode, variance, standard deviation, range, etc. The first three are used to measure centers. The rest are used to measure data variations. You also need to understand the concepts of probability.

Assignment Expectation:

This assignment is to be done by using Excel.

1. You need to get familiar with the different levels of measurements: nominal, ordinal, interval, and ratio. For instant, salary is ratio, etc.

2. You can choose individual functions such as “average” for mean, “stdev.s” for standard deviation. (Formulas, then insert function, scroll down the list to find “average”)

3. This is to calculate probabilities (see p42 formula and examples)

a. P(a male in grade E) = (# of males in grade E)/(total # of employees)

4. a. You need to rearrange the data from largest to smallest before you can find the cut off

b. A z-score is the signed distance between a selected value, designated X, and the population mean , divided by the population standard deviation, σ.

The formula is:

You can also review the example on page 58, 59.

c. through g. You need to use distribution table on page 56 to find the probabilities. Also review the example on p58-60.

Reference

Lind,D., Marchal, W., & Wathen, S. (2010). Statistical Techniques in Business and Economics (14th ed). McGraw-Hill

Ashford 2: - Week 1 - 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.

Language

Numbers and measurements are the language of business. Organizations look at results in many ways: expenses, quality levels, efficiencies, time, costs, etc. What measures does your department keep track of? Are they descriptive or inferential data, and what is the difference between these? (Note: If you do not have a job where measures are available to you, ask someone you know for some examples, or conduct outside research on an interest of yours, or use personal measures.)

Guided Response: Review several of your classmates’ posts. Respond to at least two of your classmates by providing recommendations for the measures being discussed

Ashford 2: - Week 1 - 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.

Probability

Read the article, "Better Living Through...Statistics?!" and give an example of how you might use increasing information to make actual business decisions. Respond to at least two of your classmates’ posts.

Guided Response: Review several of your classmates’ posts. Respond to at least two classmates by commenting on the situations that are being illustrated.

Better Living Through...Statistics?!

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You’ve probably heard of Nate Silver. He’s the “King of Quants,” and his book The Signal and the Noise is an excellent discussion of some of the problems we have with prediction. You’ve probably never heard of the Reverend Thomas Bayes, who is responsible for a theorem (called “Bayes’ Theorem”) that helps us understand how we can update our estimates of the probabilities of different events given new pieces of information.

It’s still pretty counter-intuitive. Fortunately, the people at Nowsourcing, Inc, who have provided content for this space before, were kind enough to produce the infographic below that introduces Bayes’ Theorem with a contrived example involving baseball: what’s a good estimate of the probability that the Yankees will win game #101 if they have won 72 of their first 100 games and Sportscaster Bob–who is correct 55% of the time when he predicts a Yankees victory–has predicted that they will win?

Since the Yankees have won 72 of 100 games, a good estimate of the probability that they will win their 101st game would be 72%. Now, we introduce some information: since Bob is right just over half the time when he predicts a Yankees victory, it will nudge our estimate of the probability of a Yankees victory up just a little bit (if Sportscaster Bob were right less than half the time, it would nudge our estimate of the probability downward).

Our estimate of the probability changes as we add more information. Is it a night game? Who are the Yankees playing? Who is pitching? Did it rain last night? Is a key player injured? And so on: the more accurate information we add, the better our estimates will be. The applications are numerous and important: while Bayesian reasoning can help us understand baseball (except for the Yankees’ hypothetical 72-28 record in this example), it also helps us understand far more important things like medical diagnostics. And elections. And all sorts of other interesting things.

I am grateful to my Samford colleague Tom Woolley for comments and suggestions. The original version of the infographic appears here courtesy of sports-management-degrees.com.

Ashford 2: - Week 1 - Assignment

Problem Set Week One

Week One Assignment will require students to utilize the following resources to complete the assignment. Assignment instructions are contained within the following resources.

All statistical calculations will use the Employee Salary Data Set and Week 1 assignment sheet.

Carefully review the Grading Rubric for the criteria that will be used to evaluate your assignment.