Poisson Distribution Facts - Some Really Interesting Stuff

The Poisson Distribution is a probability distribution.  A probability distribution assigns the probability of an event occurring in a random experiment.  In fact, it assigns the probability of every possible event occurring.  That's what makes it a distribution.

Understanding probability distributions empowers us to estimate how likely an event is to occur.   Different distribution models fit different types of data.  In 1898, Ladislaus Bortkiewicz published the book The Law of Small Numbers.  He discussed an interesting question, "How many Prussian cavalrymen are killed by horse kicks."

You may have no interest in the number of deaths per horse kick per year in a cavalry, but you probably do have your own questions.  You can use a Poisson probability distribution model if your data meets these criteria:

1.  The likelihood of the event you want to measure is small (thus the title "The Law of Small Numbers").
2.  The events of interest are independent.  For instance, when you flip a coin more than once, the second toss does not depend on the outcome of the first toss.
3.  The event can be counted in whole numbers, like how many times a salesman rings your doorbell.
4.  You would not ask how many times something did not happen, like how many times a salesman did not ring your doorbell.

The first step in constructing a Poisson distribution is to collect data and determine how often the event really does occur in the data.  But that is a topic for another day.

Don't be afraid to ask questions and construct your own data sets!

Happy experimenting.

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Examples of the Anchoring Effect

Are you thinking about buying a new car?  What about a house?  The salesperson is, no doubt, trained in using the anchoring effect to bring your expectation of the price up to their sales goal.

In a negotiation, the anchoring effect works by making sure your "opponent" has a higher or lower number in mind than what you really expect them to agree to.

The application to sales is pretty easy to see.  The case that surprised me was jail sentences.  Research has shown (see previous blog for references) that judges award longer sentences when the prosecuting attorneys ask for them.  This is being attributed to the anchoring effect.

I have wondered why students that harangue instructors win arguments for better grades.  Maybe the anchoring effect makes a difference in those discussions that go something like, "I deserve a 98, but you gave me a 90."

Now that you are aware of the anchoring effect, watch for it.  You may be surprised at the many places it appears.  However, be warned that even after receiving instruction on the anchoring effect, test subjects were still affected by it!

Happy negotiating!

This Post Could Change Your Life - The Anchoring Effect

While this article is a little more technical than usual, it is worth the read.

Researchers Amos Tversky and Daniel Kahneman hypothesized that initially presented, irrelevant numbers influence human judgment.  They called their hypothesis the “anchoring effect” and argued that “…people make estimates by starting from an initial value that is adjusted to yield the final answer…Adjustments are typically insufficient.  That is, different starting points yield different estimates, which are biased toward the initial value” (Tversky & Kahneman, 1974, p. 1129).  The outcome of their research has application to all aspects of daily life that includes numbers, such as the length of criminal sentences, medical diagnoses, and purchase decisions.  

The phenomenon of insufficient adjustment of initial values was tested with an experiment wherein subjects were asked to estimate various quantities in percentages.  After having been presented with a question, subjects spun a wheel of fortune.  They were then instructed to state whether the answer to the question was higher or lower than the number that came up on the wheel.  Finally, they estimated the answer to the question by moving up or down from the number the wheel produced.

In one particular trial, subjects were asked how many African countries belonged to the United Nations.  They were shown the numbers 10 and 65.  The median estimates for these respondents were 25% and 45% respectively.  Based on the fact that approximately 80% of all African countries belonged to the United Nations at the time, the majority of the respondents were estimating and not citing facts from memory.

The anchoring effect has many practical applications.  It changes outcomes in legal proceedings; medical diagnoses; and purchasing decisions, including major purchases such as real estate, as well as more minor consumer purchases (Smith, R., 2011, p. 110).  Besides proving the reality of the anchoring effect, the Tversky and Kahneman study suggests the impact of the anchoring effect is practically significant and warrants further investigation.  Specifically, the awareness of and ability to mitigate the anchoring effect can influence the outcome of daily events in profound ways.

Smith, A. (2011). Exploring the relationship between knowledge and anchoring effects: is the type of      knowledge important? (Doctoral Dissertation).  Retrieved from University of Iowa, Iowa Research Online (http://ir.uiowa.edu/etd/1264).

Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185, 1124-1130.

Example to come...

Quick Note on How I Choose Advertisers

My criteria for advertisers is:

1.  Do they offer a quality product?
2.  Do they offer a relevant product?
3.  Do they offer a unique product?

For the most part, I am a customer of these advertisers.  Occasionally I choose an advertiser I have not done business with, but I would be willing to try.

Please let me know of your experience with these advertisers.  If I receive any complaints, I will remove the offending advertiser from the site in order to maintain an excellent user experience!

Happy shopping!

What does "robust" mean to process, software, and product developers and engineers?

In a nutshell, if a design (process, product, etc.) is "robust," you can't break it easily. Of course, everything is breakable. But making it robust means it is very much harder to break.

I will give you an example of robust development. On a recent job, I was asked to write a reporting tool in Microsoft's VBA for Excel. (VBA is Visual Basic for Applications--meaning for Excel and other Microsoft programs.) There was a very close deadline, so I estimated the amount of data that would be loaded into the spreadsheet for display. I used that estimate to write the upper bound of records to include in the report.

This was sloppy (not my norm), and not robust. Should the report user add just one more data set than I accounted for, the report would crash. On the next report, I wrote a subroutine to count the actual data sets loaded into the report. That report was very difficult to break. No matter how much data was included, the program could handle it.

Robust design is critical in product development. Robust products, processes, and services increase customer satisfaction, and in turn, the return on investment.

Data can provide information to designers about how robust their end product is. Look for patterns of complaints. If complaints or failures recur, look for ways to make the area of objection more robust.

Happy designing!

Process Improvement Starts with Thinking in Terms of Processes

Many times analytics are used to improve processes. These efforts will fail without one important key thought--when something goes wrong, it is the fault of the process, not the process user.

Here is an example. A few years ago a traffic circle was installed in my brother's neighborhood. I commented about the advantages of traffic circles. He said, "They may be good in other places, but people around her just don't understand them. We keep having accidents."

I was surprised by that statement. The next time I was in the area, I drove through the traffic circle, again. I noticed it was much more narrow than other traffic circles I had seen. Shortly after that, the local transportation agency removed the traffic circle and replaced it with a traditional intersection.

Did the people of the area really misunderstand how to use a traffic circle? It is possible there is a learning curve. However, traffic circles work in other neighborhoods not far away. I think it is more likely that the traffic circle (process) had inherent flaws. It appeared the road was too narrow, and the circle entrances did not have any lead area.

To improve processes using analytics, base your decisions on the quality of the process, not the capability of the users.