StatOps

1. It has a wide range of utility.
A number of fields that have very little to do with mathematics, such as biology, chemistry, or psychology, require that university students majoring in them take a statistics course. The reason why can be expressed fairly simply: statistics is the only way we can analyze data and objectively say whether something is true or not, provided that we take care to phrase the results carefully. SAS's tagline, "The Power to Know," is truer than most!

2. It has strong career potential.
Many of the jobs that relate directly to statistics (such as a career in bioinformatics) require at least a master's degree, but there are many jobs out there that one can pursue with merely a bachelor's.

Do tarot cards work? I was introduced to this site on tarot cards, which says that tarot cards are as effective as any psychic practice. And I couldn't agree more. Psychics all have about the same rate of success, which is no different than blind chance. How do we test things like this?

There are many important things to remember when it comes to testing claims of psychics and mediums, although the tips provided here can apply more generally to different types of claims. Here is the list:

1. Double blind the test.

Here are ten common statistics mistakes and errors. No advanced knowledge required to understand them!

1. Addition Rule for Probability
If the chance of contracting HIV from one exposure is 1 in 500, then if someone has been exposed to HIV 500 times, he will have HIV with 100% probability, correct? Right, and if he has 1000 exposures, he will have HIV with 200% probability. That was what one journalist implied with her article on HIV during the 1980's. Don't be her.

2. Precision and Accuracy

Infinity is a funny concept. I can give you infinitely many things while at the same time taking away infinitely many things and leave you with nothing, infinitely many things, or any number of things I want!

Think about this scenario: It's one second to noon. I give you ten gold coins (number them 1-10) and take away the first gold coin I gave you (number 1). At 1/2 second to noon I give you another ten coins (11-20) and take away the second coin I gave you (2). If I continue giving you coins 10n-9 through 10n and taking away coin n at 1/n seconds to noon, when noon arrives you will have no coins at all! (Why? Is infinity a number, so that two times infinity is greater than infinity? Google "cardinality" to learn more.)

How can we define "impossible" statistically?

As every elementary statistics or probability text will tell you, for an event A, P(A) = 0 does not mean that A cannot or will never occur. (Why is this? Do you think this is true in the "real world"?)

Obviously if a probability of zero is insufficient to make an event impossible, we must look at something different from likelihood.

Surely the only way for an event in probability-world (and maybe real life) to be impossible is to contain a contradiction. That is, an event A must contain both B and NOT B, where B is some other event.