This following article was published on the Career Services Informer (CSI), the official career blog of Simon Fraser University (SFU).  I have been fortunate to be a guest blogger for the CSI since I was an undergraduate student at SFU, and you can read all of my recent articles as an alumnus here.

As most students return to school in the upcoming semester, their academic studies and back-to-school logistics may be their top priorities.   However, if you want to pursue graduate studies or professional programs like medicine or law, then there are some important deadlines that are fast approaching, and they all involve time-consuming efforts to meet them. Now is a good time to tackle these deadlines and put forth your best effort while you are free of the burdens of exams and papers that await you later in the fall semester.

Image Courtesy of Melburnian at Wikimedia

Speaking from experience, these applications are very long and tiring, and they will take a lot of thought, planning, writing and re-writing. They also require a lot of coordination to get the necessary documents, like your transcripts and letters of recommendation from professors who can attest to your academic accomplishments and research potential.  Plan ahead for them accordingly, and consider using the Career Services Centre to help you with drafting your curriculum vitae, your statements of interest, and any interview preparation.

## Odds and Probability: Commonly Misused Terms in Statistics – An Illustrative Example in Baseball

Yesterday, all 15 home teams in Major League Baseball won on the same day – the first such occurrence in history.  CTV News published an article written by Mike Fitzpatrick from The Associated Press that reported on this event.  The article states, “Viewing every game as a 50-50 proposition independent of all others, STATS figured the odds of a home sweep on a night with a full major league schedule was 1 in 32,768.”  (Emphases added)

Screenshot captured at 5:35 pm Vancouver time on Wednesday, August 12, 2015.

Out of curiosity, I wanted to reproduce this result.  This event is an intersection of 15 independent Bernoulli random variables, all with the probability of the home team winning being 0.5.

$P[(\text{Winner}_1 = \text{Home Team}_1) \cap (\text{Winner}_2 = \text{Home Team}_2) \cap \ldots \cap (\text{Winner}_{15}= \text{Home Team}_{15})]$

Since all 15 games are assumed to be mutually independent, the probability of all 15 home teams winning is just

$P(\text{All 15 Home Teams Win}) = \prod_{n = 1}^{15} P(\text{Winner}_i = \text{Home Team}_i)$

$P(\text{All 15 Home Teams Win}) = 0.5^{15} = 0.00003051757$

Now, let’s connect this probability to odds.

It is important to note that

• odds is only applicable to Bernoulli random variables (i.e. binary events)
• odds is the ratio of the probability of success to the probability of failure

For our example,

$\text{Odds}(\text{All 15 Home Teams Win}) = P(\text{All 15 Home Teams Win}) \ \div \ P(\text{At least 1 Home Team Loses})$

$\text{Odds}(\text{All 15 Home Teams Win}) = 0.00003051757 \div (1 - 0.00003051757)$

$\text{Odds}(\text{All 15 Home Teams Win}) = 0.0000305185$

The above article states that the odds is 1 in 32,768.  The fraction 1/32768 is equal to 0.00003051757, which is NOT the odds as I just calculated.  Instead, 0.00003051757 is the probability of all 15 home teams winning.  Thus, the article incorrectly states 0.00003051757 as the odds rather than the probability.

This is an example of a common confusion between probability and odds that the media and the general public often make.  Probability and odds are two different concepts and are calculated differently, and my calculations above illustrate their differences.  Thus, exercise caution when reading statements about probability and odds, and make sure that the communicator of such statements knows exactly how they are calculated and which one is more applicable.

## Analytical Chemistry Lesson of the Day – Linearity in Method Validation and Quality Assurance

In analytical chemistry, the quantity of interest is often estimated from a calibration line.  A technique or instrument generates the analytical response for the quantity of interest, so a calibration line is constructed from generating multiple responses from multiple standard samples of known quantities.  Linearity refers to how well a plot of the analytical response versus the quantity of interest follows a straight line.  If this relationship holds, then an analytical response can be generated from a sample containing an unknown quantity, and the calibration line can be used to estimate the unknown quantity with a confidence interval.

Note that this concept of “linear” is different from the “linear” in “linear regression” in statistics.

This is the the second blog post in a series of Chemistry Lessons of the Day on method validation in analytical chemistry.  Read the previous post on specificity, and stay tuned for future posts!