Video Tutorial – Calculating Expected Counts in Contingency Tables Using Marginal Proportions and Marginal Totals

A common task in statistics and biostatistics is performing hypothesis tests of independence between 2 categorical random variables.  The data for such tests are best organized in contingency tables, which allow expected counts to be calculated easily.  In this video tutorial in my Youtube channel, I demonstrate how to calculate expected counts using marginal proportions and marginal totals.  In a later video, I will introduce a second method for calculating expected counts using joint probabilities and marginal probabilities.

In a later tutorial, I will illustrate how to implement the chi-squared test of independence on the same data set in R and SAS – stay tuned!


Video Tutorial – Useful Relationships Between Any Pair of h(t), f(t) and S(t)

I first started my video tutorial series on survival analysis by defining the hazard function.  I then explained how this definition leads to the elegant relationship of

h(t) = f(t) \div S(t).

In my new video, I derive 6 useful mathematical relationships that exist between any 2 of the 3 quantities in the above equation.  Each relationship allows one quantity to be written as a function of the other.

I am excited to continue adding to my Youtube channel‘s collection of video tutorials.  Please stay tuned for more!

Video Tutorial – The Hazard Function is the Probability Density Function Divided by the Survival Function

In an earlier video, I introduced the definition of the hazard function and broke it down into its mathematical components.  Recall that the definition of the hazard function for events defined on a continuous time scale is

h(t) = \lim_{\Delta t \rightarrow 0} [P(t < X \leq t + \Delta t \ | \ X > t) \ \div \ \Delta t].

Did you know that the hazard function can be expressed as the probability density function (PDF) divided by the survival function?

h(t) = f(t) \div S(t)

In my new Youtube video, I prove how this relationship can be obtained from the definition of the hazard function!  I am very excited to post this second video in my new Youtube channel.

Video Tutorial: Breaking Down the Definition of the Hazard Function

The hazard function is a fundamental quantity in survival analysis.  For an event occurring at some time on a continuous time scale, the hazard function, h(t), for that event is defined as

h(t) = \lim_{\Delta t \rightarrow 0} [P(t < X \leq t + \Delta t \ | \ X > t) \ \div \ \Delta t],


  • t is the time,
  • X is the time of the occurrence of the event.

However, what does this actually mean?  In this Youtube video, I break down the mathematics of this definition into its individual components and explain the intuition behind each component.

I am very excited about the release of this first video in my new Youtube channel!  This is yet another mode of expansion of The Chemical Statistician since the beginning of 2014.  As always, your comments are most appreciated!


How to Find a Job in Statistics – Advice for Students and Recent Graduates


A graduate student in statistics recently asked me for advice on how to find a job in our industry.  I’m happy to share my advice about this, and I hope that my advice can help you to find a satisfying job and develop an enjoyable career.  My perspectives would be most useful to students and recent graduates because of my similar but unique background; I graduated only 1.5 years ago from my Master’s degree in statistics at the University of Toronto, and I volunteered as a career advisor at Simon Fraser University during my Bachelor’s degree.  My advice will reflect my experience in finding a job in Toronto, but you can probably find parallels in your own city.

Most of this post focuses on soft skills that are needed to find any job; I dive specifically into advice for statisticians in the last section.  Although the soft skills are general and not specific to statisticians, many employers, veteran statisticians, and professors have told me that students and recent graduates would benefit from the focus on soft skills.  Thus, I discuss them first and leave the statistics-specific advice till the end.

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