Video Tutorial – Allelic Frequencies Remain Constant From Generation to Generation Under the Hardy-Weinberg Equilibrium

The Hardy-Weinberg law is a fundamental principle in statistical genetics.  If its 7 assumptions are fulfilled, then it predicts that the allelic frequency of a genetic trait will remain constant from generation to generation.  In this new video tutorial in my Youtube channel, I explain the math behind the Hardy-Weinberg theorem.  In particular, I clarify the origin of the connection between allelic frequencies and genotyopic frequencies in the second generation – I have not found a single textbook or web site on this topic that explains this calculation, so I hope that my explanation is helpful to you.

You can also watch the video below the fold!

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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!

You can also watch the video below the fold!

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Organic and Inorganic Chemistry Lesson of the Day – Stereogenic Centre

A stereogenic centre (often called a stereocentre) is an atom that satisfies 2 conditions:

  1. it is bonded to at least 3 substituents.
  2. interchanging any 2 of the substituents would result in a stereoisomer.

If a molecule has only 1 stereogenic centre, then it definitely has a non-superimposable mirror image (i.e. this molecule is chiral and is an enantiomer).  However, depending on its stereochemistry, it is possible for a molecule with 2 or more stereogenic centres to be achiral; such molecules are called meso isomers (or meso compounds), and I will discuss them in a later lesson.

In organic chemistry, the stereogenic centre is usually a carbon atom that is attached to 4 substituents in a tetrahedral geometry.  In inorganic chemistry, the stereogenic centre is usually the metal centre of a coordination complex.

In organic chemistry, stereogenic centres with substituents in a tetrahedral geometry are common.  Inorganic coordination complexes can also have a tetrahedral geometry.  A stereoisomer with n tetrahedral stereogenic centres can have at most 2^n stereoisomers.  The “at most” caveat is important; as mentioned above, it is possible for a molecule with 2 or more stereogenic centres to have a spatial arrangement that results in having a superimposable mirror image; such isomers are meso isomers.   I will discuss meso isomers in more detail in a later lesson.