The Science of Life

In this last lecture of the Basic Statistics Lecture Series, as promised last time , I will cover ANOVA, or ANalysis Of VAriance.  This is a process of comparing 3 or more distinct samples.  In the MLB, this means comparing the 6 different divisions of the MLB, or the three leagues of each league (National League or American League). The point of ANOVA is to test whether or not there is at least one inequality between three or more means.  This means that there could be as many groups as the experiment you're running requires, and the null hypothesis is always that the mean of every single group has a mean which is statistically equivalent to every other group mean.  If there is even one inequality in the group, then the null hypothesis is rejected. As mentioned last time, when we run multiple regression analysis on some data, there is a table called ANOVA.  For the baseball data I've been using throughout this entire lecture series, that table looks li...

As promised last time , I am going to cover hypothesis testing of proportions.  This is conceptually similar to hypothesis testing from the mean and standard deviation , but the calculations are going to be different. A proportion is the percentage of success in a sample or population, reported in decimal form.  This means that if heads comes up 50% of the time, then it is reported as p=0.50.  Because of this, the calculations are different than that of the mean and standard deviation case from last time.  For instance, when we have proportion data, we don't know the standard deviation of either the sample or the population.  This means that the standard error calculation cannot be performed as typical.  We must instead use a proportion-specific version, which is given by $\sigma_{E}=\sqrt{\frac{p*(1-p)}{n}}$, where p is the proportion and n is the sample size.  If we have the sample size and the number of successes, we can calculate the proporti...

As promised last time , I will introduce the concept of hypothesis testing.  This is finally getting to the meat and potatoes of statistical analysis. There are three things that need to be true in order for a hypothesis to be held true: The data needs to be sampled randomly.  A random sample is exactly what it says on the tin; a group from the population where each individual has an equal chance of being picked. We need to know the sample mean and standard deviation . One or both of the following: Data needs to come from a normal distribution There needs to be a large sample size (for a lot of cases, at least 30, but the more the merrier). There are 5 steps for hypothesis testing from either of two methods.  Statisticians typically distinguish between whether or not we know the population standard deviation.  Realistically, this means whether we know the standard deviation for the population (everyone) or for the sample (small portion of everyone ...