Does this claim pass the smell test?

It is hard to quickly evaluate data in an everyday situation, but a nifty shortcut I saw on the R-bloggers aggregator can help. In the simplest example, suppose you toss a coin 50 times with 32 heads and 18 tails. What are the chances the coin is fair? The handy shortcut helps to quickly evaluate…

The hypergeometric distribution

The hypergeometric distribution is used to solve the classic “balls in an urn” proble. Suppose one has 7 red balls and 3 white ball in an urn, and draws 2 balls. What is the probability that both balls are white? Let’s make a function to allow quick replication Other combinations

The binomial distribution

The binomial distribution is used when there are n (a fixed number) independent trials with two possible outcomes (“success” and “failure”) with a probability that is constant. With 10 tosses of a fair coin, what is the probability of getting 7 heads? $Prob = dbinom(7,10,0.5) = 0.1171875$ And what is the probability of getting exactly…

The Poisson distribution

A sports team scores 84 points in 21 games, so the average score is 4 points per game. What is the probability that it scores 1 point per game? Or 6 points, or more than than 4? The answer is in the Poisson distribution, where variance = mean, denoted as $\lambda$. The answer to the…

The beta distribution

Definition Using the mean Using ranges for the prior Informative vs. uninformative priors Mean, median, variance Highest Density Interval References Addenda Definition The Beta distribution represents a probability distribution of probabilities. It is the conjugate prior of the binomial distribution (if the prior and the posterior distribution are in the same family, the prior and posterior…

One-way ANOVA

For a simple exercise to understnad one-way ANOVA, I will use the data set red.cell.folate from the package ISwR (see the book “Introductory Statistics with R” by Peter Dalgaard) but will also generate our own data. And now (drum roll) … it’s time to run the ANOVA Let’s look at what this ANOVA table means….