Correlation does not imply causation, sure but, as Edward Tufte writes, “it sure is a hint.” The Pearson product-moment correlation coefficient is perhaps one of the most common ways of looking for such hints and this post describes the Bayesian First Aid alternative to the classical Pearson correlation test. Except ... [Read more...]

The Matlab syntax for creating matrices is pretty and convenient. Here is a 2x3 matrix in Matlab syntax where , marks a new column and ; marks a new row:

<div><pre>[<span>1</span>, <span>2</span>, <span>3</span>;
 <span>4</span>, <span>5</span>, <span>6</span>]
</pre></div>

Here is how to create the corresponding matrix in R:

<div><pre>matrix(c(<span>1</span>,<span>4</span>,<span>2</span>,<span>5</span>,<span>3</span>,<span>6</span>), <span>2</span>, <span>3</span>)
</pre></div>

<div><pre><span>##      [,1] [,2] [,3]</span>
<span>## [1,]    1    2    3</span>
<span>## [2,]    4    5    6</span>
</pre></div>

Functional but not as pretty, plus the default is ... [Read more...]

I just wanted to plug for three classical books on statistical graphics that I really enjoyed reading. The books are old (that is, older than me) but still relevant and together they give a sense of the development of exploratory graphics in general and the graphics system in R specifically ... [Read more...]

As spring follows winter once more here down in southern Sweden, the two sample t-test follows the one sample t-test. This is a continuation of the Bayesian First Aid alternative to the one sample t-test where I’ll introduce the two sample alternative. It will be a quite short post ... [Read more...]

It is my great pleasure to share with you a breakthrough in statistical computing. There are many statistical tests: the t-test, the chi-squared test, the ANOVA, etc. I here present a new test, a test that answers the question researchers are most anxious to figure out, a test of significance, ... [Read more...]

Student’s t-test is a staple of statistical analysis. A quick search on Google Scholar for “t-test” results in 170,000 hits in 2013 alone. In comparison, “Bayesian” gives 130,000 hits while “box plot” results in only 12,500 hits. To be honest, if I had to choose I would most of the time prefer a ... [Read more...]

pingr is an R package that contains one function, ping(), with one purpose: To go ping on whatever platform you are on (thanks to the audio package). It is intended to be useful, for example, if you are running a long analysis in the background and want to know when ... [Read more...]

The binomial test is arguably the conceptually simplest of all statistical tests: It has only one parameter and an easy to understand distribution for the data. When introducing null hypothesis significance testing it is puzzling that the binomial test is not the first example of a test but sometimes is ... [Read more...]

So I have a secret project. Come closer. I’m developing an R package that implements Bayesian alternatives to the most commonly used statistical tests. Yes you heard me, soon your t.testing days might be over! The package aims at being as easy as possible to pick up and ... [Read more...]

I’m playing blog ping-pong with John Kruschke’s Doing Bayesian Data Analysis blog as he was partly inspired by my silly post on Bayesian mascots when writing a nice piece on Icons for the essence of Bayesian and frequentist data analysis. That piece, in turn, inspired me resulting in ... [Read more...]

Why would Bayesian statistics need a mascot/symbol/logo? Well, why not? I don’t know of any other branch of statistics that has a mascot but many programming languages have. R has an “R”, Python has a python snake, and Go has an adorable little gopher. While Bayesian statistics ... [Read more...]

So R is awesome. Felt good to get that out of the way! But sometimes I long for some small syntax additions while programming away in R in the night… The picture is of a restaurant called Risotto in Berlin. Just to make it clear, I fully understand that changing ... [Read more...]

You’ve probably heard about the t distribution. One good use for this distribution is as an alternative to the normal distribution that is more robust against outliers. But where does the t distribution come from? One intuitive characterization of the t is as a mixture of normal distributions. More ... [Read more...]

In the last post I showed how to use Laplace approximation to quickly (but dirtily) approximate the posterior distribution of a Bayesian model coded in R. This is just a short follow up where I show how to use importance sampling as an easy method to shape up the Laplace ... [Read more...]

Thank you for tuning in! In this post, a continuation of Three Ways to Run Bayesian Models in R, I will: Handwave an explanation of the Laplace Approximation, a fast and (hopefully not too) dirty method to approximate the posterior of a Bayesian model. Show that it is super easy ... [Read more...]

I’m often irritated by that when a statistical method is explained, such as linear regression, it is often characterized by how it can be calculated rather than by what model is assumed and fitted. A typical example of this is that linear regression is often described as a method ... [Read more...]

In the last post I described flogs, a useful transform on proportions data introduced by John Tukey in his Exploratory Data Analysis. Flogging a proportion (such as, two out of three computers were Macs) consisted of two steps: first we “started” the proportion by adding 1/6 to each of the counts ... [Read more...]

Fractions and proportions can be difficult to plot nicely for a number of reasons: If the proportions are based on small counts (e.g., two of his three computing devices were Apple products) then the calculated proportions will only take on a number of discrete values. Depending on what you ... [Read more...]

For some reason someone dropped a pamphlet advertising SPSS for Windows 3.0 in my mail box at work. This means that the pamphlet, and the advertised version of SPSS, should be at least 20 years old! These days I’m happily using R for everything but if I was going to estimate ... [Read more...]

So in the last post I showed how to run the Bayesian counterpart of Pearson’s correlation test by estimating the parameters of a bivariate normal distribution. A problem with assuming normality is that the normal distribution isn’t robust against outliers. Let’s see what happens if we take ... [Read more...]