A t test is used to compare the means of two data sets, and it relies on calculation of a test statistic called t. This statistic is derived from the two data sets and it is defined as the difference between the means of the two data sets, x̅₁ and x̅₂ (or the difference between a mean x̅ and a reference value, x_ref) divided by the pooled standard error of the mean(s).

An F test is used to compare the variances of two data sets:

• As it is used to compare variances, the dependent data must - by definition - be numeric.
• As it is used to compare two distinct sets of data, these sets represent the two levels of a factor.

The test statistic we use to compare the variances of the two data sets is called F, and it is defined very simply: F is the larger of the two variances divided by the smaller.

Most people who want to attract birds to their gardens put out bird-seed, or - if they’re really adventurous - mealworms. However, on the East London dockside where I lived until recently, one of the residents strewed the quayside with livers in December last year. Was this was a deliberate ploy to attract carrion crows for bird-on-variety-meat action? I don’t know, but whether or not this was the intention, it was certainly the result.

Statistics can be used to describe a data set, or they can be used to infer how well a model fits a data set. In this post, we’ll look the the former kind of statistics, and how to extract them from R. The remaining posts in this series will mostly deal with statistical tests and modelling.

Descriptive statistics should usually give a measure of the central tendency of a data set (the mean and/or median), and of the variability of the data set (the range, quartiles, variance and/or standard deviation).

It’s been ages since I did one of these, and today’s will not be terribly long or exciting, for the reason that is the very title of this post. Whilst bumbling around in the fridge looking for something bland and bowel-friendly, I chanced upon a lemon that had fallen into a oubliette in the bottom of the salad drawer. Perhaps it’s just the sickness talking, but I found it rather beautiful:

You can plot data using plot(). This can be used in several ways. The simplest is to plot some numeric x-values against some numeric y-values using:

plot( x.variable.vector, y.variable.vector )

For example:

x<-c( 1:10 )
y<-1 + 2*x
plot( x, y )

However, for data you have imported into a data frame, the x and y variables are now named columns in a data frame, rather than separate vectors. To plot data in data frames, there are two options. The first is to use the dollar $ syntax to access the vector of data within the data frame (here sycamore_seeds.csv) by its column name:

Although you will occasionally type data directly into R, more often than not, you will have a spread-sheet containing data which you want to import. R can easily import data from a comma-separated variable (CSV) file. If you open a CSV file using a text-editor, you will see that they look something like this inside (this is dose_response.csv):

C,mu
0.125,0.69
0.25,0.68
0.5,0.687
1,0.63
2,0.467
4,0.252
8,0.091
16,0.021

The first row contains labels for the columns, and the remaining rows contain the data. The pair of labels, and the pairs of data, are each separated by a comma.

The sort of data you want to analyse in R may come in many forms. You will often be trying to model the interaction of some independent variables (a.k.a. input, predictor or explanatory variables, the things you’d plot on an x axis) to explain the values of some dependent variable (a.k.a. output, outcome or response variable, the thing you’d put on a y axis).

The R interpreter is controlled by typing in plain-text commands at its command-line prompt >|. R commands are just text, so you can prepare a chunk of them in a text-editor, and then copy-and-paste them directly into R to run them immediately. Try copying and pasting the line below at the prompt:

print("Hello world")

Lo and behold, R will spit out what you knew it would:

Last year, the most marvellous thing we saw in the pond-water microscopy practical was a ciliate, and this year the prize goes to that same clade. Ciliates don’t disappoint.

This is Lacrymaria olor, the “teardrop of the swan”. It’s a predator, like the Vorticella from last year, but rather than sitting rooted to the spot, Lacrymaria is an actively swimming hunter, with an enormously extendable proboscis that it uses to capture prey: