As of today, I will have spent precisely half of my life at $PLACE_OF_WORK.

I first arrived at what would become my workplace as a badly coiffured youth in 1995 to do a biology degree. South Kensington seemed a great improvement over Croydon, where I had endured my previous 18 years: there was a refreshing absence of casual street violence, and a greatly improved proximity to the grubby delights of Soho. At that time, my Hall of Residence was directly above the first-year lecture theatre, and in the same building as the Students’ Union. Despite this tempting proximity to cheap vodka - and even cheaper dates - I somehow managed to attend almost every lecture of my first year, aside from a week (a week!) of lectures on algae, which I traded for bossing Munchkins about in the Questor’s Theatre in Ealing. I met my personal tutor at least twice, survived two under-catered field-trips to somewhere, somewhere in a field in HampshireBerkshire, and made friends whom I treasure to this day.

It is frequently, and largely accurately, said that an area of Amazon rainforest the size of Wales is deforested every year. Horrendous though this statistic is, it’s worth remembering that the UK deforested an area at least the size of Wales (including most of the area commonly known as “Wales”) before anyone started keeping notes.

I’m not sure whether bagging botanical gardens is better or worse than bagging Munros, Michelin stars or the numbers off of rolling stock, but it keeps me off the streets…

London (Kew)

Just ten stops down the District Line from $WORK lies the Royal Botanic Gardens Kew. The gardens have three enormous glasshouses, a number of smaller glasshouses, and 121 hectares of trees, beds and desperately awful architecture to explore. Unfortunately, it also has an entry fee (for non-concession adults) of £14.50, which is a little steep, and possibly one of the reasons that disappointingly few of my students seem to have visited it, despite its proximity.

It’s amazing how informative an anus can be.

Take this sea urchin. The orange pucker in the middle of the spines is its “around-the-bum”, although zoologists would insist on writing that in Greek as “periproct”. The bright orange ring-piece is characteristic of this species, and marks it out as Diadema setosum, rather than any of the less rectally blessed species of Diadema.

Nonlinear regression is used to see whether one continuous variable is correlated with another continuous variable, but in a nonlinear way, i.e. when a set of x vs. y data you plan to collect do not form a straight line, but do fall on a curve that can be modelled in some sensible way by a known equation, e.g.

(v = \frac{ v_{max} \cdot [S] }{ K_M + [S] })

The technique for a one-way ANOVA can be extended to situations where there is more than one factor, or - indeed - where there are several factors with several levels each, which may have synergistic or antagonistic effects on each other.

In the models we have seen so far (linear regression, one-way ANOVA) all we have really done is tested the difference between a null model ("y is a constant", “y=y̅”) and a single alternative model ("y varies by group" or “y=a+bx”) using an F test. However, in two-way ANOVA there are several possible models, and we will probably need to proceed through some model simplification from a complex model to a minimally adequate model.

Analysis of variance is the technique to use when you might otherwise be considering a large number of pairwise F and t tests, i.e. where you want to know whether a factor with more than 2 levels is a useful predictor of a dependent variable.

For example, cuckoo_eggs.csv contains data on the length of cuckoo eggs laid into different host species, the (meadow) pipit, the (reed) warbler, and the wren.

A χ² test is used to measure the discrepancy between the observed and expected values of count data.

• The dependent data must - by definition - be count data.
• If there are independent variables, they must be categorical.

The test statistic derived from the two data sets is called χ², and it is defined as the square of the discrepancy between the observed and expected value of a count variable divided by the expected value.

Linear regression is used to see whether one continuous variable is correlated with another continuous variable in a linear way, i.e. can the dependent variable y be modelled with a straight-line response to changes in the independent covariate x:

(y = a + bx + \epsilon)

Here b is the estimated slope of the best-fit line (a.k.a. gradient, often written m), a is its y-intercept (often written c), and ϵ is the residual error. If the x and y data are perfectly correlated, then ϵ=0 for each and every x,y pair in the in the data set; however, this is extremely unlikely to occur in real-world data.

If you want a random yes/no answer to a question, like “who should kick-off this football match?” it’s very common to entrust the decision to the flip of a coin, on the assumption that the coin doesn’t care which side gets the advantage.

But what if that trust is misplaced? What if the coin gives the answer “tails - your opponent kicks-off” more often than “heads - you kick-off”, and so gives the advantage to your opponent more often than to you? And, most importantly, how could you tell if the coin is biased before you entrust your decision-making to it?