The Art of Statistics summary

Data is not just cold, hard facts – it’s subject to human judgments and biases like any other form of knowledge.

In fact, human judgment is involved in the very first step. Before we can collect data, we sometimes have to make fairly arbitrary decisions about what we’re measuring. If our problem is to count how many trees there are on the planet, then we need to define what exactly a “tree” is. For instance, most studies of this type only include trees that have achieved a diameter of at least 4 inches.

The pervasive problem of human interpretation doesn’t only affect the collection of data, but its presentation as well.

Recent years have seen a rise in the study of data visualization as a method for communicating statistical results. Data visualizations are graphical devices used to render data visible to the eye. Statisticians describe visual representations of data as inter-ocular, meaning that patterns in the data become discernible from sight alone – without having to do any mental mathematics.

Many researchers spend their entire lives combing data for important discoveries that they rarely find. The pressure to publish significant work sometimes leads researchers to massage the data a little.

Despite their fidelity to the truth, even scientists have been known to engage in some questionable research practices. One such practice is multiple testing, which is when researchers repeat tests until they get the results they want. The more a researcher repeats a test, the greater the chance that they will get false positives – results that seem to confirm a hypothesis but are actually due to chance error.

Once research has been published, it then gets reported by the media. The media, however, tends to exercise creative license.

The good news is that data journalism is flourishing. Journalists are increasingly being trained in how to interpret and communicate data. Statistics can enrich stories by bringing clarity and insight to important issues.

Inappropriate uses of averages have inspired some terrible jokes among statisticians.

Consider this one: “Most of us have more legs than average.” This is true, in a sense, if you calculate the average number of legs using the mean average, which is something like 1.9999 – brought down from 2 by people who’ve lost their legs.

The charge correlation does not imply causation has become something of a cliché among statisticians. Yet the fallacy of inferring cause from correlation is still commonly made by the media and the public alike, so it’s a message that needs to be reiterated.

This misconception is what leads to comical headlines, such as: “Why going to university increases the risk of getting a brain tumor.”

When the author was once asked why people tend to find probability difficult and counterintuitive, he replied that probability just really is difficult and counterintuitive. 

Even people running the country have problems understanding it. In 2012, 97 members of parliament in the UK were asked this question: “If you flip a coin two times, what’s the probability of getting two heads?” The answer is one quarter, since getting two heads is one eventuality out of a possible four. The majority of parliament members – 60 out of 97 – could not give the correct answer.