Statistics for Biologists

The correct use of statistics is not just good for science — it is essential.

Experimental biologists, their reviewers and their publishers must grasp basic statistics, urges David L. Vaux, or sloppy science will continue to grow.

P values, the 'gold standard' of statistical validity, are not as reliable as many scientists assume.

One-quarter of studies that meet commonly used statistical cutoff may be false.

The reliability and reproducibility of science are under scrutiny. However, a major cause of this lack of repeatability is not being considered: the wide sample-to-sample variability in the P value. We explain why P is fickle to discourage the ill-informed practice of interpreting analyses based predominantly on this statistic.

As the data deluge swells, statisticians are evolving from contributors to collaborators. Sallie Ann Keller urges funders, universities and associations to encourage this shift.

Deficiencies in methods reporting in animal experimentation lead to difficulties in reproducing experiments; the authors propose a set of reporting standards to improve scientific communication and study design.

This Review discusses the principles and applications of significance testing and power calculation, including recently proposed gene-based tests for rare variants.

Low-powered studies lead to overestimates of effect size and low reproducibility of results. In this Analysis article, Munafò and colleagues show that the average statistical power of studies in the neurosciences is very low, discuss ethical implications of low-powered studies and provide recommendations to improve research practices.

The authors analyze a large corpus of the neuroscience literature and demonstrate that nearly half of the published studies considered incorrectly compared effect sizes by comparing their significance levels.

Hierarchical models provide reliable statistical estimates for data sets from high-throughput experiments where measurements vastly outnumber experimental samples.

Alkes Price, Peter Visscher and colleagues provide recommendations on the application of mixed-linear-model association methods across a range of study designs.

A protocol providing guidelines on the organizational aspects of genome-wide association meta-analyses and to implement quality control at the study file level, the meta-level across studies, and the meta-analysis output level.

This perspective illustrates some of the problems involved in analyzing the complex data yielded by systems neuroscience techniques, such as brain imaging and electrophysiology. Specifically, when test statistics are not independent of the selection criteria, common analyses can produce spurious results. The authors suggest ways to avoid such errors.

The authors examine papers in high profile journals and find that while collection of multiple observations from a single research object is common practice, such nested data are often analyzed using inappropriate statistical techniques. The authors show that this results in increased Type I error rates, and propose multilevel modelling to address this issue.

When prioritizing hits from a high-throughput experiment, it is important to correct for random events that falsely appear significant. How is this done and what methods should be used?

There seem to be a lot of computational biology papers with 'Bayesian' in their titles these days. What's distinctive about 'Bayesian' methods?

Statistical models called hidden Markov models are a recurring theme in computational biology. What are hidden Markov models, and why are they so useful for so many different problems?

Statistics does not tell us whether we are right. It tells us the chances of being wrong.

The meaning of error bars is often misinterpreted, as is the statistical significance of their overlap.

The P value reported by tests is a probabilistic significance, not a biological one.

The ability to detect experimental effects is undermined in studies that lack power.

Use box plots to illustrate the spread and differences of samples.

Robustly comparing pairs of independent or related samples requires different approaches to the t-test.

When a large number of tests are performed, P values must be interpreted differently.

Nonparametric tests robustly compare skewed or ranked data.

Good experimental designs limit the impact of variability and reduce sample-size requirements.

Good experimental designs mitigate experimental error and the impact of factors not under study.

Quality is often more important than quantity.

For studies with hierarchical noise sources, use a nested analysis of variance approach.

When multiple factors can affect a system, allowing for interaction can increase sensitivity.

When some factors are harder to vary than others, a split plot design can be efficient.

Incorporate new evidence to update prior information.

Today's predictions are tomorrow's priors.

When multiple variables are associated with a response, the interpretation of a prediction equation is seldom simple.

Some outliers influence the regression fit more than others.

Robust regression generates more reliable estimates by detecting and downweighting outliers.

Quantile regression robustly estimates the typical and extreme values of a response.

You can look back there to explain things, but the explanation disappears. You’ll never find it there. Things are not explained by the past. They’re explained by what happens now. –Alan Watts

“Everything we see hides another thing, we always want to see what is hidden by what we see” — Rene Magritte

“With one eye you are looking at the outside world, while with the other you are looking within yourself.” —Amedeo Modigliani

“Every day sadder and sadder news of its increase. In the City died this week 7496; and of them, 6102 of the plague. But it is feared that the true number of the dead this week is near 10,000 ....” —Samuel Pepys, 1665

Realistic models of epidemics account for latency, loss of immunity, births and deaths.

“I have no idea what’s awaiting me, or what will happen when this all ends. For the moment I know this: there are sick people and they need curing.” ―Albert Camus, The Plague

“We demand rigidly defined areas of doubt and uncertainty!” —D. Adams

All that glitters is not gold. —William Shakespeare

I do not think you can start with anything precise. You have to achieve such precision as you can, as you go along. —Bertrand Russell

The exception proves the rule.

Love’s the only engine of survival. —Leonard Cohen

If you sit on the sofa for your entire life, you’re running a higher risk of getting heart disease and cancer. —Alex Honnold, American rock climber

Nature is often hidden, sometimes overcome, seldom extinguished. —Francis Bacon

Nature uses only the longest threads to weave her patterns, so that each small piece of her fabric reveals the organization of the entire tapestry. —Richard Feynman

It is the mark of an educated mind to rest satisfied with the degree of precision that the nature of the subject admits and not to seek exactness where only an approximation is possible. —Aristotle

All animals are equal, but some animals are more equal than others. —George Orwell

I don’t have good luck in the match points. —Rafael Nadal, Spanish tennis player.