Descriptive Statistics

We use statistics both to describe a sample and to compare samples to one another (e.g., two and multi-sample tests, correlation, regression). There are lots of descriptive statistics but the two that are most generally useful are the mean and confidence limits and we would suggest reporting these two whenever you describe a sample. For continuous data the usual descriptive statistics are:

  • Measures of Central Tendency: Mean (arithmetic geometric harmonic), Median, Mode
  • Measures of Dispersion: Range, Standard deviation, Coefficient of variation, Percentile, Interquartile range
  • Measures of Shape: Variance, Skewness, Kurtosis, Moments, L-moments

Here are some websites for calculating descriptive stats:

  • Calculator Soup: using a variety of formats, enter from the keyboard or copy and paste up to 2500 samples; provides details on how each statistic was calculated but does not calculate confidence limits
  • Xuru’s website: copy/paste data into a box, and get lots of useful descriptive stats including confidence limits of mean and SD
  • Graphpad: enter (up to 50 data points) or copy/paste up to 10000 data points or just enter mean and SD to get a few descriptive stats including confidence limits
  • HyperStat: basic descriptive stats with stem and leaf display, no CLs
  • Had2Know: some unusual descriptive stats (in addition to the usual ones) with good explanations but no CLs

A worked example

Dr Bruce Tufts caught 48 adult Walleye during the spawning season in Lake Nipissing and measured their fork length (a measure of total length in fish). Here are the descriptive stats for that sample:

PARAMETER   VALUE
Mean   391.91667
SD   49.52791
SEM   7.14874
N   48
90% CI   379.92161 to 403.91173
95% CI   377.53526 to 406.29807
99% CI   372.72548 to 411.10785
Minimum   288
Median   395.5
Maximum   479

The 95%CL of the mean tells him that the real mean size of spawning fish in this population is likely to be somewhere between 378 and 406 cm.

Walleye

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Antonie van Leeuwenhoek

It's a parts list... If I gave you the parts list for the Boeing 777 and it had 100,000 parts, I don't think you could screw it together and you certainly wouldn't understand why it flew

Eric Lander

What is true for E. coli is also true for the elephant

Jacques Monod

The world becomes full of organisms that have what it takes to become ancestors. That, in a sentence, is Darwinism

Richard Dawkins

Shall we conjecture that one and the same kind of living filaments is and has been the cause of all organic life?

Erasmus Darwin

Nature proceeds little by little from things lifeless to animal life in such a way that it's impossible to determine the line of demarcation

Aristotle

Cells let us walk, talk, think, make love, and realize the bath water is cold

Lorraine Lee Cudmore

In the distant future I see open fields for far more important researches. Psychology will be based on a new foundation, that of the necessary acquirement of each mental power and capacity by gradation. Light will be thrown on the origin of man and his history

Charles Darwin

It is my belief that the basic knowledge that we're providing to the world will have a profound impact on the human condition and the treatments for disease and our view of our place on the biological continuum

J. Craig Venter

Imagine a house coming together spontaneously from all the information contained in the bricks: that is how animal bodies are made

Neil Shubin

A grain in the balance will determine which individual shall live and which shall die - which variety or species shall increase in number, and which shall decrease, or finally become extinct

Charles Darwin

The stuff of life turned out to be not a quivering, glowing, wondrous gel but a contraption of tiny jigs, springs, hinges, rods, sheets, magnets, zippers, and trapdoors, assembled by a data tape whose information is copied, downloaded and scanned

Steven Pinker

We wish to discuss a structure for the salt of deoxyribose nucleic acid. (D.N.A.). This structure has novel features which are of considerable biologic interest

Rosalind Franklin

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Mary Roach

The systems approach to biology will be the dominant theme in medicine

Leroy Hood

I've always been interested in animal behavior, and I keep reading about it because it's so surprising all the time - so many things are happening around us that we neglect to look at. Part of the passion I have for biology is based on this wonderment"

Isabella Rossellini

Because all of biology is connected, one can often make a breakthrough with an organism that exaggerates a particular phenomenon, and later explore the generality

Thomas Cech

Nothing in Biology makes sense except in the light of evolution

Theodosius Dobzhansky

Biology is now bigger than physics, as measured by the size of budgets, by the size of the workforce, or by the output of major discoveries; and biology is likely to remain the biggest part of science through the twenty-first century

- Freeman Dyson

Nothing can be more incorrect than the assumption one sometimes meets with, that physics has one method, chemistry another, and biology a third

- Thomas Huxley