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.