Summarize 16 plots
Live seedling density in the plots (1-m radius) the class sampled at LP_H in 2026. Each circle is one plot, the sampling unit; the sample size is n = 16 plots.
What each one tells you
- Mean and median: two measures of a typical plot. They are close here, so the data are roughly symmetric.
- Range and SD: how much plots differ from each other. More plots will not make them shrink.
- SE: how uncertain the site mean is. SE = SD / √n, where n is the number of plots, so it shrinks with more plots. Error bars in your figures are ±2 SE.
LP_H, 2026: seedlings/m² in each plot
Fewer plots?
What if the class had characterized LP_H with fewer plots? Each sample draws n plots at random from our 16 (with replacement, so a plot can be drawn twice), treating the 16 as stand-ins for the whole site.
- Mean
- SD
- SE = SD/√n
- Samples
- SD of sample means
- Predicted, SD/√n
- ±2 SE includes 6.90
Predict, then click
- With n = 4 plots instead of 16, will a sample's mean be farther from 6.90? About how much wider will its ±2 SE bar be?
- Single plots are lumpy, not bell-shaped. Will the sample means be?
Halving n does not halve your certainty: SE grows with 1/√n. And means of several plots pile up in a bell shape even when single plots do not (the central limit theorem).
The latest sample's plots (filled) and its mean ± 2 SE
Means from every sample, with the normal curve predicted by SD/√n
Detect a change?
Fine litter cover (<7.6 cm) at LP_H. The sampling unit is the belt transect (one value per transect, the average of its two cover circles); n is the number of transects. What if the class had sampled fewer transects each year?
- All transects
- This subset
- Across 1,000 subsets
Predict, then click
- Compare 2018 with 2025. With all transects, do the ±2 SE bars separate? Would they with only 3 transects per year?
- Now compare 2024 with 2025. Does sampling fewer transects ever make a difference appear?
A smaller n (fewer transects) means wider error bars, so real changes are missed more often. With very few transects, SE itself is unreliable, and an occasional subset shows a "difference" that the full data do not.