1 / 17

Statistical Principles in Dendrochronology

1. Statistical distributions

- Why are we interested in average growing

conditions over time? - Average SIGNAL. Means we must shoot for an

average or mean when we sample. - Suggests we also must know the variability about

this mean. - Which means we must be familiar with statistical

distributions, which are defined by mean and

variance - e.g., the normal distribution, the

t-distribution, the z-distribution, the Weibull

distribution

1. Statistical distributions

- population
- samples are drawn
- uncertainty sampling error noise
- maximize signal ( average), minimize noise
- be aware of sampling bias examples?
- easy access
- physical limitations (altitude, health)
- low budget
- downright laziness!

1. Statistical distributions

- samples are drawnfrom a population
- descriptive statistics arecalculated (e.g. mean,

median,mode, standard deviation,minimum,

maximum,range) - frequency distributionis calculated

2. Central Limit Theorem

a. Sample statistics have distributions. b. Thes

e are normally distributed (considers both mean

and variance). c. As one increases sample size,

our sample statistic approaches the population

statistic.

Example from a population of five trees, we can

only sample three. For the year 1842, the five

trees had the following ring widths 0.50 0.75 1.

00 1.50 2.00 population mean ? average of all

sample means ?

2. Central Limit Theorem

population mean 1.15 (0.500.751.00)/3

0.75 (0.500.751.50)/3 0.92(0.500.752.00)/3

1.08(0.501.001.50)/3 1.00(0.501.002.00)

/3 1.17(0.501.502.00)/3 1.33(0.751.001.5

0)/3 1.08(0.751.502.00)/3

1.42(1.001.502.00)/3 1.50 average of all

sample means 1.14 (rounding error here)

0.50

0.75

1.00

1.50

2.00

2. Central Limit Theorem

Sample size means everything! The more samples

one collects, the closer one obtains information

on the population itself!

- Average conditions become more prominent.
- The variability about the mean becomes less

prominent. - Notice relationship with S/N ratio! Signal

increases while noise decreases!

3. Sampling Design

- A procedure for selecting events from a population

- Pilot sample (or pretest)
- Simple random sample
- random number generators are handy for x/y

selection

3. Sampling Design

- Systematic random sample
- select k-th individual from gridded population
- lay out a line transect, sample individual

nearest the pre-selected point

3. Sampling Design

- Stratified random sample
- population is layered into strata and then we

conduct random or systematic sampling within each

cell

3. Sampling Design

- Stratified, systematic, unaligned point

sampling - Hybrid technique, favored among geographers

3. Sampling Design

- Stratified, systematic, unaligned point

sampling - Hybrid technique, favored among geographers

3. Sampling Design

- Transect line sampling, but must have a random

component! (How can this be accomplished?) - Many variations
- Sample all individuals along the transect (row

1)

- Sample quadrats along the transect (row 2)

- Sample all individuals within a belt (row 3)

3. Sampling Design

- Targeted sampling non-random sampling
- Is this a legitimate technique?
- It is often necessary because of
- Time constraints
- Budget constraints
- Lack of field labor
- Physical limitations of field labor
- Topographic limitations
- Advantages?
- Maximize information with minimum resources
- Target areas where samples are known to exist
- Less time needed and less money wasted

3. Sampling Design

- Targeted sampling non-random sampling
- Used in practically all types of dendro research

fire history, climate reconstruction, insect

outbreak studies,

3. Sampling Design

- Specifically sample only trees that have best

record of fire scars. (dots trees, circles

trees collected with fire scars, Xs fire

scars, but not sampled poor record.) - What issues must we consider? Topography, slope,

aspect, hydrology, tree density all affect

susceptibility to scarring by fire.

Shallow slope area Valley bottom

Steep slope area

3. Sampling Design

- Complete inventory is possible
- Sample all trees that have fire scars, regardless

of number of scars or quality of preservation,

but - Not very efficient (time, money, labor)
- Benefits are considerable, though.