Lecture 2Forestry 3218

Lecture 2

Statistical Methods

Avery and Burkhart,Chapter 2

Forest Mensuration II Forest Mensuration II

Avery and Burkhart,Chapter 2

Lecture 2Forestry 3218

Bias, Accuracy, PrecisionBias, Accuracy, Precision

Bias– systematic distortion of measurements – sources: measurement flaw, incorrect sampling method

Accuracy– success of estimating the true value of a quantity

Precision– clustering of sample values about their own average

Lecture 2Forestry 3218

Bias, Accuracy, Bias, Accuracy, PrecisionPrecision

Precise

Imprecise

Unbiased Biased

Lecture 2Forestry 3218

Independent events

Mutually exclusive

Calculating ProbabilitiesCalculating Probabilities

Relative frequency with which an event takes place in the long run

n

xAP )(

)()...()(

)...,(

21

21

n

n

aPaPaP

aaaP

)()...()(

)...,(

21

21

n

n

aPaPaP

aaaP

Lecture 2Forestry 3218

Population vs. SamplePopulation vs. Sample

Population– The aggregate of all

arbitrarily defined, nonoverlapping sample units

– Finite vs. infinite

Sample– An aggregation of sample

units from which measurements or observations are taken

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Parameter vs.VariableParameter vs.Variable

Parameter– A constant that describes

the population as a whole

Variable– A characteristic that may

vary from one sample to the next

N,,dbhheight,

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Frequency DistributionFrequency Distribution

The relative frequency of different values that occur of a variable in a population

Types– Normal – Binomial – Poisson

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Statistical computationsStatistical computations

Mean (the average) Median (the middle value) Mode (the most frequently

appearing value)

nxx

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Statistical computationsStatistical computations (measures of dispersion)(measures of dispersion)

Range– Easy to compute– Fails to take into account

how the data are distributed

Variance– A measure of dispersion

among individual observations about their average value

Standard deviation (s)

1

2)(2

nxxs

MinMax-xxR

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Coefficient of variation– A percentage of the standard

deviation to the mean of a sample

– Allows a comparison of relative variability about different-sized means

)100(xsCV

Statistical computationsStatistical computations (measures of dispersion)(measures of dispersion)

Lecture 2Forestry 3218

Standard error of the mean– A measure of variation

of among sample means

– A standard deviation among the means of samples of a fixed n

Statistical computationsStatistical computations (measures of dispersion)(measures of dispersion)

)(2

N

nNs

n

sx

– when sampling from a finite population

Calculation – for simple random sampling

from an infinite population

n

sxs

2

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Confidence limitConfidence limit

The confidence limits for population mean

Mean t(standard error)

xx tsxtsx to

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averagesamplex )( or

samplex

samples of number total n

variances2

deviationstandards )(or

variation of tcoefficienCV

meanthe of error standardsx

ReviewReview