lecture 2 forestry 3218 lecture 2 statistical methods avery and burkhart, chapter 2 forest...
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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
Lecture 2Forestry 3218
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,
Lecture 2Forestry 3218
Frequency DistributionFrequency Distribution
The relative frequency of different values that occur of a variable in a population
Types– Normal – Binomial – Poisson
Lecture 2Forestry 3218
Statistical computationsStatistical computations
Mean (the average) Median (the middle value) Mode (the most frequently
appearing value)
nxx
Lecture 2Forestry 3218
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
Lecture 2Forestry 3218
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
Lecture 2Forestry 3218
Confidence limitConfidence limit
The confidence limits for population mean
Mean t(standard error)
xx tsxtsx to
Lecture 2Forestry 3218
averagesamplex )( or
samplex
samples of number total n
variances2
deviationstandards )(or
variation of tcoefficienCV
meanthe of error standardsx
ReviewReview