Lecture 2 Forestry 3218 Lecture 2 Statistical Methods Avery and Burkhart, Chapter 2 Forest...
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![Page 1: Lecture 2 Forestry 3218 Lecture 2 Statistical Methods Avery and Burkhart, Chapter 2 Forest Mensuration II Avery and Burkhart, Chapter 2.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f035503460f94c170e8/html5/thumbnails/1.jpg)
Lecture 2Forestry 3218
Lecture 2
Statistical Methods
Avery and Burkhart,Chapter 2
Forest Mensuration II Forest Mensuration II
Avery and Burkhart,Chapter 2
![Page 2: Lecture 2 Forestry 3218 Lecture 2 Statistical Methods Avery and Burkhart, Chapter 2 Forest Mensuration II Avery and Burkhart, Chapter 2.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f035503460f94c170e8/html5/thumbnails/2.jpg)
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
![Page 3: Lecture 2 Forestry 3218 Lecture 2 Statistical Methods Avery and Burkhart, Chapter 2 Forest Mensuration II Avery and Burkhart, Chapter 2.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f035503460f94c170e8/html5/thumbnails/3.jpg)
Lecture 2Forestry 3218
Bias, Accuracy, Bias, Accuracy, PrecisionPrecision
Precise
Imprecise
Unbiased Biased
![Page 4: Lecture 2 Forestry 3218 Lecture 2 Statistical Methods Avery and Burkhart, Chapter 2 Forest Mensuration II Avery and Burkhart, Chapter 2.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f035503460f94c170e8/html5/thumbnails/4.jpg)
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
![Page 5: Lecture 2 Forestry 3218 Lecture 2 Statistical Methods Avery and Burkhart, Chapter 2 Forest Mensuration II Avery and Burkhart, Chapter 2.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f035503460f94c170e8/html5/thumbnails/5.jpg)
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
![Page 6: Lecture 2 Forestry 3218 Lecture 2 Statistical Methods Avery and Burkhart, Chapter 2 Forest Mensuration II Avery and Burkhart, Chapter 2.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f035503460f94c170e8/html5/thumbnails/6.jpg)
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,
![Page 7: Lecture 2 Forestry 3218 Lecture 2 Statistical Methods Avery and Burkhart, Chapter 2 Forest Mensuration II Avery and Burkhart, Chapter 2.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f035503460f94c170e8/html5/thumbnails/7.jpg)
Lecture 2Forestry 3218
Frequency DistributionFrequency Distribution
The relative frequency of different values that occur of a variable in a population
Types– Normal – Binomial – Poisson
![Page 8: Lecture 2 Forestry 3218 Lecture 2 Statistical Methods Avery and Burkhart, Chapter 2 Forest Mensuration II Avery and Burkhart, Chapter 2.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f035503460f94c170e8/html5/thumbnails/8.jpg)
Lecture 2Forestry 3218
Statistical computationsStatistical computations
Mean (the average) Median (the middle value) Mode (the most frequently
appearing value)
nxx
![Page 9: Lecture 2 Forestry 3218 Lecture 2 Statistical Methods Avery and Burkhart, Chapter 2 Forest Mensuration II Avery and Burkhart, Chapter 2.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f035503460f94c170e8/html5/thumbnails/9.jpg)
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
![Page 10: Lecture 2 Forestry 3218 Lecture 2 Statistical Methods Avery and Burkhart, Chapter 2 Forest Mensuration II Avery and Burkhart, Chapter 2.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f035503460f94c170e8/html5/thumbnails/10.jpg)
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)
![Page 11: Lecture 2 Forestry 3218 Lecture 2 Statistical Methods Avery and Burkhart, Chapter 2 Forest Mensuration II Avery and Burkhart, Chapter 2.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f035503460f94c170e8/html5/thumbnails/11.jpg)
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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Lecture 2Forestry 3218
Confidence limitConfidence limit
The confidence limits for population mean
Mean t(standard error)
xx tsxtsx to
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Lecture 2Forestry 3218
averagesamplex )( or
samplex
samples of number total n
variances2
deviationstandards )(or
variation of tcoefficienCV
meanthe of error standardsx
ReviewReview