statistical concepts (part iii)
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Statistical Concepts(part III)
• Concepts to cover or review today:– Population parameter– Sample statistics– Mean– Standard deviation– Coefficient of variation– Standard error– Confidence interval– Estimating totals– Estimating standard deviation, standard error, confidence intervals,
coefficient of variation for totals– Sample size estimation
• You should understand these terms by the end of the lecture and be able to conduct estimations.
Estimation Problem:• Mice weights (g):
21.219.315.926.1
1816.820.616.210.819.3
1
)(1
2__
n
XXsStdev
n
i
i
nStdevSE
CI95 = Mean ± 1.96 * SE
n
XXMean
n
i
i 1
__
• Estimate:
Answers
MEAN 18.42STD 4.02
CV 21.8241
se 1.271236
low CI 15.92838up CI 20.91162
Distribution of Means
16 17 18 19 20
Weight (g)
Freq
uenc
y (n
)
Mean = 18.0SD = 3.6
n = 100
1 se1 se2 se 2 se
2.5 %2.5 %
(truth)
Mean
1 se1 se2 se 2 se1 se1 se2 se 2 se1 se1 se2 se 2 se
Elzinga et al. (2001:76)
Target/Statistical Population
Sample Unit
Individual objects(in this case, plants)
Density to Totals
Estimating Means or Density
1
)(1
2__
n
XXStdev
n
i
i
nStdevSE
CI95 = Mean ± 1.96 * SE
n
XXMean
n
ii
1__
CV = Stdev / Mean
Estimating Totals of Target Population
1
)(1
2__
n
XXNsStdev
n
ii
totaltotal
nStdevSE total
total
CI95 = Total ± 1.96 * SEtotal
n
XNXNTotal
n
i
i 1
__
CV = Stdevtotal / Total
CV = Stdevmean / Mean
(both CVs are the same value)
N = Total number of sample units
Example: Total
number of sagebrush
Target/Statistical Population
Sample Unit
Individual objects in sample unit(sagebrush plants)
Estimating Total Sagebrush Plants
N = 355
n = 25
Estimating Totals
68420
1057920
125
43892068
11473
Mean = 5.40
Stdevmean = 3.48
CV = 0.64
Total = 1917
Stdevtotal = 1230
SEtotal = 246
95% CItotal = 1435, 2399
Sagebrush per sampled plot
Target/Statistical Population
Sample Unit
Individual objects in sample unit(sagebrush plants)
Want Total to be ± 250 plants our first attempt was ± 482 plants
N = 355
n = 25
• How might we do this ?
Calculating Sample Size
nStdevSE total
total
CI95 = Total ± 1.96 * SEtotal
total
total
SEStdevn
2
total
total
SEStdevn
1.96 * SEtotal = 250 SEtotal = 250 / 1.96
Sagebrush Example:
• We want to get within ± 250 shrubs• How many units do we need to sample ?
2
SEStdevn total
SE = 250 / 1.96 = 127.6
Stdevtotal = 1230
n = (1230 / 127.6)2 = 93
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