Objective: We need to know how many observations to collect so our estimate of the mean has a useful precision. For example, how many animals should be measured in order to have an 80% chance that the 95% confidence interval for weight will be no wider than 20 kg? In addition to those 3 numbers, we also need an estimate of the std. deviation. Suppose the best situation expected has SD=20kg, but we also want to see what changes if SD=40kg,
SAS: Run this code
proc power;
onesamplemeans ci=t
alpha = 0.05
halfwidth = 10
stddev = 20 40
probwidth = 0.80
ntotal = .;
run;
data adjust;
samplesize=22;
population=1200;
adjsamplesize=ceil(samplesize/(1 + ((samplesize-1)/population)));
run;
proc print; run;
The 95% confidence interval is requested by setting alpha=0.05.
The 80% chance that our experiment will satisfy our objectives is specified by probwidth=0.80.
The "no wider than 20" objective is addressed with halfwidth=10, assuming the 20 kg width referred to the entire confidence interval.
The two SD that we want to explore are listed after stddev=.
Ntotal is set to missing, as it is the unknown quantity to be calculated.
Results are 22 observations needed for SD=20, but 73 observations would be needed if SD turned out to be 40kg.
Following the proc power code, an adjustment for finite population size can be used if the population being sampled is small. Here we might be dealing with a rare species, with only 1200 still alive. Note that the adjustment results in no change. Populations must be quite small in order to affect sample size requirements.
R: There are several power and sample size packages in R, but none appear to have the feature of requesting that we be 80% sure the experiment will meet the objectives.
For example this code returns a sample size of 16, smaller than SAS's 22 because it ignores variation among experiments. We are not 80% sure our particular experiment will succeed.
library(samplingbook)
sample.size.mean(10, S=20, N = Inf, level = 0.95)
sample.size.mean(10, S=20, N = 1200, level = 0.95)
Where do I get SD? Values may be available in publications, or you may have preliminary data from which to calculate SD. If not, then useful guesses are SD=0.2*mean to SD=0.4*mean, based on generally observed coefficients of variation for biological data. The last resort is to take the range of expected observed values and divide by 4, based on 95% of normally distributed data being within plus or minus 2 SD.
SAS: Run this code
proc power;
onesamplemeans ci=t
alpha = 0.05
halfwidth = 10
stddev = 20 40
probwidth = 0.80
ntotal = .;
run;
data adjust;
samplesize=22;
population=1200;
adjsamplesize=ceil(samplesize/(1 + ((samplesize-1)/population)));
run;
proc print; run;
The 95% confidence interval is requested by setting alpha=0.05.
The 80% chance that our experiment will satisfy our objectives is specified by probwidth=0.80.
The "no wider than 20" objective is addressed with halfwidth=10, assuming the 20 kg width referred to the entire confidence interval.
The two SD that we want to explore are listed after stddev=.
Ntotal is set to missing, as it is the unknown quantity to be calculated.
Results are 22 observations needed for SD=20, but 73 observations would be needed if SD turned out to be 40kg.
Following the proc power code, an adjustment for finite population size can be used if the population being sampled is small. Here we might be dealing with a rare species, with only 1200 still alive. Note that the adjustment results in no change. Populations must be quite small in order to affect sample size requirements.
R: There are several power and sample size packages in R, but none appear to have the feature of requesting that we be 80% sure the experiment will meet the objectives.
For example this code returns a sample size of 16, smaller than SAS's 22 because it ignores variation among experiments. We are not 80% sure our particular experiment will succeed.
library(samplingbook)
sample.size.mean(10, S=20, N = Inf, level = 0.95)
sample.size.mean(10, S=20, N = 1200, level = 0.95)
Where do I get SD? Values may be available in publications, or you may have preliminary data from which to calculate SD. If not, then useful guesses are SD=0.2*mean to SD=0.4*mean, based on generally observed coefficients of variation for biological data. The last resort is to take the range of expected observed values and divide by 4, based on 95% of normally distributed data being within plus or minus 2 SD.
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