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Standard scores, also called z-scores or standardized data, are scores which have had the mean subtracted and which have been divided by the standard deviation to yield scores which have a mean of 0 and a standard deviation of 1.
Recall standarderror is the standard deviation of sample means, which is what this example involves, but the logic is the same as for standard deviations of cases.
is the sample standard deviation, used as an estimate of the unknown population standard deviation, and n is the sample size.
Standarderror quantifies the uncertainty that comes from measuring only a sample of a population rather than measuring the entire population.
First, larger samples produce a smaller standarderror, as shown in the table under the sample sizes for 1000 and 25, and the standarderror will become larger when the observed percentage is closer to 50% than either 5% or 95% (see table).
StandardError is used to calculate the error rate of a forecast population value, so we can estimate the range of the actual population value from the observed value of a sample proportion.
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