StatsExam

μ

Population mean

σ

Population standard deviation

σ2

Population variance

X ̅

Sample mean (also, unbiased estimate of the population mean)

N

Sample size

s

Sample standard deviation

s2

Sample variance

s ̂

Standard deviation estimate. Positive square root of s ̂2 [i.e., √(SS/N-1)]

σx ̅

Standard error of the mean (also referred to as the standard deviation of a sampling distribution of the mean) - reflects the accuracy with which sample means estimate a population mean. Represents an average deviation of the sample means from the population mean. (If σx ̅ is small, then the sample means based on a given sample size (N) will tend to be similar and all will tend to be close to the population mean.) = σ/√N. Standard error of the mean is influenced by sample size and the variability of scores in the population.

s ̂x ̅

Unbiased estimate of standard error of the mean (i.e., estimated standard error of the mean) = s ̂/√N. We rarely know the population standard deviation, therefore, we estimate the standard deviation of the mean by substituting a sample estimate of the population standard deviation for σ.

s ̂2x ̅

Unbiased estimate of the variance of sampling distribution of the means

s ̂2

Variance estimate (i.e., sample estimate of the population variance ) (SS/N-1)* By reducing the size of the denominator, the subtraction of 1 from N makes the variance estimate larger than the sample variance and, therefore, corrects for the tendency of the sample variance to underestimate the population variance. On average the variance estimate will be closer to the population variance than will the sample variance.

σ2x ̅

Variance of sampling distribution of the means