CH4-2300

Variability

A quantitative measure of the differences between scores that describes how spread out or clustered together the scores are.

Range

The distance covered by the scores in a distribution from the smallest value to the highest value.

Standard Deviation

A measure of the average distance from the mean, indicating how closely scores are clustered around the mean.

Variance

The average squared distance from the mean, providing a measure of variability.

Sum of Squares (SS)

The sum of the squared deviations of scores from the mean used to calculate variance.

Degrees of Freedom

The number of scores in a sample that are independent and free to vary, calculated as n - 1.

Population Variance

The variance of a population, represented by σ², which is the average of the squared deviations from the population mean.

Sample Variance

The variance calculated from a sample, represented by s² and using n - 1 in the denominator.

Definitional Formula

A formula for calculating SS that involves finding each deviation score from the mean, squaring it, and summing up the squared deviations.

Computational Formula

An algebraically rearranged formula for calculating SS that uses the sum of scores and squared scores to find the total.

Biased Estimate

An estimate that systematically overestimates or underestimates a population parameter.

Unbiased Estimate

An estimate where the average value of the statistic is equal to the population parameter.

Real Limits

The boundaries used in continuous data to define the range of scores.

Mean Deviation

The average of distances from the mean; always equals zero since deviations sum to zero.

Variance for a Sample

Calculated as the Sum of Squares divided by n - 1, providing an unbiased estimate of population variance.

Transformation of Scale

The process of changing the scores by adding or multiplying constants, affecting the mean and sometimes the standard deviation.