Measurement Data Types Measurement data are categorized as either continuous or discrete Continuous data, also called variable data, are based on a continuum of numbers, such as heights, weights, times, and dollars Discrete data, also called attribute data, are based on counts or classes, such as proportions, defects, yes/no or pass/fail, A, B, C, D Grades or a 5-point survey scale
Determining Sample Size for Continuous Data where Z = the standardized Z score at a specified confidence interval (e.g., a 95% confidence level = 1.96 Z score) S = sample standard deviation, or an estimate of the population standard deviation E = acceptable measurement error, expressed as a number.
Example Imagine that a Six Sigma team wants to estimate the sample size required to determine the mean time to process an insurance claim with a 95% confidence interval. The standard deviation is estimated at 29 min. The acceptable measurement error (E) is ±4 min from the mean. The calculation is:
Determining Sample Size for Discrete Data where Z2 = square of the standardized Z score at a specified confidence interval [e.g., a 95% confidence level = (1.96)2] p = estimated proportion of correct observations (successes) q = (p – 1) = estimated proportion of defects (failures) E2 = square of the acceptable measurement error.
Example If a Black Belt wants to determine the sample size required to estimate the proportion of defective billing statements (one or more errors on a statement) with 95% confidence and with a measurement error of no more than ±5% between the true proportion and the sample proportion, a sample size of 227 is required, as illustrated in Equation. The Black Belt estimates the proportion of defective billing statements at 18%, based on preliminary sampling: