Chapter 24 Survey Methods and Sampling Techniques

Sample Statistics Mean, Median, Mode and standard deviation When calculated from sample data are called sample statistics When calculated from the entire population, they are called population parameters. For practical reasons we usually analyze a portion (sample). Each sample statistic posses a probability distribution know as its sampling distribution. A sample survey gathers information from a portion of the population.

Planning a questionnaire Designers job: Define the purpose of the survey Choose the questions to include Determine appropriate future actions based on survey results. Voice of Customer (VOC) – Six Sigma’s approach to listening to the customer

Steps to conduct a survey Clearly define project goals – what do you need to know about the customer? (VOC) Determine population – whom should be surveyed Select sample of respondents Systematic sampling is a common sampling method Consider using random cluster sampling when each member of the population belongs to a subgroup Consider the need for precise results when choosing sample size and confidence interval Select survey method. Create the questionnaire – what should be asked? Pilot testing – test questions in a controlled environment. Conduct interviews and collect data –ask the questions Analyze the data Prepare statistical tables and figures Consider using the mean to measure for centrality for equal-interval data If the median has been selected to measure centrality, use the interquartile range as the measure of variability Remember that the standard deviation has a special relationship to the normal curve For moderately asymmetric distributions, the mode, median and mean satisfy the formula: mode = 3x median -2 X mean Estimate error margins Report results

Target population and Sample size We must identify the correct target population, and choose an appropriate sample size. Sample size can be calculated statistically, but factors such as cost, time and confidence level must play a part. Sample size: Census – includes every member of the target population Sample survey – a portion of the target population.

Determining Sample Size Until the sample becomes a sizeable fraction, accuracy is determined by sample size alone: Where : SD = Standard deviation p = proportion where score is 1 ` n=sample size. The standard error of estimate (SE); the standard deviation of the possible p values based on the sample estimate is given by: A general formula for determining sample size is: Where : N= size of total number of cases n=sample size a = expected error t=value taken from t distribution corresponding to confidence level p=probability of event

Determining Sample Size For determining sample size for z-test: None of these solutions is exact, but are close. A better approach for Lean Sigma practitioners: Test some minimum, predetermined , number of subjects Stop if the P value is <.01 or ≥ 0.36 Otherwise, increase the sample size

How to conduct survey? The purpose and target audience will help determine the method Personal Interview Costly, but targeted and extensive Telephone survey Quick, but intrusive, interviewer bias Mail Cost effective, long time to complete, no probing Computer Direct Interview Quick, targeted, respondents must have computer access Email Economical and fast, include pictures and sound, technological incompatibility to overcome.

Random selection Simple random sampling – purest form of probability sampling Each member of the population has an equal and known chance of being selected. Could draw names or use a table of random numbers EXAMPLE 24.3 Uses Minitab to generate a random number table Calc>Random Data>Integer Simulate random selection of 100 companies

Distributions Probability Distribution is the probability distribution derived from the information on all elements of a population. Sampling Distribution of X-bar is the probability distribution of X-bar calculated from all possible samples of the same size selected from a population.

Sampling and Nonsampling errors Sampling error is the difference between the value of a sample statistic and the value of the corresponding population parameter: MEAN Sampling error =X – m Most common error sources are: Poorly designed questionnaire Use of an inadequate design Recording and measurement errors Nonresponse problems and related issues