Service Quality - Correct Sampling Key to Accurate Delivery

WHAT IT IS
Sampling is the process of selecting part of a population to determine parameters and characteristics of the whole population.

Sampling may be random or purposeful. The major difference between the two is that random sampling is more confirmatory while purposeful sampling is more exploratory. Both types of sampling may be applied to:

• Attribute Data: To reach a conclusion about a population in terms of the proportion, percentage, or total number of items which possess some characteristic (attribute) or fall into some defined classification. Typically, the classifications defined when sampling for attributes are some variation of "in compliance" or "not in compliance." Examples of attribute sampling includes tests of compliance with voucher processing controls, tests of compliance with controls over fixed asset additions, and surveys which provide demographic information or answers to “yes/no” questions.

• Variables Data: To draw conclusions about a population in terms of numbers, such as dollar amounts, height, weight, etc. It is usually used in substantive testing to determine the reasonableness of recorded amounts. Generally, variable sampling involves calculation of the difference between the actual and recorded values of a sample and projecting this difference across the population. Examples of variable sampling include tests of inventory quantities, tests of total assessed taxes uncollected, and surveys which gather ratings or interval variable data.

DEFINITIONS used in Sampling

• Confidence level the percentage of times the sample accurately represents the population. A 95 percent confidence level indicates that if 100 samples were drawn from the population, 95 would be representative
• Desired precision (d) (margin of error) the amount of deviation from the estimate one is willing to accept. In opinion poll (simple random sampling), figures quoted often have a listed "margin of error" of, for example, + 3 percent. This means if 52 percent of respondents say they will vote for a political candidate, the actual percentage in the population may be as low as 49 percent or as high as 55
  percent.
• Expected percent error rate (p)
• Normal distribution occurs when data are distributed in a symmetrical bell shape such that the number of data points decreases the farther they are from the mean (average).
• Standard deviation (σ) indicates the dispersion of data which are normally distributed. The actual standard deviation of a population is rarely known since this can only be determined by a census (100 percent sample). Typically, the sample standard deviation (s) is used in calculations once samples have been drawn.
• Tolerable rate indicates the maximum acceptable error rate in the population. 
  

z relates to confidence level. The z-value is a standardized value which indicates how far from the population mean (or proportion) a sample mean (or proportion) can be and still represent the population. The z-value is critical when calculating sample size. The most common z-values for two-tailed tests are:
                              Confidence                Level z
                                   99 %                        2.58
                                   98 %                        2.33
                                   95 %                        1.96
                                   90 %                        1.64
The most common z-values for one-tailed tests are:
                              Confidence                Level z
                                   99 %                        2.33
                                   98 %                        2.05
                                   95 %                        1.64
                                   90 %                        1.29

HOW TO PREPARE FOR SAMPLING

1. Determine the objectives of sampling based on the project objectives.
2. Define the population and the sample. Since the informational objectives are known at this point in the process, the identity and characteristics of the population should be fairly clear. The most important thing is to define the population rigorously and thoroughly since this definition will serve as the benchmark against which each potential sample is measured. In defining the population and the sample, consider these questions:
1. What is the larger group (population) about which general statements or predictions are required? What are the characteristics of this group, and which of these characteristics are of greatest interest? 
2. Under which circumstances is one most likely to find information about the characteristics of interest? When, where, and why do the members of the population exhibit these characteristics?
3. Which subgroup (sample) of the population is most likely to exhibit the characteristics of interest in a way that allows gathering data in an efficient, effective, and economical way?
4. When and where is one most likely to capture the sample data sought?

When answering this last question, take stock of information already available, such as statewide data bases, agency records, mailing or telephone directories and lists, client lists, and so on. Other issues to consider include:
— How much will it cost to design and execute the sample?
— Has this study been done before?
— If data are available from multiple sources, which source is best?
— What kinds of statements, predictions, or decisions might arise from the
data?
— How precise must the results be?
— Are the resources required to collect and analyze the data at hand?


FORMULAS FOR DETERMINING SAMPLE SIZE


For variable sampling using simple random samples, the formula for determining the
sample size is: