Randomness in samples of data

A random sample is a subset of a population selected by a process that makes all samples of a specified size equally likely to occur. In statistics, you use a random sample to make generalizations, or inferences, about a population.

A sample must be randomly collected to accurately represent the entire population from which it comes. You should carefully plan your data collection process to ensure that your sample is random. In addition, the process or population that the data come from should be stable.

Random samples eliminate selection bias. Selection bias means that some subjects are more likely to be in the sample than other subjects are. If the sample is biased, you can describe only the subjects in the sample. You cannot make inferences about the entire population.

Suppose you want to start a new ad campaign. You are unsure whether print, radio, or television is the best way to get to your customers. A survey of all of your customers is neither practical nor cost-effective, but a survey of a random sample is possible. At first, you are inclined to survey only those customers who have returned a mail-in rebate. You think that these customers are more likely to respond to a survey. However, this sample does not represent the entire population because each customer does not have an equal chance of being selected. This could lead to bad business decisions. Instead, you decide to randomly select customers from an alphabetical list of all customers. From this data, you can make inferences about your customer base to determine the best way to allocate your advertising dollars.

Determine whether a sample is random by using a runs test

After you collect the data, one way to check whether your data are random is to use a runs test to look for a pattern in your data over time. To perform a runs test in Minitab, choose:
  • Mac: Statistics > 1-Sample Inference > Runs Test
  • PC: STATISTICS > One Sample > Runs Test
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