Drawing Conclusions from Sample Surveys

Instructor: Gerald Lemay

Gerald has taught engineering, math and science and has a doctorate in electrical engineering.

In this lesson, we look at a fictitious survey and show how to draw conclusions based on several criteria. Being able to discern the criteria of a good survey allows valid conclusions to follow the statistical analysis.

Drawing Conclusions from Sample Surveys

It's Fred's first venture into a startup business. Following the recommendations from friends, he has developed some wonderful questions for a survey. It seems like he is doing everything right. His sample group truly represents the population. He is focusing on some well-defined independent variables. And now the data is in from his survey, and he wants to make some conclusions.

Fred's business idea is to open a specialty store and sell ice cream. His survey questions focus on purchases of ice cream, the number of people who own surfboards, and the temperature.

Some Pitfalls to Avoid

Here are the questions in Fred's survey:

1. Have you bought or will you buy ice cream today?

2. What is the temperature right now?

3. Do you own a surfboard?

Ice cream sales correlated with temperature

After collecting the data, Fred sees a very strong correlation between buying ice cream and temperature while measuring almost zero correlation between buying ice cream and surfboard ownership.

Ice cream sales uncorrelated with surfboards

There may be some causation between higher temperature and increased ice cream sales. Note: the reverse causation (increased ice cream sales causing higher temperatures) is not true.

Fred truly wants his business to succeed, mostly because he really likes to eat ice cream. He must be careful to avoid this bias in his conclusions. In other words, even before starting the process of the survey, he already wants his results to show a certain conclusion. It is very important when preparing a survey, collecting data, and analyzing results to be as neutral as possible.

Also, there is a causation problem with his survey variables. An increase in the number of surfboards owned does not cause more ice cream to be sold. These variables may be related to temperature but one of them is not conditioned on the other. The purchase of a surfboard is not conditioned on the purchase of ice cream.

Sales of ice cream is a variable which depends on temperature. Sales of ice cream is the dependent variable while the temperature is the independent variable. Selecting an independent variable, the temperature, while ignoring other variables is called cherry picking. Examples of other variables to measure might include the amount of discretionary income and the number of families (with children) in the area. Fred might also consider the number of competing and already well-established ice cream stores in the vicinity of his proposed specialty store. The ability to clearly identify one independent variable (the temperature) causing changes to the dependent variable (sales of ice cream) is a measure of the internal validity of the survey. With lots of other independent variables, the internal validity of Fred's survey would be low.

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