# Statistics : Choosing Sample Size

Select one of these articles and provide an overview of the contents and apply the concepts to the Job Satisfaction survey. It is important to cover the concept of the techniques used to estimate sample size.

Simple rules shape proper sample size

Section: Special report

RESEARCH ? A numbers game

How low can you go? No, not the limbo. We re talking about how many people you'll want to include in your study. Today's research budgets are tight, and selecting a sample size that is large enough to provide the accuracy you need, but not so large it wastes research dollars, is crucial. By answering just a couple of questions, you'll be on the right track to determining the appropriate sample size for your project.

Two key questions are: Are you going to analyze your data by the entire sample or do you plan on a more detailed examination of subgroups within the sample? And, how accurate do you want your results to be?

The question of number of subgroups is important, not only in determining sample size but also for ensuring that your research can be translated into action. For example, let's say you want to understand the use of MP3 players by 15- to 18-year-olds. You need to decide whether you are interested in the differences between males and females or if gender is irrelevant. Should you look at the market as a whole or look at males and females separately? This choice will affect the sample size. Understanding how you'll use the data is crucial to designing an appropriate sampling strategy.

After deciding which groups you'll want to analyze, you need to consider the level of accuracy required in the research results. If a greater level of accuracy is required, you'll need a larger sample. This, in turn, costs more. The trick is to balance cost with accuracy, without compromising the quality and usability of the research.

When a project focuses on only one group of individuals, determining the appropriate number of people to include in the research is defined by the desired level of accuracy.

Many researchers aim for a maximum range of error of ±5.0% at a 95% confidence level, whereas some have set internal ranges of error between ±5.0% and ±10%, depending on the type of decisions to be made. A ± 5.0% level of accuracy means that if the same study were repeated 100 times, in 95 of those times the results would not vary more than 5.0 percentage points, higher or lower, from the results of the original study. This level of accuracy corresponds to a sample size of about 400 (±4.9%). A level of accuracy of ± 10% would require a sample size of only about 100.

Back to our example of MP3 player use among 15- to 18-year-olds. Let's say you re testing the preference of two popular MP3 players--A and B. Results show that player B is preferred by 35% of 15- to 18-year-olds and player A is preferred by 25%. These results appear to tell a clear picture that player B is preferred over player A. But, let's take a look at what happens to the accuracy of these results when sample size changes.

With a sample size of 1,600, MP3 player B is clearly preferred over player A. With a sample size of 400, player B is probably preferred more often than player A, but might also be preferred equally as much. With a sample size of 100, B is probably preferred or they could be equally preferred or A could be preferred more than B. It's clear from this example how the total number of respondents surveyed can have a direct bearing on accuracy and the interpretation of the data.

If one of the objectives of the research is to examine differences between two or more subgroups in your sample, a slightly different set of rules apply. For many projects, it is the differences between two or more groups that provide the greatest insight into the client's target market. And, once the differences have been identified, pro ling each group allows the client to understand some of the key inputs to creating effective product development, marketing or sales strategies. Defining the appropriate subgroup size can be more crucial to a study than the overall sample size.

Two questions to consider if you anticipate dividing your data into separate subgroups: Are you interested in conducting additional analyses within each subgroup or are you only going to compare subgroups against one another?

If you need to conduct an in-depth examination of a subsample, the recommended minimum number of respondents is 100 (±9.8%). This size allows for fairly robust analyses, while also being economical. If you only need to conduct comparisons across a set of subsamples, then the minimum required number of interviews is 30. This size is large enough for running statistically valid z and t tests to see if significant differences across subsamples exist. Creating an analysis plan before beginning data collection ensures that the completed interviews meet your research needs.

Let's revisit the MP3 example. Suppose you want to know the level of awareness of your company's MP3 player vs. competitive products. You conduct a study with a total sample size of 400 respondents with six target respondent groups, based on gender and age--males 15 to 18, 19 to 24 and 25 to 29 years old, and females with the same age breakouts. With these group sizes, you'll be able to accurately identify any significant differences between age groups or differences by gender. But, you will not be able to pro le each gender within each of the age groups with respect to the group's music listening habits, spending habits or additional demographics. This would require at least 100 respondents in each of the six groups, with a minimum total sample size of 600.

By using these simple principles to develop a sampling plan, you help ensure the usability and cost effectiveness of the research you've conducted.

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By Jason Ball

Jason Ball is director of methodology for Bardsley & Neidhart Inc., a marketing research company based in Portland, Ore

#### Solution Summary

Sample size is discussed.