Marketing researchers make decisions about the sample sizes for interviews, experiments, product test markets, or Web surveys. A basic understanding of statistics is required for determining sample size. Statistical concepts and terminology allow us to understand the important characteristics of distributions. Descriptive statistics are used to summarize distributions. A frequency distribution summarizes data by arraying it in a frequency table. A proportion is the percentage of elements in the distribution that met a certain criterion. Summarizing the information from collected data often requires the description of "typical" values. The common measures of central tendency vary in application by scale or data and include the mean, median, and mode. Measures of variability describe how scores cluster or scatter in a distribution. The variance, standard deviation, range, interquartile range, and quartile deviation are the indices of variability for metric (interval and ratio) data. The measures of distribution shape, skewness and kurtosis, describe departures from the symmetry and the distribution's relative flatness (or peakedness), respectively.
The distribution of values for any variable that has a normal distribution is governed by a mathematical equation. The normal distribution is a symmetrical, bell-shaped curve where the mean, median, and mode are all equal. Many variables of interest have distributions that approximate a standard normal distribution. The standard normal distribution is a standard of comparison for describing distributions of sample data and is used with inferential statistics that assume normally distributed variables. In a standard normal distribution, all values are given as standard scores. Standard scores tell us how many units an individual case is above or below the mean.
Techniques for computing population estimates were described in terms of point and interval estimates, the standard error of the mean, and the confidence level. Changing confidence intervals were also described. The central limit theorem informs us of the relationships between population and sampling distributions. Even if the population is not normally distributed, the distribution of sample means will be normal if there is a large enough set of samples.
To determine the sample size for questions involving means, we need the following information:
The precision desired and how to quantify it:
(1) The confidence level we want with our estimate.
(2) The size of the interval estimate.
The expected dispersion in the population for the investigative question used to measure precision.
Whether a finite population adjustment is needed.
To compute the sample size for questions involving proportions, we use the same procedure—also deciding on an acceptable interval estimate and the degree of confidence— except we substitute p (the proportion of the population that has a given attribute) for the arithmetic mean and, instead of the standard deviation, dispersion is measured by p × q (in which q is the proportion of the population not having the attribute, and q = (1 - p)). The measure of dispersion of the sample statistic also changes from the standard error of the mean to the standard error of the proportion.
