1. MARKETING RESEARCH ESSENTIALS WITH DATA ANALYSIS IN EXCEL AND SPAA McDaniel │ Gates │ Sivaramakrishnan │ Main Chapter Twelve: Sample Size Determination

2. LEARNING OBJECTIVES Understand the financial and statistical issues in the determination of sample size and explore methods for determining sample size Understand what a normal distribution is Understand population, sample, and sampling distributions Distinguish between point and interval estimates Recognize problems involving sampling means and proportions Understand Type I and Type II errors in statistical conclusions Chapter Twelve: Sample Size Determination

3. Sample Size for Probability Samples Budget available for survey study Use of “rule of thumb” Number of subgroups to be analyzed Application of traditional statistical methods

4. Normal Distribution Central Limit Theorem: –A distribution of a large number of sample means or sample proportions will approximate a normal distribution, regardless of the distribution of the population from which they were drawn Normal Distribution: –The continuous distribution that is bell shaped and symmetrical about the mean –The mean, median, and mode are equal

5. Normal Distribution Proportionate Properties: –The number of observations falling between the mean and a given number of standard deviations from the mean is the same for all normal distributions Standard Normal Distribution: –Normal distribution with a mean of zero and a standard deviation of one

6. Normal Distribution Standard Deviation: Measure of dispersion calculated by: 1.Subtracting the mean of the series from each value in a series 2.Squaring each result 3.Summing the results 4.Dividing the sum by the number of observations minus 1, and taking the square root of this value

7. Population and Sampling Distributions Population Distributions: –Frequency distribution of all the elements of population Sampling Distributions: –Frequency distribution of all elements of an individual sample Sampling Distribution of the Mean: –Theoretical frequency distribution of the means of all possible samples of a given size drawn from a population –It is normally distributed. Standard Error of the Mean: –Standard deviation of a distribution of sample means

8. Point and Interval Estimates Point Estimate: –Estimate of a population value Interval Estimate: –Interval or range of values within which the true population value is estimated to fall Confidence Level: –The probability that a particular interval will include the true population value Confidence Interval: –The interval that, at the specified confidence level, includes the true population value

9. Sampling Distribution of the Proportion Sampling Distribution of the Proportion: –Relative frequency distribution of the sample proportions of many random samples of a given size drawn from a particular population –It is normally distributed

10. Determining Sample Size Problems involving means:

11. Determining Sample Size Problems involving proportions:

12. Statistical Power Probability of not making a type II error Type I Error: –The error of concluding something that doesn’t exist –E.g., concluding that there is a difference in the responses of 2 groups when there is no difference Type II Error: –The failure to conclude something when it indeed exists –E.g., concluding there is no difference in the responses of the two groups when there is a difference

13. Key Sampling Considerations Time to generate sample Scope of the research Budget available Experience with sampling Level of accuracy desired Your knowledge of the population

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