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Marketing Research Aaker, Kumar, Day Seventh Edition Instructor’s Presentation Slides Chapter Fifteen Sample Size and Statistical Theory Sample Size and Statistical Theory Determining the Sample Size Use of statistical techniques or ad hoc methods Ad Hoc Methods Used when a person knows from experience what sample size to adopt Used when budgetary constraints dictate the size of the sample Marketing Research 7th Edition © Aaker, Kumar, Day Rule of Thumb Sample should be large enough, so that when it is divided into groups, each group will have a minimum sample size of 100 or more If analysis involves comparison between subgroups, sample size in each subgroup should be 20 to 50 Use disproportionate sampling if one of groups of population is relatively small Marketing Research 7th Edition © Aaker, Kumar, Day Rule of Thumb (Contd.) Budget Constraints Researcher must decide whether sample size dictated by budget constraints allows a worthwhile study to be conducted Comparative Studies Find similar studies and use their sample sizes as a guide Marketing Research 7th Edition © Aaker, Kumar, Day Factors Determining Sample Size Number of groups and subgroups within the sample Value of information in the study Accuracy level required in results Cost of sample Variability of the population Marketing Research 7th Edition © Aaker, Kumar, Day Population Characteristics/parameters Population Mean Normally unknown Determine its value as closely as possible by taking a sample from population Population Variance Measure of population dispersion Based on degree to which a response differs from population average response The difference of each value from it’s mean is squared and averaged across all responses Marketing Research 7th Edition © Aaker, Kumar, Day Population Characteristics/parameters (Contd.) Sample Characteristics/Statistics Population mean is not known and must be estimated from a sample Sample mean (X) is used to estimate the unknown population mean Sample Reliability X will vary from sample to sample As sample size (n) increases, variation in X will decrease Marketing Research 7th Edition © Aaker, Kumar, Day Population Characteristics/parameters (Contd.) Variation of X Standard error depends on sample size Assume that variation of X follows normal distribution Sampling distribution Indicates probability of getting a particular sample mean Marketing Research 7th Edition © Aaker, Kumar, Day Interval Estimation X varies from sample to sample The difference between the sample mean (X) and the population mean is the sampling error X + sampling error = interval estimate of sample mean Interval size depends on the confidence level the researcher wants for the interval to contain the true population mean If the population standard deviation is not known, it is necessary to estimate it with the sample standard deviation Marketing Research 7th Edition © Aaker, Kumar, Day Interval Estimate of the Population Mean X + sampling error sx - population standard deviation Or x + z sx / n N - sample size Marketing Research 7th Edition © Aaker, Kumar, Day Size of Interval Estimate Confidence level Population standard deviation Sample size Marketing Research 7th Edition © Aaker, Kumar, Day Sample - Size Question Size of the sampling error that is desired Confidence level Sample size n = Z2 s2 /(sampling error)2 Marketing Research 7th Edition © Aaker, Kumar, Day Determining the Population Standard Deviation Use a sample standard deviation obtained from a previous comparable survey or from a pilot survey Estimate the sample standard deviation (s) subjectively Marketing Research 7th Edition © Aaker, Kumar, Day Sample Size When Proportions Are Used n = z2 p(1 - p)/(sampling error)2 Researcher may require the sample estimate be within plus or minus G percentage points of the population value D = Gm Marketing Research 7th Edition © Aaker, Kumar, Day Sample Size Formula N = s2 Z2 /(sampling error)2 N = s2 Z2 / D2 = C2 Z2 / g2 Coefficient of variation: C=(s/m) Marketing Research 7th Edition © Aaker, Kumar, Day