Lecture Marketing research (12th edition) - Chapter 15: Sample size and statistical theory

Chapter 15 - Sample size and statistical theory. In this chapter, the following content will be discussed: Determining the sample size, factors determining sample size, population characteristics/parameters, sample characteristics/statistics,...

1 Marketing Research Aaker, Kumar,  Leone and Day  Twelfth Edition Instructor’s  Chapter Fifteen Sample Size and Statistical Theory Marketing Research 12th Edition Determining the Sample Size 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 Rule of Thumb  • • • Sample should be large enough, so that when 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 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 12th Edition 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 12th Edition Population  Characteristics/Parameters Population Mean • • Normally unknown Determine 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 its mean is squared and averaged  across all responses Marketing Research 12th Edition Population  Characteristics/Parameters The population opinion on symphony starting time (7:30 P.M. on weekdays) Marketing Research 12th Edition Sample Characteristics/Statistics • X Sample mean (    ) is used to estimate the unknown population mean Example: A sample of symphony season­ticket holders Marketing Research 12th Edition Sample Characteristics/Statistics (Contd.) Sample mean Marketing Research 12th Edition Sample Reliability • • X will vary from sample to sample As sample size (n) increases, variation in X will decrease standard error of                decreases as the sample size gets  larger Marketing Research 12th Edition 10 Sampling Distribution Indicates probability of getting a particular sample mean The normal distribution of X Marketing Research 12th Edition 11 Sampling Distribution (Contd.) X The effect of increasing sample size on the normal distribution of Marketing Research 12th Edition 12 Interval Estimation • • • • X      varies from sample to sample  The difference between the sample mean (  ) and the  X population mean is the sampling error X 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 12th Edition 13 Interval Estimation (Contd.) Size of Interval Estimate depends on: • • • Confidence level Population standard deviation Sample size Marketing Research 12th Edition 14 Sample Size Question • • • Size of the sampling error that is desired Confidence level Expected variance Marketing Research 12th Edition 15 Determining the Population Standard Deviation Options: • • 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 12th Edition 16 Proportions Population variance, Marketing Research 12th Edition 17 Sample Size Formulas Marketing Research 12th Edition 18 Coefficient of Variation • Researcher may require the sample estimate  be within plus or minus G percentage points of  the population value Therefore,  D=Gà ã Thesamplesizeformulamaybewrittenas: Marketing Research 12th Edition 19 StratifiedSampling ã • Useful when: ▫ The population standard deviation differs by strata ▫ The interview cost differs by strata  Optimal allocation of sampling budget to various strata: Neyman’s solution where Marketing Research 12th Edition 20 Allocating Sample Size to Strata where Marketing Research 12th Edition 21 End of Chapter Fifteen Marketing Research 12th Edition ...2 Chapter? ?Fifteen Sample Size and Statistical Theory Marketing Research 12th Edition Determining the? ?Sample? ?Size Ad Hoc Methods • • Used when a person knows from experience what? ?sample? ?size? ?to adopt... Sample? ?Characteristics/Statistics (Contd.) Sample mean Marketing Research 12th Edition Sample? ?Reliability • • X will vary from? ?sample? ?to? ?sample As? ?sample? ?size? ?(n) increases, variation in X will decrease standard error of                decreases as the? ?sample? ?size? ?gets ... The effect of increasing? ?sample? ?size? ?on the normal distribution of Marketing Research 12th Edition 12 Interval Estimation • • • • X      varies from? ?sample? ?to? ?sample? ? The difference between the? ?sample? ?mean (  )? ?and? ?the