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Essentials of Marketing Research

Essentials of Marketing Research. Chapter 13: Determining Sample Size. WHAT DO STATISTICS MEAN?. DESCRIPTIVE STATISTICS NUMBER OF PEOPLE TRENDS IN EMPLOYMENT DATA INFERENTIAL STATISTICS MAKE AN INFERENCE ABOUT A POPULATION FROM A SAMPLE. POPULATION PARAMETER VERSUS SAMPLE STATISTICS.

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Essentials of Marketing Research

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  1. Essentials of Marketing Research Chapter 13: Determining Sample Size

  2. WHAT DO STATISTICS MEAN? • DESCRIPTIVE STATISTICS • NUMBER OF PEOPLE • TRENDS IN EMPLOYMENT • DATA • INFERENTIAL STATISTICS • MAKE AN INFERENCE ABOUT A POPULATION FROM A SAMPLE

  3. POPULATION PARAMETERVERSUSSAMPLE STATISTICS

  4. POPULATION PARAMETER • VARIABLES IN A POPULATION • MEASURED CHARACTERISTICS OF A POPULATION • GREEK LOWER-CASE LETTERS AS NOTATION, e.g. m, s, etc.

  5. SAMPLE STATISTICS • VARIABLES IN A SAMPLE • MEASURES COMPUTED FROM SAMPLE DATA • ENGLISH LETTERS FOR NOTATION • e.g., or S

  6. MAKING DATA USABLE • Data must be organized into: • FREQUENCY DISTRIBUTIONS • PROPORTIONS • CENTRAL TENDENCY • MEAN, MEDIAN, MODE • MEASURES OF DISPERSION • range, deviation, standard deviation, variance

  7. Frequency Distribution of Deposits

  8. MEASURES OF CENTRAL TENDENCY • MEAN - ARITHMETIC AVERAGE • MEDIAN - MIDPOINT OF THE DISTRIBUTION • MODE - THE VALUE THAT OCCURS MOST OFTEN

  9. Number of Sales Calls Per Day by Salespersons Number of Salesperson Sales calls Mike 4 Patty 3 Billie 2 Bob 5 John 3 Frank 3 Chuck 1 Samantha 5 26

  10. Sales for Products A and B, Both Average 200 Product A Product B 196 150 198 160 199 176 199 181 200 192 200 200 200 201 201 202 201 213 201 224 202 240 202 261

  11. MEASURES OF DISPERSION • THE RANGE • STANDARD DEVIATION

  12. Low Dispersion Versus High Dispersion 5 4 3 2 1 Low Dispersion Frequency 150 160 170 180 190 200 210 Value on Variable

  13. 5 4 3 2 1 High dispersion Frequency 150 160 170 180 190 200 210 Value on Variable

  14. Standard Deviation 2 (X - X) n - 1 2 S S = =

  15. THE NORMAL DISTRIBUTION • NORMAL CURVE • BELL-SHAPED • ALMOST ALL OF ITS VALUES ARE WITHIN PLUS OR MINUS 3 STANDARD DEVIATIONS • I.Q. IS AN EXAMPLE

  16. NORMAL DISTRIBUTION MEAN

  17. Normal Distribution 13.59% 13.59% 34.13% 34.13% 2.14% 2.14%

  18. An example of the distribution of Intelligence Quotient (IQ) scores 13.59% 13.59% 34.13% 34.13% 2.14% 2.14% 70 85 100 115 130 IQ

  19. STANDARDIZED NORMAL DISTRIBUTION • SYMMETRICAL ABOUT ITS MEAN • MEAN IDENTIFIES HIGHEST POINT • INFINITE NUMBER OF CASES - A CONTINUOUS DISTRIBUTION • AREA UNDER CURVE HAS A PROBABILITY DENSITY = 1.0 • MEAN OF ZERO, STANDARD DEVIATION OF 1

  20. A STANDARDIZED NORMAL CURVE 1 2 -2 -1 0

  21. STANDARDIZED SCORES

  22. POPULATION DISTRIBUTION • SAMPLE DISTRIBUTION • SAMPLING DISTRIBUTION

  23. POPULATION DISTRIBUTION -s s m x

  24. SAMPLE DISTRIBUTION _ C X S

  25. SAMPLING DISTRIBUTION ¾ C µX SX

  26. STANDARD ERROR OF THE MEAN • STANDARD DEVIATION OF THE SAMPLING DISTRIBUTION

  27. CENTRAL LIMIT THEOREM

  28. PARAMETER ESTIMATES • POINT ESTIMATES • CONFIDENCE INTERVAL ESTIMATES

  29. RANDOM SAMPLING ERROR AND SAMPLE SIZE ARE RELATED

  30. SAMPLE SIZE • VARIANCE (STANDARD DEVIATION) • MAGNITUDE OF ERROR • CONFIDENCE LEVEL

  31. Determining Sample SizeRecap

  32. Sample Accuracy • How close the sample’s profile is to the true population’s profile • Sample size is not related to representativeness, • Sample size is related to accuracy

  33. Methods of Determining Sample Size • Compromise between what is theoretically perfect and what is practically feasible. • Remember, the larger the sample size, the more costly the research. • Why sample one more person than necessary?

  34. Methods of Determining Sample Size • Arbitrary • Rule of Thumb (ex. A sample should be at least 5% of the population to be accurate • Not efficient or economical • Conventional • Follows that there is some “convention” or number believed to be the right size • Easy to apply, but can end up with too small or too large of a sample

  35. Methods of Determining Sample Size • Cost Basis • based on budgetary constraints • Statistical Analysis • certain statistical techniques require certain number of respondents • Confidence Interval • theoretically the most correct method

  36. Notion of Variability Little variability Great variability Mean

  37. Notion of Variability • Standard Deviation • approximates the average distance away from the mean for all respondents to a specific question • indicates amount of variability in sample • ex. compare a standard deviation of 500 and 1000, which exhibits more variability?

  38. Measures of Variability • Standard Deviation: indicates the degree of variation or diversity in the values in such as way as to be translatable into a normal curve distribution • Variance = (x-x)2/ (n-1) • With a normal curve, the midpoint (apex) of the curve is also the mean and exactly 50% of the distribution lies on either side of the mean. i

  39. Normal Curve and Standard Deviation

  40. Notion of Sampling Distribution • The sampling distribution refers to what would be found if the researcher could take many, many independent samples • The means for all of the samples should align themselves in a normal bell-shaped curve • Therefore, it is a high probability that any given sample result will be close to but not exactly to the population mean.

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