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Statistical Insights: Determining Sample Size and Data Interpretation

Explore the essentials of statistics in marketing research, including sample size determination, descriptive and inferential statistics, and analyzing trends using mean, median, mode, and measures of dispersion. Learn how to make data usable and draw meaningful inferences from population parameters to sample statistics.

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Statistical Insights: Determining Sample Size and Data Interpretation

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  1. Essentials of Marketing ResearchWilliam G. Zikmund Chapter 13: Determining Sample Size

  2. What does Statistics Mean? • Descriptive statistics • Number of people • Trends in employment • Data • Inferential statistics • Make an inference about a population from a sample

  3. Population Parameter Versus Sample Statistics

  4. Population Parameter • Variables in a population • Measured characteristics of a population • Greek lower-case letters as notation

  5. Sample Statistics • Variables in a sample • Measures computed from data • English letters for notation

  6. Making Data Usable • Frequency distributions • Proportions • Central tendency • Mean • Median • Mode • Measures of dispersion

  7. Frequency Distribution of Deposits Frequency (number of people making deposits Amount in each range) less than $3,000 499 $3,000 - $4,999 530 $5,000 - $9,999 562 $10,000 - $14,999 718 $15,000 or more 811 3,120

  8. Percentage Distribution of Amounts of Deposits Amount Percent less than $3,000 16 $3,000 - $4,999 17 $5,000 - $9,999 18 $10,000 - $14,999 23 $15,000 or more 26 100

  9. Probability Distribution of Amounts of Deposits Amount Probability less than $3,000 .16 $3,000 - $4,999 .17 $5,000 - $9,999 .18 $10,000 - $14,999 .23 $15,000 or more .26 1.00

  10. Measures of Central Tendency • Mean - arithmetic average • µ, Population; , sample • Median - midpoint of the distribution • Mode - the value that occurs most often

  11. Population Mean

  12. Sample Mean

  13. 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

  14. 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

  15. Measures of Dispersion • The range • Standard deviation

  16. Measures of Dispersion or Spread • Range • Mean absolute deviation • Variance • Standard deviation

  17. The Range as a Measure of Spread • The range is the distance between the smallest and the largest value in the set. • Range = largest value – smallest value

  18. Deviation Scores • The differences between each observation value and the mean:

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

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

  21. AverageDeviation

  22. Mean Squared Deviation

  23. The Variance

  24. Variance

  25. Variance • The variance is given in squared units • The standard deviation is the square root of variance:

  26. Sample Standard Deviation

  27. Population Standard Deviation

  28. Sample Standard Deviation

  29. Sample Standard Deviation

  30. 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

  31. Normal Distribution MEAN

  32. Normal Distribution 13.59% 13.59% 34.13% 34.13% 2.14% 2.14%

  33. Normal Curve: IQ Example 70 145 85 115 100

  34. Standardized Normal Distribution • Symetrical 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

  35. Standard Normal Curve • The curve is bell-shaped or symmetrical • About 68% of the observations will fall within 1 standard deviation of the mean • About 95% of the observations will fall within approximately 2 (1.96) standard deviations of the mean • Almost all of the observations will fall within 3 standard deviations of the mean

  36. A Standardized Normal Curve z 1 2 -2 -1 0

  37. The Standardized Normal is the Distribution of Z –z +z

  38. Standardized Scores

  39. Standardized Values • Used to compare an individual value to the population mean in units of the standard deviation

  40. Linear Transformation of Any Normal Variable Into a Standardized Normal Variable s s m X m Sometimes the scale is stretched Sometimes the scale is shrunk -2 -1 0 1 2

  41. Population distribution • Sample distribution • Sampling distribution

  42. Population Distribution m -s s x

  43. Sample Distribution _ C X S

  44. Sampling Distribution

  45. Standard Error of the Mean • Standard deviation of the sampling distribution

  46. Central Limit Theorem

  47. Standard Error of the Mean

  48. Parameter Estimates • Point estimates • Confidence interval estimates

  49. Confidence Interval

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