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S519: Evaluation of Information Systems

S519: Evaluation of Information Systems. Social Statistics Chapter 7: Are your curves normal?. Last week. This week. Why understanding probability is important? What is normal curve How to compute and interpret z scores. What is probability?. The chance of winning a lotter

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S519: Evaluation of Information Systems

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  1. S519: Evaluation of Information Systems Social Statistics Chapter 7: Are your curves normal?

  2. Last week

  3. This week • Why understanding probability is important? • What is normal curve • How to compute and interpret z scores.

  4. What is probability? • The chance of winning a lotter • The chance to get a head on one flip of a coin • Determine the degree of confidence to state a finding

  5. Normal curve Symmetrical: (bell-shaped) mean=median=mode Asymptotic: tail closer to the horizontal axis, but never touch.

  6. Normal distribution • Figure 7.4 – P157 • Almost 100% of the scores fall between (-3SD, +3SD) • Around 34% of the scores fall between (0, 1SD)

  7. Normal distribution

  8. Z score – standard score • If you want to compare individuals in different distributions • Z scores are comparable because they are standardized in units of standard deviations.

  9. Z score • Standard score X: the individual score : the mean S: standard deviation

  10. Z score • Z scores across different distributions are comparable • Z scores represent a distance of z score standard deviation from the mean • Raw score 12.8 (mean=12, SD=2)  z=+0.4 • Raw score 64 (mean=58, SD=15)  z=+0.4 Equal distances from the mean

  11. Excel for z score • Standardize(x, mean, standard deviation) • (a2-average(a2:a11))/STDEV(a2:a11)

  12. What z scores represent? • Raw scores below the mean has negative z scores • Raw scores above the mean has positive z scores • Representing the number of standard deviations from the mean • The more extreme the z score, the further it is from the mean,

  13. What z scores represent? • 84% of all the scores fall below a z score of +1 (why?) • 16% of all the scores fall above a z score of +1 (why?) • This percentage represents the probability of a certain score occurring, or an event happening • If less than 5%, then this event is unlikely to happen

  14. Exercise Lab • In a normal distribution with a mean of 100 and a standard deviation of 10, what is the probability that any one score will be 110 or above? 16% Table B.1 (s-p357)

  15. If z is not integer Lab • Table B.1 (S-P357-358) • Exercise • The probability associated with z=1.38 • 41.62% of all the cases in the distribution fall between mean and 1.38 standard deviation, • About 92% falls below a 1.38 standard deviation • How and why?

  16. Between two z scores • What is the probability to fall between z score of 1.5 and 2.5 • Z=1.5, 43.32% • Z=2.5, 49.38% • So around 6% of the all the cases of the distribution fall between 1.5 and 2.5 standard deviation.

  17. Exercise Lab • What is the percentage for data to fall between 110 and 125 with the distribution of mean=100 and SD=10 • Answer: 15.25%

  18. Excel • NORMSDIST(z) • To compute the probability associated with a particular z score

  19. Exercise Lab • The probability of a particular score occurring between a z score of +1 and a z score of +2.5 15%

  20. What can we do with z score? • Research hypothesis presents a statement of the expected event • We use statistics to evaluate how likely that event is. • Z tests are reserved for populations • T tests are reserved for samples

  21. Exercise Lab • Compute the z scores where mean=50 and the standard deviation =5 • 55 • 50 • 60 • 57.5 • 46

  22. Exercise Lab • Based on a distribution of scores with mean=75 and the standard deviation=6.38 • What is the probability of a score falling between a raw score of 70 and 80? • What is the probability of a score falling above a raw score of 80? • What is the probability of a score falling between a raw score of 81 and 83? • What is the probability of a score falling below a raw score of 63?

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