1 / 22

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

laurel-mckee
Download Presentation

S519: Evaluation of Information Systems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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?

More Related