Notes

Outline

Statistics 5 Probability, Z-Scores, Sampling Sherril M. Stone, Ph.D. Department of Family Medicine OSU-College of Osteopathic Medicine

Probability Probability - fraction or proportion of an outcome in a population Example 1 - A, B, C, or D = 6 A's, 3 B's, 10 C's and 9 D's Probability of A =                  # of A’s               =   p(A) =   6                                # of possible outcomes                    28 Example 2 - probability of tossing coin and getting heads =  1  = .50           2

Random Sampling Random Sampling – equal chance of being selected Constant probability –sampling with replacement Example 1 – draw a jack of clubs =    1                                                             52 Example 2 – draw a jack of hearts =   1                                                                    51 (if jack of clubs not returned to deck)

Normal Distribution Symmetrical distribution – aka Bell-shaped curve Largest frequency of data occurring at the middle Mean = Median = Mode Area under the curve = 1.00           1.00 μ The area between the mean and one SD above the mean = .3413 Unit Normal Distribution - normal distribution based on z-scores

Z-Scores Standardizes your data distribution Convert raw scores into z-scores If X = 10, SD = 2, X = 11.7 z =  11.7 - 10  = 1.7 = .85               2            2 Use z Table to find area under bell curve 1st column is z-score 2nd column is proportion between mean and z 3rd column is proportion in the tail beyond z

Example 1 X = 10, SD = 2, X = 11.7  SD = 1 .5000          .3023        .1977     ___________________________________________ -3           -2            -1           0           1          2           3     z-scores .85 X = 11.7 z = .85 p(X > 11.7) = .1977

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Sample Probability Sample Means (X) should pile around population mean (m) should produce a normal distribution curve larger the sample n, the closer to m lower sample n, more widely scattered scores   1    2 3      4 5 Sample Xs

Central Limit Theorem CLT for any m and s, distribution of X and SD approaches normal distribution as n approaches infinity N > 30 – distribution is almost normal Standard error – measures difference between X and m Rule of large numbers as samples sizes increase, the error decreases n = 1, large error (n = 1, error = SD) SE  =    s                       Ön

Other Descriptive Measures Standard Deviation measures standard distance between X and m (X - m) measure of variability of population scores Standard Error measures standard distance between X and m measure of variability of sample scores measures reliability (similar scores each time) Sampling error – discrepancy between the X and m

Reporting SE

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