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# PSCH 343; Statistical Methods In Behavior Science. Week Three Notes PSCH 343

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This 9 page Class Notes was uploaded by Katie on Monday February 1, 2016. The Class Notes belongs to PSCH 343 at University of Illinois at Chicago taught by Liana Peter-Hagene in Spring 2016. Since its upload, it has received 29 views. For similar materials see Statistics Methods In Behavioral Science in Psychlogy at University of Illinois at Chicago.

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Date Created: 02/01/16

Instructor: Liana Peter-Hagene PSCH 343 Statistics Methods In Behavioral Science Week Three Notes Properties of the Normal Distribution (Z-scores) Inferential Statistics -We conduct studies on samples, but we draw conclusions about populations -Can we claim that the differences or relationships we found in our study represent differences or relationships in the “real world”? -Inferential statistics allow us to draw conclusions that go beyond data from a study Examples: 1. Is the enthusiasm for statistics experienced by people in this classroom representative of all UIC students? 2. A survey of 100 jurors shows more men than women voted guilty. Can we say these results represent all men and women jurors – even those who were not in the study? Population V. Sample Instructor: Liana Peter-Hagene -All people who go through CBT for anxiety versus 50 people in a clinical trial Sampling Methods Why Does Sampling Work? -We assume characteristics (data) are normally distributed in a population Normal curve: • Bell-shaped frequency distribution • Symmetrical, unimodal • Specific mathematical properties • Commonly found in nature Normal Distribution Properties -Specific mathematical properties Normal curve: Instructor: Liana Peter-Hagene -34% of scores between mean and 1 SD -14% of scores between 1 SD and 2 SDs -2% of scores beyond 2 SDs -The properties of normal distribution allow us to create standardized scores based on the raw scores, means, and SDs -These standardized scores are very informative and allow us to compare performance on different measures with different scales Z-Scores -A score tells little about how it relates to the whole distribution -David’s score on his stats exam was 45 -Linda’s score was 56 -Comparing a score to the mean tells whether it is above or below average -What if the mean of the test were 50? -David scored below the mean; Linda above the mean -What if the mean of the test were 60? -David and Linda scored below the mean -The SD helps determine how far below/above the mean a score is, compared to other scores M = 50, SD = 2 M = 50, SD = 5 Instructor: Liana Peter-Hagene -Z-scores tell us just that: How many standard deviations a score is below or above the mean • EXAM QUESTION: How can the exact same score get one student an A in one statistics class, and another student a C in another statistics class? Can this happen even if the two classes have the same mean? Z-scores help with comparing two people’s performance -Z-scores can also convert scores on different measure into the same metric so they can be compared. Instructor: Liana Peter-Hagene -Can literally allow us to compare apples and oranges Apple eating contest, apples eaten M = 27, SD = 5 Sam ate 35 apples Orange eating contest, oranges eaten M = 45, SD = 7 Maria ate 47 oranges Who did better – David in the apple eating contest or Alice in the orange eating contest? 1. Calculate Sam and Maria’s Z-scores based on their own distribution means and SDs 2. Compare the Z scores Answer, David did better. Z-Scores Help Compare One Person’s Scores On Two Measures Paula took a survey measuring life satisfaction. On the scale of job satisfaction, which had a mean of 25 and a standard deviation of 12, Sabrina scored 50. On the scale of personal life satisfaction, which had a mean of 55 and a standard deviation of 10, she scored 62. Is Paula more satisfied with her job, or her personal life? What % of scores will you find between – 1 SD and +1 SD in a Z distribution? Instructor: Liana Peter-Hagene Convert these scores to Z-scores and compute the M and SD of the Z-score distribution M = 5, SD = 2 1. Calculate Z scores 2. Calculate mean of Z scores. Is it 0? 3. Calculate deviation scores (Z-M ) –Zwhat do you notice? 4. Square and sum deviation scores 5. Divide by N = 5 6. You have the SD of the Z scores. Is it 1? Why We Use Z-Scores -The sign (+/-) tells us immediately whether a score is above or below the mean -The number tells us immediately how far the score is from the mean, in standard deviation units. We can use this information to assess % of scores above or below it -They are standardized scores that bring different scales to the same metric -Help us compare performance on different measures, for the same person or for different people Z-Scores Help Compare One Person’s Scores On Two Measures Paula took a survey measuring life satisfaction. On the scale of job satisfaction, which had a mean of 25 and a standard deviation of 12, Paula scored 50. On the scale of personal life satisfaction, which had a mean of 55 and a standard deviation of 10, she scored 62. Is Paula more satisfied with her job, or her personal life? Limitations Of Z-Scores 1. Because a person’s score is expressed relative to the group, the same person can have different z- scores when assessed in different samples Instructor: Liana Peter-Hagene If the absolute score is meaningful or of psychological interest, it will be obscured by transforming it to a relative metric. e.g., number of suicides/year in different countries number of correct responses on a math test Normal Distribution Properties And Z-Scores Normal Distribution And Probability -Probability: The expected relative frequency of an outcome; the proportion of successful outcomes to all outcomes Probability Example: Instructor: Liana Peter-Hagene How Does This Relate To The Normal Curve? -A test of knowledge about the environment is normally distributed. M = 50, SD = 10 Question: -If you were to pick a person completely at random, what is the probability you would pick someone with a score: Higher than 60? Instructor: Liana Peter-Hagene Higher than 40? Lower than 40? Normal Distribution Properties And Probability • M = 50, SD = 10 The same information can be expressed with Z-scores: What is the probability of randomly picking a someone with: a Z-score higher than +1? a Z-score higher than -1? a Z-score lower than -1?

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