chpt 5 - Chapter 5 Learning Outcomes 1 Chapter 5 z-Scores:...

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PSY230 Chapter 5 Notes 1 Chapter 5 z-Scores: Location of Scores in a Distribution Chapter 5 Learning Outcomes • Understand z-score as location in distribution 1 • Transform X value into z-score 2 • Transform z-score into X value 3 • Describe effects of standardizing a distribution 4 • Transform scores to standardized distribution Theory • Descriptive statistics provides meaning to raw data • Up to now we looked at the characteristics of the distribution of scores as a whole • Now we want to look at the value of every score in a distribution with respect to the other scores in the distribution Purpose of z-Scores • Identify and describe location of every score in the distribution • Standardize an entire distribution • Takes different distributions and makes them equivalent and comparable Example: You got a score of 76 on your last statistics test. How did you do with respect to the other students in the class? Hard to tell. Even if you know that the mean is 70, you know that you scored above the mean, but how far? Depends on the standard deviation. In case (a) where σ =3 then you did pretty well. In case (b) where σ = 12, then you really did not do as well. Comparison of Scores • One way to do this is to “standardize” our raw scores • Describe the score with respect to the mean and standard deviation of the distribution • To do this we calculate a z-score • A z-score describes a raw score in terms of the mean and standard deviation of the distribution
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PSY230 Chapter 5 Notes 2 z-Score • A z-score tells the exact location of each X value within a distribution • The SIGN of the z-score tells if the X is above (+) or below ) the mean
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chpt 5 - Chapter 5 Learning Outcomes 1 Chapter 5 z-Scores:...

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