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Chapter 6

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PSYC 1010

Chapter 6- Normal curve, Standardization, z Scores Feb. 11th Normal Curve - Specific bell-shaped curve that is unimodal, symmetric and defined mathematically - Describes the distributions of many characteristics and measures that vary - A distribution resembles a normal curve as the size of the sample approaches the size of the population (if the population is normally distributed) Standardization - Converts individual scores to standard scores for which we know the percentiles (if data is normally distributed) - Converts individual scores from different normal distributions to a shared normal distribution with a known mean, standard deviation and percentiles Z-Scores - The number of standard deviations a particular score is from the mean - Give us the ability to convert any variable to a standard distribution, allowing us to make comparisons among variables - Any score using any measure can be converted to a z distribution (ex. height and weight can be compared using z scores) - Create an oppurtunity to make meaningful comparisons by putting different variables on a common scale 1) Z scores give us a sense of where a score falls in relation to the mean of its population 2) Z scores allow us to compare scores from different distributions 3) Z scores can be transformed into percentiles - Transforming Raw Scores into z Scores:  We need the mean and standard deviation of the population of interest in order to convert a raw score into a z score  Z distribution always has a mean of 0 (if you are exactly at the mean than you are 0 standard deviations from the mean)  Z distribution always has a standard deviation of 1 - Steps in calculating z scores :  Determine the distance of a particular score from the population mean- X-  Express this distance in terms of standard deviations- z= (divide the distance by the standard deviation of the population) - Transforming z Scores into Raw Scores  If we already know the z score, we can reverse our calculations to determine the raw score - Steps in calculating raw score from z score  Mulatiply the z score by the standard deviation of the population  Add the mean of the population to this product  Converting z Scores to Percentiles - Normal curve allows us to convert scores to percentiles- 100% of the population is represented under the bell-shaped curve - The midpoint in a normal curve is the 50th percentile - Z distribution- a normal distribution of standardized scores - Standard normal distribution- a normal distribtion of z scores - The standardized z distribution allows us to : 1) Transform raw scores into standardized scores called z scores 2) Transform z scores back into raw scores 3) Compare z scores to each other- even when the z scores represent raw scores on different scales 4) Transform z scores into percentiles that are more easily
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