psych stat chpt 5 - I. The Normal Curve A. Important in...

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I. The Normal Curve A. Important in behavioral sciences. 1. Many variables of interest are approximately normally distributed. 2. Statistical inference tests have sampling distributions which become normally distributed as sample size increases. 3. Many statistical inference tests require sampling distributions that are normally distributed. B. Characteristics 1. Symmetrical, bell-shaped curve. 2. Equation: Shows that the curve is asymptotic to the abscissa; i.e., it approaches the X axis and gets closer and closer but never touches it. 3. Area contained under the normal curve: a. Area under the curve represents the percentage of scores contained within the area. b. 34.13% of scores between mean ( μ ) and +1 σ ; 13.59% of area contained between a score equal to μ + 1 σ and a score of μ + 2 σ ; 2.15% of area is between μ + 2 σ and μ + 3 σ ; and 0.13% falls beyond μ + 3 σ . c. Since the curve is symmetrical, the same percentages hold for scores below the mean. II. Standard Scores ( z Scores) A. Converts raw scores into standard scores symbolized as z . 1. Definition. A standard score is a transformed score which designates how many standard deviation units the corresponding raw score is above or below the mean.
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2. Equation: B. Comparisons between different distributions. 1. Allows comparisons even when the units of the distributions are different. 2. Percentile ranks are possible. C. Characteristics of z scores. 1. z scores have the same shape as the set of raw scores from which they were transformed. 2. μ z = 0. The mean of z scores equals zero. 3. σ z = 1.00. The standard deviation of z scores equals 1.00. D. Using z scores. 1. Finding the percentage or frequency (area) corresponding to any raw score. z = ( X - μ ) / σ Use above formula to calculate z score. Then use table to determine the area under the normal curve for the various values of z. 2. Finding the raw score corresponding to a given percentage or frequency of scores in the distribution. X = μ + σz Use above formula substituting the value of z that designates the area under the curve one wishes, and solve for X , the raw score. On a sheet of paper, fill in the blanks with word(s), number(s), or equation(s) that best completes each sentence. Check your answers on the Concept Review Solutions page. The (1) ________ curve is extremely important in the behavioral sciences. Many (2)
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This note was uploaded on 07/19/2009 for the course PSY 3204 taught by Professor Shahramghiasinejad during the Summer '09 term at University of Central Florida.

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psych stat chpt 5 - I. The Normal Curve A. Important in...

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