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School of Psychology Dpt. Experimental Psychology Design and Data Analysis in Psychology I English group (A) Salvador Chacón Moscoso Susana Sanduvete Chaves Milagrosa Sánchez Martín Lesson 4 Normal distribution 1. Normal distribution The normal distribution is represented as the limit of a bar chart (increasing indefinitely the number of bars). 6 5 4 20 18 16 14 12 3 2 10 8 6 1 4 2 0 0 3 1. Normal distribution: characteristics 1 0 - + This distribution depends on 2 parameters : and 4 1. Normal distribution: characteristics 2 Mo = Mdn = The normal curve has a single maximum. 5 1. Normal distribution: characteristics 3 1 1 The normal curve has 2 inflection points 6 1. Normal distribution: characteristics 4 The normal curve is asymptotic to the abscissa. 7 1. Normal distribution: characteristics 5 As = 0 It is a symmetric distribution (As = 0) 8 1. Normal distribution: characteristics 6 Kr = 0 It is a mesokurtic distribution (Kr = 0). 9 1. Normal distribution The parameter gives the center of the distribution and the parameter the variability , verifying the following relations: , 10 1. Normal distribution -3 -2 - 68 % 2 3 95,5 % 99,7 % 11 1. Normal distribution A B C A B C 12 2. Standard normal distribution It exists infinite normal distributions, each one with their means and standard deviations. Solution: to convert raw scores into standard scores. It implies to convert the normal distribution into a standardized normal distribution (with mean 0 and standard deviation 1). 13 2. Standard normal distribution: use of table, example 1 What standard distance does represent the 33.4% of data immediately over the mean? 14 2. Standard normal distribution: use of table, example 1 Z=0.97 15 2. Standard normal distribution: use of table, example 2 In a normal distribution with mean 100 and standard deviation 15, which proportion do the values between 70 and 130 have? 16 2. Standard normal distribution: use of table, example 2 Xi X Z S 70 100 30 Z1 2 15 15 130 100 30 Z1 2 15 15 17 2. Standard normal distribution: use of table, example 2 p=0.4772x2=0.9544 18 2. Standard normal distribution: use of table, example 3 In a normal distribution with mean 100 and standard deviation 15, what raw score does define the highest 10% of data? 19 2. Standard normal distribution: use of table, example 3 40% Z=1.28 10% 20 2. Standard normal distribution: use of table, example 3 Xi X Z S X 100 1.28 15 1.28 x15 X 100 19.2 X 100 19.2 100 X X 119.2 21