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# Week 5 Notes - Psychology 211 Psychology 211

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This 8 page Class Notes was uploaded by Kennedy Patterson on Sunday February 8, 2015. The Class Notes belongs to Psychology 211 at University of Alabama - Tuscaloosa taught by Andre Souza in Spring2015. Since its upload, it has received 592 views. For similar materials see Psychology 211-003 Elem Statistical Methods in Psychlogy at University of Alabama - Tuscaloosa.

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Date Created: 02/08/15

Psychology 211 Chapter 6 Normal Distribution Week 5 22152615 O O O Variable can take at least 2 different values Random values Each possible value has a probability that it occurs A variable is discrete if the possible outcomes are a set of separate values A variable is continuous if the possible outcomes are an infinite continuum Probability distribution lists all possible outcomes and probability Example how many dates does one go on before first kiss y possible answers Py probability y PM One 0 0 01 Three 1 s 1 03 Sixty 2 s 2 60 TwentyThree 3 s 3 23 Twelve 4 s 0 1 2 3 4 5 4 12 One 5 Y 5 01 o How long it takes a girl to get rid of an annoying guy 0 1 minute high probability 132145 minutes low probability 339487 minutes low probability Possible outcomes are continuous The probability of occurrence of any value between 2 values is very small A probability distribution for a continuous variable provides probabilities for intervals of numbers Pylt 10 or Pygt25 Smooth continuous curve Area uncler curve gives probability of numbers between those intervals Psychology 211 Week 5 Chapter 6 Normal Distribution 22152615 0 Some probability distributions are important because they approximate the distance of variables in the real world 0 Others are important because of their uses in stat inference Normal Probability Distribution is important for both 0 Symmetric bellshaped the mean u and Standard Deviation is O39 u6 o2 024681012 0 34 u 6 039 Probability of a number above 6 is 50 below 6 is 50 Probability of a number between 6 amp 8 is 34 34 73 a 2 Probability of a number above 73 is 50 below 73 is 50 Probability of a number 67 69 71 73 75 77 79 between 73 amp 75 is 34 73 34 0 4 Probability of a number above 73 is 50 below 73 is 50 Probability of a number between 73 amp 77 is 34 If the deviation changes the 61 65 69 73 77 81 85 probability of the intervals stays the same Psychology 211 Chapter 6 Normal Distribution Week 5 22152615 0 False can be ANY number 0 Standard Deviation 1 ALWAYS 0 Mean 0 ALWAYS 1 9 1 600 Two standard deviations one above and one below the mean 0 2 9 2 95 Two above and two below the mean 3 9 3 997 Three above and three below the mean L b 3 2 1 0 1 2 33 O 9 3 5000 3 O 5000 0 The whole area under the curve is 1 0 To know any probability for any normal distribution we need to compare it to the standard normal distribution 0 This will transform the values in the original normal distribution into values in the standard normal distribution 0 Values in the standard normal distribution are called zscores 0 Because we know that the standard normal distribution has a mean of zero and a standard deviation of one we can convert any value of X into a zscore by ZxJ O39 140 150 160 170 180 190 200 l y L 3 2 1 o 1 2 33 p X 180 180170 1 standard deviation p 170 10 0 10 160170 1 standard deviation 10 Psychology 211 Chapter 6 Normal Distribution 140 150 160 170 180 190 200 V z negative p Left 4i 170 a 10 Taler than 170 50 Height of 140 or 200 not likely 160180 very likely Right tx q zpositive Week 5 22152615 167170 3 standard 10 deviations below the mean 3 6179 on ztable 6179 9 Probability of someone taller than 167cm Probability of 13 amp below use Leftznegative probability of 13 amp above use Rightznegative probability of 13 amp below Use Leftzpositive k V probability of 13 amp above use Rightzpositive The average grad in the class is 73 a girl got a 65 and the standard deviation is 13 What is the variance Mean 73 O O O O 0 Standard deviations 13 Her grade 65 Z Variance 132 169 000 gtltN IIIIq 83 2 127 183 a a 273 x 7 273 549 x 2199 9 22 Psychology 21 1 Week 5 Chapter 6 Normal Distribution 22152615 Probability of higher than 320 o 28732 2 x u 32028732 o a 1243 0 1243 0 x 320 z 263 263 on ztable 9957 9957 9 9957 9 1oo9957 43 28732 320 probability of being higher than 320 What about between 28732 and 320 9975 50 4957 probability of being between 28732 and 320 4 28732 320 39 what is the top 5 z x39 55 O 55 87 o 039 87 O z 0 100 5 9500 95 5 95 on ztable 165 v I v 165 x 56 X 87 x 703 What about the bottom 5 z x 56 500 87 Make 165 negative 39 x 56 165 x 56 87 x 417 Psychology 211 Week 5 Chapter 6 Normal Distribution 22152615 o The sampling distribution of SAT scores among graduating high school students can often be approximated by a normal distribution assuming the whole population of observations could be obtained 0 The normal distribution is asymptotic to the horizontal axis 0 The sampling distribution of intelligence scores among residents of a city can often be approximated by a normal distribution assuming the whole population of observations could be obtained 0 The normal distribution is symmetrical 0 Most statistical procedures you will use in the fundamentals of behavioral statistics require an assumption that a variable has a normal distribution 0 The normal distribution is bellshaped o The sampling distribution of shoe sizes among all second graders can often be approximated by a normal distribution assuming the whole population of observations could be obtained 0 Why would you want to transform a set of raw scores into a set of z scores To be able to describe the location of a raw score in the distribution of raw scores To make it possible to compare scores from two different distributions fill in the following table Hb Level gmdl Location Description Z Score Patient 1 118 2 below mean 2 Patient 2 138 12 above mean 05 Patient 3 136 14 above mean 025 Patient 4 110 3 below mean 3 Patient 5 126 1 below mean 1 0 Mean 134 gmdl 0 Standard Deviation 08 gmdl Psychology 211 Week 5 Chapter 6 Normal Distribution 22152615 o The following are the scores for some students tests scores 0 Mean 202 0 Standard Deviation 382 The teacher wants to identify those Student Test Score Z Score students who may need extra A 205 008 challenge or extra help At his first cut B 199 oos he decides to look at students who C 266 L68 have 2 scores above z200 or below D 222 052 Z200 E 188 037 F 172 079 For 2 200 test score 278 G 184 O47 For 2 200 test score 126 H 215 034 0 Mean 146 0 Standard Deviation 35 413 3413 13 9 L3 22150 15 013 013 3 2 1 O 1 2 3 41 76 111 146 181 216 251 o What is the score 3 standard deviations above the mean Lower limit 251 o What is the score 3 standard deviations above the mean Upper limit 41 o The probability that a student will have a score between 41 and 251 is 9974 100 13 13 9974 0 A score of 181 is one standard deviation above the mean As a result the percentage of students with scores below 181 is 8413 100 13 215 1359 8413 0 You can infer that 9772 of the students have scores above 76 Psychology 211 Chapter 6 Normal Distribution Week 5 22152615 O O O T Scores set of scores with mean of 50 and standard deviation of 10 Z Score number of standard deviations that a score is above or below the mean Linear Transformation transformation involving the addition subtraction multiplication or division of or by a constant Standard Normal Distribution normal distribution with a mean equal to 0 and a standard deviation equal to 1 it is denoted as N01 Ordinate vertical Y axis Standardization process of computing standard scores Standard Scores scores with a mean of 0 and a standard deviation of 1

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