PSY 201: Statistics in Psychology, Lecture notes of Psychology

Download PSY 201: Statistics in Psychology and more Lecture notes Psychology in PDF only on Docsity! PSY 201: Statistics in Psychology Lecture 08 Normal distribution Business decisions. Greg Francis Purdue University Fall 2019 Greg Francis (Purdue University) PSY 201: Statistics in Psychology Fall 2019 1 / 26 NORMAL DISTRIBUTIONS when the distribution is a normal distribution, we can describe the distribution by just specifying I Mean: X I Standard deviation: s I Noting it is a normal distribution that’s all we need! That’s part of our goal: describe distributions Greg Francis (Purdue University) PSY 201: Statistics in Psychology Fall 2019 2 / 26 USE same as all other distributions I identify key aspects of the data I percentiles I percentile rank I proportion of scores within a range I ... make it easier to interpret data significance! Greg Francis (Purdue University) PSY 201: Statistics in Psychology Fall 2019 3 / 26 AREA UNDER CURVE proportional to the frequency of scores within the designated endpoints suppose you want to know the proportion of scores between the mean and another score (z-score) -4 -2 0 2 4 Score 0 0.1 0.2 0.3 0.4 Greg Francis (Purdue University) PSY 201: Statistics in Psychology Fall 2019 4 / 26 AREA UNDER CURVE solving for the area requires calculus and numerical analysis (ack!) fortunately, we can also use computers our text provides Greg Francis (Purdue University) PSY 201: Statistics in Psychology Fall 2019 5 / 26 CALCULATOR how would you find the area between z = 0.3 and z = 2.4? -4 -2 0 2 4 Score 0 0.1 0.2 0.3 0.4 Greg Francis (Purdue University) PSY 201: Statistics in Psychology Fall 2019 6 / 26 CALCULATOR how would you find the area below z = 1.4? -4 -2 0 2 4 Score 0 0.1 0.2 0.3 0.4 Greg Francis (Purdue University) PSY 201: Statistics in Psychology Fall 2019 7 / 26 PROPORTIONS suppose you have 250 scores from a test that are normally distributed you want to know how many scores are between 1.0 standard deviations below the mean and 1.5 standard deviations above the mean two steps 1 calculate the area under the standard normal between z = 1.0 and z = 1.5. 2 convert the area under the curve to number of scores Greg Francis (Purdue University) PSY 201: Statistics in Psychology Fall 2019 8 / 26 PROPORTIONS -4 -2 0 2 4 Score 0 0.1 0.2 0.3 0.4 We find that 77.45% of the scores lie between one standard deviation below the mean and 1.5 standard deviations above the mean so how many scores are in that range? multiply the total number of scores (250) with the percent in the range (decimal form) (0.7745)⇥ (250) = 193.625 ⇡ 194 Greg Francis (Purdue University) PSY 201: Statistics in Psychology Fall 2019 9 / 26 PROPORTIONS suppose you have 250 scores from a test that are normally distributed you want to know how many scores are below 0.5 standard deviations above the mean, and how many scores are beyond 2.5 standard deviations above the mean. two steps 1 calculate the area under the standard normal below z = 0.5 and above z = 2.5. 2 convert the area under the curve to number of scores Greg Francis (Purdue University) PSY 201: Statistics in Psychology Fall 2019 10 / 26 PROPORTIONS -4 -2 0 2 4 Score 0 0.1 0.2 0.3 0.4 We find that 69.77% of the scores lie below 0.5 standard deviation above the mean or beyond 2.5 standard deviations above the mean so how many scores are in that range? multiply the total number of scores (250) with the percent in the range (decimal form) (0.6997)⇥ (250) = 174.925 ⇡ 175 Greg Francis (Purdue University) PSY 201: Statistics in Psychology Fall 2019 11 / 26 PERCENTILES X th percentile is score for which X percent of scores fall at or below 50th percentile is the median (and the mean!) -4 -2 0 2 4 Score 0 0.1 0.2 0.3 0.4 Greg Francis (Purdue University) PSY 201: Statistics in Psychology Fall 2019 12 / 26