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Lecture 2

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Department
Psychology
Course
PSYC 2002
Professor
Steven Carroll
Semester
Winter

Description
Lecture 2: frequency distributions What is a frequency distribution? - What does ‘frequency’mean? • The ‘commonness’of occurrence • ‘How often does thing X happen?’ Based on a 1996 study of US college students - Average number of drinks per week by GPA • 3.3 per week =Astudent • 4.8 per week= B student • 6.1 per week= C student • 9 per week= D/F student - This is an ordinal scale, because it is on an alphabetical order What is a frequency distribution? - An organised tabulation showing the number of individuals located in each category on a scale of measurement - Can be either a table (‘news’example) or a graph (drink example) - Frequency distributions always show two things: • The categories that make up the scale • The frequency, or number of individuals, in each category Examples - Timbits consumed during meetings by old office mate (per meeting over the course of 20 weekly meetings) - 8, 6, 4, 1, 5, 8, 9, 6, 5, 8, 5, 6, 2, 4, 8, 10, 6, 2, 5 How to do it - Let’s pick a “data range” • It must be inclusive of all possible scores • (0-10) - Aside: is this data nominal, ordinal, interval, or ratio? • Ratio scale X f 10 1 9 1 8 4 7 0 6 4 5 4 4 3 3 0 2 2 1 1 0 0 Some interesting things to note - The X column is the scale of measurement, NOT the actual scores • The X column is like a ruler • It contains space enough for all possible raw scores in the sample - Add up the ‘f’column • What do you suppose is meant by the following question? f= N • The sum of the frequency = the population size Obtaining X from a frequency distribution table X f 5 2 4 2 3 3 2 1 2 2 1 - Calculate X • How many people got a score of 5? (2) • How many people got a score of 4? (2) • How many people got a score of 3? (3) • How many people got a score of 2? (1) • How many people got a score of 1? (2) • X = 31 (X is multiplied by the frequency) Obtaining X from a table - With frequency distributions like this one: - X = Xf • The sum of X = the sum of X multiplied by f X f Xf 5 2 10 4 2 8 3 3 9 2 1 2 1 2 2 - Xf= 31 Proportions - What is a ‘proportion’? - Find proportion by count number of people who are asleep, and divide it by the number of people in the class. Proportions - What proportion of people earned a score of 5? X f 5 2 4 2 3 3 2 1 1 2 - How many people were measured in this study? • N = f = 10 - What proportion of people earned a score of 5? • .2 - So, what proportion of people earned a score of 5? • Proportion = p = f/N • = 2/10 = .2 Proportions - What is p? (sum of the proportions) (add up all the p) • The sum is 1 - You know you have done everything properly if the SUM OFTHE PIS EQUALTO 1!!! - No proportion can be higher than 1 and no proportion can be lower than 0 X f p = f/N 5 2 2 / 10 = .2 4 2 2 / 10 = .2 3 3 3 / 10 = .3 2 1 1 / 10 = .1 1 2 2 / 10 = .2 Percentages - What percentage of people earned a score of 3? X f 5 2 4 2 3 3 2 1 1 2 - %= p(100) - = (f/N)(100) - = (3/10) (100) - = 300/10 (or .3(100)) - = 30 - 30% means that for every 100 people, 30 have the score in this frequency category Proportions - What is %? X f % = p(100) 5 2 .2(100) = 20 4 2 .2(100) = 20 3 3 .3(100) = 30 2 1 .1(100) = 10 1 2 .2(100) = 20 - The sum of the percentage must be between 0 and 100% Aproblem... - Imagine I had 200 students, all with marks on a test ranging from 50 to 99 - The mark represents ‘number of correct responses’on a test with 99 questions - How many rows would my frequency distribution have if I included all possible mark results? • That is: how many ‘X’categories would there be? • Hint: This is a ratio scale Grouped frequency distribution tables - Sometimes there is just too much variability in the raw data to allow you to have a simple, single-digit x-column ‘ruler’ - So how do instructors cope with this sort of thing? Consider the following - Only 10 categories to manage - It’s easy to see what is happening here X f 95 – 99 17 90 – 94 15 85 – 89 19 80 – 84 11 75 – 79 4 70 – 74 6 65 – 69 7 60 – 64 3 55 – 59 4 50 – 54 14 - W
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