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Lecture1 Definitions & Scales

# Lecture1 Definitions & Scales - Welcome to PSYC 11...

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Unformatted text preview: Welcome to PSYC 11! Spring 2010 Ryne Sherman Introduction Introduction to Statistics Basic Concepts & Definitions What to expect from this course Why do we even have to take this course? I thought I was a psychology major? 2 Statistical Thinking is Important! "In 1938 in World Brain (Methuen & Co.), English writer H. G. Wells predicted that for an educated citizenship in a modern democracy, statistical thinking would be as indispensable as reading and writing. At the beginning of the 21st century, nearly everyone living in an industrial society has been taught reading and writing but not statistical thinking--how to understand information about risks and uncertainties in our technological world. That lack of understanding is shared by many physicians, journalists, and politicians who, as a result, spread misconceptions to the public." Gigerenzer, 2009, Scientific American 3 Example Approximately 1% of women get breast cancer. The probability that a mammogram will show a positive result if someone has breast cancer is 80%. The probability that the mammogram will show a positive result if someone does not have breast cancer is 10%. What is the probability a woman with a positive result has breast cancer? 4 Answer 7.5% 5 Let's Make a Deal 3 doors, one with a car and 2 with goats You pick a door The host opens one door that has a goat behind it, and offers you the option to switch to the remaining door. Should you switch or keep your door? Answer: You should switch Or does it even matter? 6 What are Statistics? Statistics is the science of using data to gain insight Two Major Types Scientific Method Descriptive Statistics Inferential Statistics Summarizes data Used to draw conclusions about unmeasured populations based on evidence from a sample 7 Populations? Samples? Population Sample All of the members or elements of a specific group A subset of the population 8 Populations & Samples 9 Examples of Populations & Samples Population Sample All students in college Baseball players All cats in Riverside UCR students Anaheim Angels Cats living in your house/apartment 10 Defining More Terms Parameter Statistic A numerical or nominal characteristic of population that is constant (so long as the population does not change). A numerical or nominal characteristic of sample, often used to estimate the population parameter. 11 Examples of Parameters & Statistics Mean Standard Deviation Variance Correlation Proportion Name Parameters 2 Statistics M s or s2 or 2 r p 12 Mathematical Symbols & Operators * ** or ^ or xbar ^ or hat or sqrt or NE > < Summation Product Power Mean Frequency Predicted Division Square root Not equal Approximately Greater than Less than 13 Variables and Observations Variable Something that exists in more than one form or more than one amount e.g. Height, Gender, Happiness, Extraversion, Amount of Pain Reliever Observational Units The "things" being measured e.g. People, Rats, Trees, Rooms 14 Weight People on a roller coaster Loudness of people screaming on a roller coaster Rats Rat racing times Typing speed Number of computer viruses Pipe Pipe length 15 Are these variables or observational units? Weight variable People on a roller coaster observational unit Loudness of people screaming on a roller coaster variable Rats observational unit Rat racing times variable Typing speed variable Number of computer viruses variable Pipe observational unit Pipe length variable 16 Are these variables or observational units? Two Types of Variables Quantitative Variables that have continuous scores that tell you about the "degree" or "amount" of something e.g. Height, Weight, Time Qualitative Do not have a continuous nature e.g. Gender, Ethnicity, Political Party 17 Are these quantitative or qualitative? Gallons of Gasoline Flowers in a garden Seconds required to run 100M Psychological Disorders Millions of dollars Tons of grain 18 Are these quantitative or qualitative? Gallons of Gasoline quantitative Flowers in a garden qualitative Seconds required to run 100M quantitative Psychological Disorders qualitative Millions of dollars quantitative Tons of grain quantitative 19 Scales of Measurement Nominal Ordinal Different names mean different things Numbers have no quantitative value Different numbers mean different things. Order matters (higher = more, lower = less) 20 Scales of Measurement Interval Ratio Different numbers mean different things Order matters (higher = more, lower = less) Equal intervals between the numbers Different numbers mean different things Order matters (higher = more, lower = less) Equal intervals between the numbers Absolute zero exists (0 means "none") 21 Examples of Nominal Measurement Gender (male, female) Job Type (custodian, teacher, astronaut) Pets (dog, cat, elephant) Music Genre (classical, rock, jazz) Soda Type (coke, pepsi, 7up) Course Type (psychology, biology, history) 22 Examples of Ordinal Measurement Rankings e.g. college basketball, teachers How do you feel from 1100? Finish positions in the olympics e.g. Gold, Silver, Bronze 23 Examples of Interval Measurement Temperature (F, C) SAT & GRE Scores Time e.g. seconds, dates, years, etc 24 Gas mileage Examples of Ratio Measurement Number of homeruns for a baseball player Number of people in class today Temperature (K) 25 Solving the Cancer Problem Approximately 1% of women get breast cancer. The probability that a mammogram will show a positive result if someone has breast cancer is 80%. The probability that the mammogram will show a positive result if someone does not have breast cancer is 10%. What is the probability a woman with a positive result has breast cancer? 26 Walkthrough part 1 "Approximately 1% of women get breast cancer." Imagine that 1000 women were tested How many would have breast cancer out of 1000 women? 10 Therefore, 10 have breast cancer and 990 do not. 27 Diagram Have breast cancer 10 1000 Do not have breast cancer 990 28 Walkthrough part 2 The probability that a mammogram will show a positive result if someone has breast cancer is 80%. So 80% of the 10 people who actually have breast cancer, will test positive. 80% of 10 is 8. 29 Diagram Have breast cancer 10 Test Positive 1000 Do not have breast cancer Test Negative 2 990 8 30 Walkthrough part 3 The probability that the mammogram will show a positive result if someone does not have breast cancer is 10%. Out of the 990 who do not have breast cancer, 10% will test positive. 10% of 990 is 99. 31 Diagram Have breast cancer 10 Test Positive 1000 Do not have breast cancer Test Negative 2 Test Positive 990 Test Negative 891 8 99 Out of 1000 women, 107 test positive (99 + 8) for breast cancer, but only 7.5% actually have breast cancer (8 / 107)! 32 ...
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