Basic Quantitative Methods in the Social Sciences

(AKA Intro Stats)02-250-01Lecture 1

Course Outline Highlights!

Instructor:Jeremy B. Frank, M.A.Office:Chrysler Hall South,Room 173-2

OfficeHours:Wednesdays, 2:00 PM 4:00 PMTelephone:253-3000 ext. 2216E-mail:stats250@jfrank.sent.com Class Times:Mondays and Wednesdays, 4:00 - 6:50 PMClass Location:Education Building, 1101

Course Outline Highlights!

Course Description: Introduction to measurement of variables, organization and description of numerical data, testing hypotheses, inference, and interpretation of findings in the Social Sciences. Topics include: Descriptive statistics, normal distribution, probability, sampling, hypothesis testing, t-tests, correlation, and chi-square tests.Objectives: By the end of the course, students should have a basic understanding of how to interpret numerical data using direct calculation.

Anti-RequisitesStudents cannot receive credit for more than one introductory statistics course. The anti-requisites for this course are 65-205 (formerly called 65-253), 65-250, 65-251, 73-105, 73-205, and 85-222. If you have received credit for any of these courses, you are not eligible to receive credit for 02-250. If you are unsure, contact the Registrars office to clarify.

Required TextbookHowell, D. C. (1999). Fundamental Statistics for the Behavioral Sciences. 4th Ed. Pacific Grove, CA: Duxbury Press.Recommended TextbookKranzler, J. H. (2003). Statistics for the terrified. 3rd Ed. Upper Saddle River, NJ: Pearson Education Inc.

Course WebpageThis course has a comprehensive webpage. You MUST visit this page frequently (at least once a week), as it is updated regularly with important information.The web page is where you will download lecture slides, read announcements, the course outline, evaluation details, and see your grades.The website address is: http://www.uwindsor.ca/stats250

Lecture NotesApproximately one week before each lecture, Powerpoint slides will be available on the web. You should download these slides, and print them out to bring to each class. If you do not have them, you will NOT have time to copy the slides during the lecture. You should also bring your lecture slides from the preceding class to each class.

Course Outline Highlights!Important Dates:May 12First class - 4:00 PM sharp!May 12 May 19 Participant pool signup!May 16 Last day to registerMay 19Victoria Day, No Class June 4 Midterm Examination June 6 Last day to voluntarily dropJune 16 Assignment due in class at 4:00 PM Sharp!June 18 Last classJune 25 Final Examination - 7 - 10pm

Course Outline Highlights!Written Assignment: There will be ONE written assignment worth 25% (due AT THE BEGINNING OF CLASS on June 16) consisting of problems that will resemble problems on the midterm and final exams. Assignments received after 4:00 PM on the due date will NOT BE ACCEPTED. You must show all relevant calculations to receive full marks on these assignments. If you cannot attend class on June 16, hand the assignment in to J. Franks mailbox in the Psychology Department. Please remember to have your assignment dated and time stamped (i.e., by 4:00 pm on June 16) and signed by one of the departmental secretaries.

Course Outline HighlightsAll tests are open-book format (i.e., you may bring your textbook, with any written notes in the book, but no other outside material, e.g., photocopied sheets of paper)You should also bring pens, pencils, and a calculator to the Mid-term and Final exams

Course Outline HighlightsCalculators capable of storing information entered by the user are not allowed and sharing of calculators or other materials (i.e., textbook) is not permitted under any circumstances so dont forget your textbook for the exams!You must bring your U of W student ID Card to the exams

Course Outline Highlights!Grading Scheme:One written assignment = 25%1 Mid-term test = 30% of final gradeFinal Examination = 45% of final gradeTOTAL: 100%

Course Outline Highlights!You may earn up to two bonus points in this classYou can earn these in two ways:Participation in researchCompletion of a bonus assignment (described in the course outline)

Sign Up for Participant Pool!!see Psychology research first hand!earn up to 2 bonus pointsHOW????sign up on the web (takes less than 5 minutes):www.uwindsor.ca/psychology/signupor access through psych homepageYou MUST sign up by 9:00 am May 19 to be included

Course Outline HighlightsAttendance: Regular attendance is strongly advisedStated differently, this is NOT a course where you will be able to keep up just by reading the book and doing the exercisesIt is your responsibility to obtain notes for any missed lectures from a classmate

Course Outline HighlightsMissed Tests: Students MUST take the midterm and final exams during the scheduled timesIf a scheduled test is missed, the student will receive a grade of zero for that test except in cases of medical/family emergency or extreme circumstances (these do not include travel, special occasions, or job-related scheduling conflicts), in which case supporting documents (e.g., physicians note) must be submitted to one of the instructors within one week following the missed test

Course Outline HighlightsNote: The final exam cannot be re-written at another timeIf it is missed for a valid reason, the student must apply for aegrotat standing through the Registrars Office

Course Outline HighlightsThe University Calendar explains the regulations regarding plagiarism and other academic dishonestyIt is your responsibility to familiarize yourself with these regulations

Hints for StatsDates for topics covered are approximate (see the Course Outline)Keep up with the work this is a subject which builds upon itself dont get left behind

More Hints for StatsAttend class! It is very easy to be left behind if you miss classesYou are responsible for all class material covered and assigned readings. If you have to miss class, you are responsible for getting the notes from another student

HELP CLINICTammy Whitlock, a senior graduate student will be available on a drop-by first-come-first-serve basis for extra help in the Statistics Help Clinic. The clinic is located in Chrysler Hall North, room G134. You can call the help clinic at 253-3000 ext. 2393 as well during the help clinic hours. The Help Clinic hours are TBA, and will be posted here as soon as I know them. Tammy is available for the following:working on extra practice problems getting help with what you don't understand reviewing your assignment and exams clarification of grades

IMPORTANT NOTEI am available during my office hours (as noted above) on a first-come-first-serve basis. Due to the high enrollment in the class, any questions or issues about course content or exams should be directed to the Help Clinic, and not to myself. For instance, if you want help understanding t-tests or if you wish to review your mid-term exams, you should go to the Help Clinic. If you miss an exam or if you have a problem that cannot be dealt with at the Help Clinic, you should come to my office hours.

More Hints for StatsWork in groups on practice problems

IMPORTANT NOTE: This class is both theoretical and applied know how to calculate formulae and why (i.e., test selection well explain this in the coming weeks)

Final HintFor many students, you have put this class off for as long as possibleTry not to get stressed out! This class is as easy or hard as you make it!If you put the time in, you will be fine

Finally, Some Math Review (see Appendix A)Unless otherwise indicated, the order of mathematical operations is:Work within parentheses firstSquare or find the square rootMultiply or divideAdd or subtract

Order of Operations Summary PEMDAS Please Excuse My Delayed Assignment SirParenthesesExponentsMultiply and DivideAdd and Subtract

More Math ReviewPerform mathematical operations:Contained within a set of parentheses () first, to find the quantity (2+4)2 = (6)2 = 36Also perform operations within the square root sign first, then take the square root of the quantityPerform operations above or below the dividing line of a fraction prior to dividing

More Math ReviewIn rounding off decimals, if the first digit is equal to or greater than 5 (e.g., .7), round upIn rounding off decimals, if the first digit is less than 5 (e.g., .3), round downRULE: While working on a problem, round your calculations to 4 decimal places. When reporting your final answer, round your calculation to 2 decimal places (unless otherwise directed).

So Lets Get Started!DefinitionsStatisticsPopulations and SamplesParameters and StatisticsVariablesOperational Definitions

DefinitionsStatistics (as a discipline): The body of rules and procedures for describing and evaluating numerical informationA set of procedures or rules for a) reducing large masses of data to manageable portions and b) allowing us to draw conclusions from those data

More StatisticsThe subject matter of Statistics is usually divided into 2 broad groups of techniques and procedures:Descriptive StatisticsInferential Statistics

Descriptive StatisticsDescriptive Statistics: The techniques for organizing, summarizing, representing and extracting information from numerical dataThese are used to describe data, e.g.: AverageStandard Deviation

Inferential StatisticsInferential Statistics: The rules and procedures for inferring the characteristics of populations from sample data (inferring parameters from statistics well explain these later)These are used to make inferences about a population, e.g., t-testCorrelation

Definitions: PopulationsPopulation: Any defined group of objects, organisms, or events that youre interested inA population must be defined in enough detail to determine whether to include a given individual or event A population contains all members of the defined group

Example 1: Population of U of W Statistics StudentsThis population would be described as all students enrolled in 02-250 during the 2003 calendar year (so a student enrolled in 115 Introductory Psychology would not be part of this population)

Example 2: Population of Canadian TeenagersThis population would be described as all teenagers in Canada between the ages of 13 and 18Note: A population is the entire group you are interested in

More Definitions!Sample: Any subset of the population, usually meant to represent the populationIf the population was defined as all students enrolled in 02-250 during all three 2003 calendar year semesters (that is, Fall, Winter, Intersession 2003), then this class would be a sample of the populationPopulation = three 02-250 classesSample = this 02-250 class (a subset of the population)

Samples cont.If a population was defined as all teenagers in Canada between the ages of 13 and 18 then the teenagers between 13 and 18 in Windsor would be a sample of this populationPopulation: All teens in CanadaSample: All teens in Windsor (a subset of the population)

Relationship Between Population and Sample

Samples vs. PopulationsWhile populations are usually large (in number of events or persons), size is not the defining characteristic of populationsIf you are only interested in the events or organisms which have been directly observed (which you have data for), then those events (or organisms) are considered the population, regardless of size

Samples vs. Populations cont.On the other hand, if you wish to generalize the findings from an observed group to events (or organisms) which have not been directly observed, then the actually observed events (or organisms) are a sample (of a population)

Samples vs. Populations cont. E.g., You measure the height of 115 students who you randomly approach in the CAW Centre. If you wish to simply state the average height of these 115 people, then they are a population If, however, you want to estimate the average height of all U of W students, then these 115 students are a sample of the population of all U of W students

Sample vs. Population: You Decide!Researcher X wants to know how tall the average University hockey player is. She measures and records the heights of 30 University of Windsor hockey players. These 30 athletes are.?Researcher Y wants to know the average income of Windsor Liberal party members. She obtains financial data from all Liberal party members in Windsor. These data are from a ..?

Populations vs Samples cont.For us to draw accurate conclusions about a population, our sample must be representative. In a representative sample the characteristics of the sample accurately reflect the characteristics of the population

Populations vs Samples cont.To obtain a representative sample, we select a random sampleA random sample allows for all possible scores in the population to have the same chances of being included

Random SamplingIn order to obtain a random sample, we must use a random sampling technique, where every data point has an equal chance of being selected e.g.:Coin tossRandom numbers table

Definitions cont.Parameter: A term which describes or summarizes a population E.g., the average age (mean) of all students enrolled in 02-250 during the 2003 calendar year (the population)A parameter does one thing: it describes a population

Definitions cont.Statistic: A term which describes or summarizes a sampleE.g., the average age (mean) of students in this class (as a sample of the population of all students enrolled in 02-250 during the 2003 calendar year)A statistic does two things:1) it describes a sample and2) it estimates a parameter

Statistics vs. ParametersIt is often impractical to directly observe and measure every person or event in a population, so we must estimate population characteristics (parameters) using data obtained from samples (statistics)

Statistics vs. Parameters cont.Collecting the age of all students enrolled in 02-250 during the 2003 calendar year would be very time consuming, so we can take a sample of those students (this class), collect their age data, and calculate the average (mean) ageThis average age would then be an estimate (statistic) of the average age of all students who have taken 02-250 in the 2003 calendar year.

Statistics vs Parameters cont. ParameterStatistic

Definitions: DataData: Any recordable observationsData which has not been analyzed is called raw data

Definitions: VariablesVariable: Any observable property of objects, organisms, or events which might be of interestUsed to refer to whatever event we are interested in observing or knowing more about (e.g., age, height, weight, GPA, gender)

Variables and Data

VariablesQualitative Variable: A variable in which individuals (or elements) differ because of possession of some characteristic - they differ in kind rather than amount (note: Howell calls this Categorical Data)This is a classification variable, e.g., gender, eye colour, ethnicity, type of personalityE.g., gender has 2 kinds male and female

More VariablesQuantitative Variable: A variable whose measurement results in a numerical value which reflects the amount (or quantity) of the characteristic (note: Howell calls this Measurement Data)e.g., peoples height or weight, reaction time (something you can measure the amount of)

Quantitative Variable: DiscreteDiscrete Variable: A variable which can only assume certain valuesDiscrete variable data are usually obtained by counting (e.g., number of students in this class)You can have 10 students in the class, but you cant have 10.7 students in the class (the number of students cannot be described with a decimal).

Quantitative Variable: ContinuousContinuous Variable: A variable which can assume any value between minimum and maximum limitsContinuous variable data are usually obtained by measuring (e.g., someones height or weight, or the probability of contracting a disease)

What Type of Variable am I ?Researcher A wants to know if Political Science profs take the bridge or tunnel more often when crossing the border. This is a qualitative variable because they are classified as taking either the bridge or the tunnel (notice how they are classifying the profs method of crossing the border).Mother Goose wants to know how far the average goose flies south in November.This is a quantitative variable, as she is measuring the distance traveled. It is also a continuous variable.

Operational DefinitionsOperational Definition: An operational definition of a variable specifies the measure takenIf a researcher wants to measure success, a definition for success is needed:

Operational Definitions cont. Success could mean:amount of money madejob status level of education completed or grade point averagenumber of races won

More Operational DefinitionsThere are 2 fundamental concepts to an operational definition:They indicate clearly how the data was obtained (specifies the measure taken; e.g., amount of money made)2. They are arbitrary devices to represent the variable of interest (e.g., does amount of money made adequately encompass the meaning of the concept success?)