Basic Quantitative Methods in the Social Sciences (AKA Intro Stats)

Basic Quantitative Basic Quantitative Methods in the Social Methods in the Social

SciencesSciences

(AKA Intro Stats)(AKA Intro Stats)02-250-0102-250-01

Lecture 1Lecture 1

Course Outline Highlights!Course Outline Highlights!

Instructor: Jeremy B. Frank, M.A.

Office:Chrysler Hall South, Room 173-2

OfficeHours:

Wednesdays, 2:00 PM – 4:00 PM

Telephone: 253-3000 ext. 2216

E-mail: [email protected]

Class Times:

Mondays and Wednesdays, 4:00 - 6:50 PM

Class Location:

Education Building, 1101


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-RequisitesAnti-Requisites

• Students cannot receive credit for Students cannot receive credit for more than one introductory statistics more than one introductory statistics course. course.

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

Required TextbookRequired Textbook

• Howell, D. C. (1999). Fundamental Statistics for the Behavioral Sciences. 4th Ed. Pacific Grove, CA: Duxbury Press.

Recommended TextbookRecommended Textbook

• Kranzler, J. H. (2003). Statistics for Kranzler, J. H. (2003). Statistics for the terrified. 3the terrified. 3rdrd Ed. Upper Saddle Ed. Upper Saddle River, NJ: Pearson Education Inc.River, NJ: Pearson Education Inc.

Course WebpageCourse Webpage

• This course has a comprehensive webpage. This course has a comprehensive webpage. You MUST visit this page frequently (at You MUST visit this page frequently (at least once a week), as it is updated least once a week), as it is updated regularly with important information.regularly with important information.

• The web page is where you will download The web page is where you will download lecture slides, read announcements, the lecture slides, read announcements, the course outline, evaluation details, and see course outline, evaluation details, and see your grades.your grades.The website address is: The website address is:

http://www.uwindsor.ca/stats250http://www.uwindsor.ca/stats250

http://www.uwindsor.ca/stats250

Lecture NotesLecture Notes

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


Important Dates:Important Dates:May 12May 12 First class - 4:00 PM sharp!First class - 4:00 PM sharp!

May 12 – May 19 May 12 – May 19 Participant pool signup!Participant pool signup!

May 16 May 16 Last day to registerLast day to register

May 19May 19 Victoria Day, No ClassVictoria Day, No Class

June 4 June 4 Midterm Examination Midterm Examination

June 6 June 6 Last day to voluntarily dropLast day to voluntarily drop

June 16 June 16 Assignment due in class at 4:00 PM Assignment due in class at 4:00 PM Sharp!Sharp!

June 18 June 18 Last classLast class

June 25 June 25 Final Examination - 7 - 10pmFinal Examination - 7 - 10pm


Written AssignmentWritten Assignment: :

• There will be ONE written assignment worth 25% There will be ONE written assignment worth 25% (due AT THE BEGINNING OF CLASS on June 16) (due AT THE BEGINNING OF CLASS on June 16) consisting of problems that will resemble problems consisting of problems that will resemble problems on the midterm and final exams. Assignments on the midterm and final exams. Assignments received after 4:00 PM on the due date will NOT BE received after 4:00 PM on the due date will NOT BE ACCEPTED. You must show all relevant calculations to ACCEPTED. You must show all relevant calculations to receive full marks on these assignments. receive full marks on these assignments.

• If you cannot attend class on June 16, hand the If you cannot attend class on June 16, hand the assignment in to J. Frank’s mailbox in the Psychology assignment in to J. Frank’s mailbox in the Psychology Department. Please remember to have your Department. Please remember to have your assignment dated and time stamped (i.e., by 4:00 pm assignment dated and time stamped (i.e., by 4:00 pm on June 16) and signed by one of the departmental on June 16) and signed by one of the departmental secretaries. secretaries.

Course Outline HighlightsCourse Outline Highlights

• All tests are open-bookopen-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 calculatorcalculator to the Mid-term and Final exams


• Calculators capable of storing information entered by the user are not allowed and sharing of calculators or other materials (i.e., textbooktextbook) is not permitted under any circumstances so don’t forget your textbook for the

exams!

• You must bring your U of W student ID Card to the exams


Grading Scheme:Grading Scheme:

• One written assignment = 25%

• 1 Mid-term test = 30% of final grade

• Final Examination = 45% of final grade

• TOTAL: 100%


• You may earn up to two bonus You may earn up to two bonus points in this classpoints in this class

• You can earn these in two ways:You can earn these in two ways:Participation in researchParticipation in research

Completion of a bonus assignment Completion of a bonus assignment (described in the course outline)(described in the course outline)

Sign Up for Participant Sign Up for Participant Pool!!Pool!!

• see Psychology research first hand!see Psychology research first hand!

• earn up to earn up to 2 bonus points2 bonus points

• HOW????HOW????

• sign up on the web (takes less than 5 minutes):sign up on the web (takes less than 5 minutes):

• www.uwindsor.ca/psychology/signupwww.uwindsor.ca/psychology/signup

• or access through psych homepageor access through psych homepage

• You You MUSTMUST sign up by 9:00 am May 19 to be sign up by 9:00 am May 19 to be includedincluded


• Attendance: Regular attendance is strongly advised

• Stated differently, this is NOT a course where you will be able to keep up just by reading the book and doing the exercises

• It is your responsibility to obtain notes for any missed lectures from a classmate

Course Outline HighlightsCourse Outline Highlights• Missed Tests: Students MUST take the midterm

and final exams during the scheduled times

• If 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., physician’s note) must be submitted to one of the instructors within one weekone week following the missed test


• Note: The final exam cannot be re-written at another time

• If it is missed for a validvalid reason, the student must apply for aegrotat standing through the Registrar’s Office


• The University Calendar explains the regulations regarding plagiarism and other academic dishonesty

• It is your responsibility to familiarize yourself with these regulations

Hints for StatsHints for Stats

• Dates for topics covered are Dates for topics covered are approximate (see the Course approximate (see the Course Outline)Outline)

• Keep up with the work – this is a Keep up with the work – this is a subject which builds upon itself – subject which builds upon itself – don’t get left behinddon’t get left behind

More Hints for StatsMore Hints for Stats

• Attend class! It is very easy to be left Attend class! It is very easy to be left behind if you miss classesbehind if you miss classes

• You are responsible for all class You are responsible for all class material covered and assigned material covered and assigned readings. readings.

• If you have to miss class, you are If you have to miss class, you are responsible for getting the notes responsible for getting the notes from from another studentanother student

HELP CLINICHELP CLINIC• Tammy Whitlock, a senior graduate student will be Tammy Whitlock, a senior graduate student will be

available on a drop-by first-come-first-serve basis available on a drop-by first-come-first-serve basis for extra help in the Statistics Help Clinic. The for extra help in the Statistics Help Clinic. The clinic is located in Chrysler Hall North, room G134. clinic is located in Chrysler Hall North, room G134. You can call the help clinic at 253-3000 ext. 2393 You can call the help clinic at 253-3000 ext. 2393 as well during the help clinic hours. The Help Clinic as well during the help clinic hours. The Help Clinic hours are TBA, and will be posted here as soon as hours are TBA, and will be posted here as soon as I know them. Tammy is available for the following:I know them. Tammy is available for the following:

• working on extra practice problems working on extra practice problems

• getting help with what you don't understand getting help with what you don't understand

• reviewing your assignment and exams reviewing your assignment and exams

• clarification of grades clarification of grades

IMPORTANT NOTEIMPORTANT NOTE• I am available during my office hours (as I am available during my office hours (as

noted above) on a first-come-first-serve noted above) on a first-come-first-serve basis. Due to the high enrollment in the basis. Due to the high enrollment in the class, any questions or issues about course class, any questions or issues about course content or exams content or exams should be directed to should be directed to the Help Clinic, and not to myself.the Help Clinic, and not to myself.

• For instance, if you want help understanding For instance, if you want help understanding t-tests or if you wish to review your mid-t-tests or if you wish to review your mid-term exams, you should go to the Help term exams, you should go to the Help Clinic. If you miss an exam or if you have a Clinic. If you miss an exam or if you have a problem that cannot be dealt with at the problem that cannot be dealt with at the Help Clinic, you should come to my office Help Clinic, you should come to my office hours. hours.

More Hints for StatsMore Hints for Stats

• Work in groups on practice problemsWork in groups on practice problems

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

Final HintFinal Hint

• For many students, you have put this For many students, you have put this class off for as long as possibleclass off for as long as possible

• Try not to get stressed out! This class Try not to get stressed out! This class is as easy or hard as you make it!is as easy or hard as you make it!

• If you put the time in, you will be fine If you put the time in, you will be fine

Finally, Some Math Review Finally, Some Math Review (see Appendix A)(see Appendix A)

Unless otherwise indicated, the order Unless otherwise indicated, the order of mathematical operations is:of mathematical operations is:Work within parentheses firstWork within parentheses first

Square or find the square rootSquare or find the square root

Multiply or divideMultiply or divide

Add or subtractAdd or subtract

Order of Operations Order of Operations Summary Summary

• PEMDAS – Please Excuse My PEMDAS – Please Excuse My Delayed Assignment SirDelayed Assignment SirParenthesesParentheses

ExponentsExponents

Multiply and DivideMultiply and Divide

Add and SubtractAdd and Subtract

More Math ReviewMore Math Review

• Perform mathematical operations:Perform mathematical operations:Contained within a set of parentheses () Contained within a set of parentheses ()

first, to find the quantity (2+4)first, to find the quantity (2+4)2 2 = (6)= (6)2 2 = 36= 36Also perform operations within the square Also perform operations within the square

root sign first, then take the square root of root sign first, then take the square root of the quantitythe quantity

Perform operations above or below the Perform operations above or below the dividing line of a fraction prior to dividingdividing line of a fraction prior to dividing

More Math ReviewMore Math Review

• In rounding off decimals, if the first digit is In rounding off decimals, if the first digit is equal to or greater than 5 (e.g., .7), round equal to or greater than 5 (e.g., .7), round upup

• In rounding off decimals, if the first digit is In rounding off decimals, if the first digit is less than 5 (e.g., .3), round downless than 5 (e.g., .3), round down

• RULE: While working on a problem, round RULE: While working on a problem, round your calculations to 4 decimal places. your calculations to 4 decimal places. When reporting your final answer, round When reporting your final answer, round your calculation to 2 decimal places your calculation to 2 decimal places (unless otherwise directed).(unless otherwise directed).

So Let’s Get Started!So Let’s Get Started!

• DefinitionsDefinitionsStatisticsStatisticsPopulations and SamplesPopulations and SamplesParameters and StatisticsParameters and Statistics

• VariablesVariables

• Operational DefinitionsOperational Definitions

DefinitionsDefinitions

• Statistics (as a discipline)Statistics (as a discipline):: The body of rules and procedures for describing and evaluating numerical information

• A 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 StatisticsMore Statistics

• The subject matter of Statistics is usually divided into 2 broad groups of techniques and procedures:Descriptive StatisticsDescriptive Statistics

Inferential StatisticsInferential Statistics

Descriptive StatisticsDescriptive Statistics

• Descriptive StatisticsDescriptive Statistics:: The techniques for organizing, summarizing, representing and extracting information from numerical data

• These are used to describe data, e.g.: AverageStandard Deviation

Inferential StatisticsInferential Statistics

• Inferential StatisticsInferential Statistics:: The rules and procedures for inferring the characteristics of populations from sample data (inferring parameters from statistics – we’ll explain these later)

• These are used to make inferences about a population, e.g., t-test

Correlation

Definitions: PopulationsDefinitions: Populations

• PopulationPopulation:: Any defined group of objects, organisms, or events that you’re interested in

• A 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 Example 1: Population of U of W Statistics Studentsof W Statistics Students

• This 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 Example 2: Population of Canadian TeenagersCanadian Teenagers

• This population would be described as all teenagers in Canada between the ages of 13 and 18

• Note: A population is the entire group you are interested in

More Definitions!More Definitions!

• SampleSample:: Any subset of the population, usually meant to represent the population

• If 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 classthis class would be a sample of the populationPopulation = three 02-250 classes

Sample = this 02-250 class (a subset of the population)

Samples cont.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 Relationship Between Population and SamplePopulation and Sample

Samples vs. PopulationsSamples vs. Populations

• While populations are usually large (in number of events or persons), size is not the defining characteristic of populations

• If 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 Samples vs. Populations cont.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 Samples vs. Populations cont.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 thesethese 115 people, then they are a population

• If, however, you want to estimate the average height of all U of W studentsall U of W students, then these 115 students are a sample of the population of all U of W students

Sample vs. Population: You Sample vs. Population: You Decide!Decide!

• Researcher X wants to know how tall the Researcher X wants to know how tall the average University hockey player is. She average University hockey player is. She measures and records the heights of 30 measures and records the heights of 30 University of Windsor hockey players. University of Windsor hockey players. These 30 athletes are….?These 30 athletes are….?

• Researcher Y wants to know the average Researcher Y wants to know the average income of Windsor Liberal party members. income of Windsor Liberal party members. She obtains financial data from all Liberal She obtains financial data from all Liberal party members in Windsor. These data are party members in Windsor. These data are from a …..?from a …..?

Populations vs Samples Populations vs Samples cont.cont.

• For us to draw accurate conclusions For us to draw accurate conclusions about a population, our sample about a population, our sample must be representative. In a must be representative. In a representative samplerepresentative sample the the characteristics of the sample characteristics of the sample accurately reflect the characteristics accurately reflect the characteristics of the populationof the population

Populations vs Samples Populations vs Samples cont.cont.

• To obtain a representative sample, To obtain a representative sample, we select a random samplewe select a random sample

• A A random samplerandom sample allows for all allows for all possible scores in the population to possible scores in the population to have the same chances of being have the same chances of being includedincluded

Random SamplingRandom Sampling

• In order to obtain a random sample, In order to obtain a random sample, we must use a we must use a random samplingrandom sampling techniquetechnique, where every data point , where every data point has an equal chance of being has an equal chance of being selected e.g.:selected e.g.:Coin tossCoin toss

Random numbers tableRandom numbers table

Definitions cont.Definitions cont.

• ParameterParameter:: A term which describes or summarizes a population

• E.g., the average ageaverage 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.Definitions cont.

• Statistic:Statistic: A term which describes or summarizes a sample

• E.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 and

2) it estimates a parameter

Statistics vs. ParametersStatistics vs. Parameters

• It 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 Statistics vs. Parameters cont.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) age

• This 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 Statistics vs Parameters cont.cont.

ParameterParameterStatisticStatistic

Definitions: DataDefinitions: Data

• DataData:: Any recordable observations

• Data which has not been analyzed is called raw dataraw data

Definitions: VariablesDefinitions: Variables

• VariableVariable:: Any observable property of objects, organisms, or events which might be of interest

• Used to refer to whatever event we are interested in observing or knowing more about (e.g., age, height, weight, GPA, gender…)

Variables and DataVariables and Data

VariablesVariables• Qualitative VariableQualitative 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 classificationclassification variable, e.g., gender, eye colour, ethnicity, type of personality

• E.g., gender has 2 kinds – male and female

More VariablesMore Variables

• Quantitative VariableQuantitative 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., people’s height or weight, reaction time (something you can measure the amount of)

Quantitative Variable: Quantitative Variable: DiscreteDiscrete

• Discrete VariableDiscrete Variable:: A variable which can only assume certain values

• Discrete 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 can’t have 10.7 students in the class (the number of students cannot be described with a decimal).

Quantitative Variable: Quantitative Variable: ContinuousContinuous

• Continuous VariableContinuous Variable:: A variable which can assume any value between minimum and maximum limits

• Continuous variable data are usually obtained by measuring (e.g., someone’s height or weight, or the probability of contracting a disease)

What Type of Variable am What Type of Variable am I ?I ?

• Researcher A wants to know if Political Researcher A wants to know if Political Science profs take the bridge or tunnel more Science profs take the bridge or tunnel more often when crossing the border. often when crossing the border. This is a qualitative variable because they are This is a qualitative variable because they are

classified as taking either the bridge or the classified as taking either the bridge or the tunnel (notice how they are tunnel (notice how they are classifyingclassifying the profs the profs method of crossing the border).method of crossing the border).

• Mother Goose wants to know how far the Mother Goose wants to know how far the average goose flies south in November.average goose flies south in November.This is a quantitative variable, as she is This is a quantitative variable, as she is measuringmeasuring the distance traveled. It is also a the distance traveled. It is also a continuous variable. continuous variable.

Operational DefinitionsOperational Definitions

• Operational DefinitionOperational Definition:: An operational definition of a variable specifies the measure taken

• If a researcher wants to measure “success”, a definition for “success” is needed:

Operational Definitions Operational Definitions cont.cont.

• Success could mean:•amount of money made

•job status

•level of education completed or grade point average

•number of races won

More Operational DefinitionsMore Operational Definitions

• There are 2 fundamental concepts to an operational definition:

1. 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”?)

Basic Quantitative Methods in the Social Sciences (AKA Intro Stats)

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