Data Analysis STA2300 - Transtutors · Data Analysis STA2300 Professor Shahjahan Khan, PhD School...

Data Analysis STA2300

Professor Shahjahan Khan, PhD

School of Agricultural, Computational and Environmental SciencesFaculty of Health, Engineering and Sciences

University of Southern Queensland

Lecture 1

Professor Shahjahan Khan, PhD Lecture 1

To get started. . .MaterialsOverview

Appendix A: Mathematics Review

Part I

Introduction

Welcome to STA2300

Warm Welcome to STA2300 Data Analysis CourseMy name is Shahjahan Khan

The Tajmahal built by Mughal Emperor ShahjahanWorked and lived in 9 different countriesExaminer of the course for this semesterI hope to work with you through out the semester

General Announcements

Announcements

Tutorials start this week:Bring textbook; Studybook (containing tutorialquestions); calculator

Use StudyDesk via UConnect regularlyCheck the News Forum at least once a week!Check the Social/Topics Forum at least once a week!Check your Umail regularly

Announcements

AssessmentThree assignments and 2 hour exam are compulsory

Three assignments (5%, 20% and 25%)Online Assignment 1 (i.e., Quiz 1) due Friday of nextweek! (Complete online through StudyDesk by 11.55pm)Assignments 2 & 3 submit as pdf document viaStudyDesk by 11.55 pm of due dateExam (50% total weighting):

Part A is 20 multiple choice questionsPart B is 30 marks of short answer questions

Passing grade: (1) at least 50% of total weightedmarks and (2) at least 40% of the 50% (ie 20/50) inthe final exam.

What you need to have access toWhat we provide

Materials you needDe Veaux, Velleman & Bock 4th edition (3rd ed is also OK)

Introductory Material (on StudyDesk )Study Book (on StudyDesk )Text book: Intro Stats by De Veaux, Velleman & Bock(4th edition) with ActivStats CD (Or Stats: data andmodels, 4th Global Edn)Calculator (with STAT mode)Access to the SPSS (also called IMB SPSS) software

Available for purchase from the bookshop orbuy online 6 month’s licence from Hearne Scientifichttps://www.hearne.software/Software/SPSS-Grad-Packs-for-Students-by-IBM/EditionsAvailable in all USQ PC labs

We provide:We provide them—but you must use them to get the benefit

Lectures, tutorials to on-campus studentsSPSS Exercises (on StudyDesk )Face-to-face, StudyDesk forums, telephone, ande-mail assistance via UAskLTS support (The Learning Centre)MEET-UP program (see StudyDesk for details)Feedback on assignmentsWeb resources: discussion forums etc. onStudyDesk

LTS supportThe Learning Centre

The Learning Centre is located near the bookshopSuccess in Mathematics for Statistics Online TutorialsCalculator bookletsDrop-in and phone-in mathematics supportAcademic Skills WorkshopsMore details from postings and links on theStudyDesk

Why do this course?

You are doing it because, it isan essential skill of your degreedecided by your faculty lecturers/professors for youa skill expected by good employersessential for any research studies (eg honours)providing statistical literacy for everyday life

Why do this course?

Why Statistics?

Contributions of Statistics?

Statistical disciplines

Statistics at the top

The basics of what we will learn

We will learnthe language of statistics (all Modules)how to summarise data (verbally, graphically andnumerically) (Modules 1 to 4)how to collect data (and how not to) (Module 5)how to generalise our observations to the wider world(Modules 6 to 11)

OutlineGeneral AnnouncementsWhat you need to have access toWhat we provide

1 Appendix A: Mathematics Review

What is Appendix A of the Study Book?

Appendix A is the assumed mathematics knowledgefor the course.It provides some of the essential mathematical skillsnecessary for Data AnalysisReturn to this chapter if your mathematics skills needrefreshing during the courseContact The Learning Centre for help with thismaterials support.It is not directly examinable, and not supported bythe course teaching team.

§1.1 What is/are Statistics?§1.2 About data

§1.3 Displaying categorical data

Part II

Module 1: Exploring andunderstanding data

Outline

2 §1.1 What is/are Statistics?Why do Data Analysis?

3 §1.2 About dataSome languageTypes of data

4 §1.3 Displaying categorical dataBar chartsPie chartsContingency tables

§1.3 Displaying categorical dataWhy do Data Analysis?

Outline

Why learn Data Analysis?SB §1.1

Data are generated by repeated observationData analysis finds the information in dataInformation is used to learn about the world and helpdecision making

Who needs to know statistics?

If your job is: Statistics helps you:Collecting data know how much data you need

get max. information at min. costcommunicate with your analyst

Analysis extract informationmake correct decisions

Making decisions justify your decisionsmake informed decisionscommunicate with your analyst

Why do Data Analysis?

Statistics used correctly can assist good decisionmakingStatistics used incorrectly can misinform‘Figures don’t lie, but liars can figure’‘Figures fool, when fools figure’Your choice: user or victim!

Use, Abuse and Misuse of Statistics

On 5 October 2012 the US Bureau of Labor Statisticsreported unemployment rate dropped from 8.1% to 7.8%.

Use, Abuse and Misuse of Statistics

In November 2015, the republican Presidential Candidatein the USA, Donald Trump tweeted

“Whites killed by blacks - 81%”,citing “Crime Statistics Bureau of San Francisco”.

The US fact-checking site Politifact found that this“Bureau” did not exist, and thetrue figure is around 15%.

When confronted, Trump shrugged and said,“Am I going to check every statistic?”

Some languageTypes of data

Outline

Some languageSB §1.2

Cases are the individuals or objects being describedA variable is any characteristic of a caseData are the observed values of the variablesA data set contains the observed values of thevariables for a group of individuals

ExampleGender is a variable; ‘Male’ and ‘Female’ are theobserved values of the variable (ie data)

A typical data setThe data here is loaded in SPSS

Understanding the SPSS window

This is a dataset: it contains the observed values ofvariables for a group of individuals (cases)Variables are in the columnsCases are in the rowsThe variable names are: gender; height; faculty; etc.

An example of a variable in the data set

An example of a case in the data set

Types of data: Quantitative dataKnowing the type of data means we can select the correct techniques later

Quantitative data: (Scale in SPSS) take on numericalvalues for which mathematical operations (like +, ÷)make senseHas unit of measurement.

ExampleQuantitative variables in the SPSS data: height (in cm)

Quantitative data: (Scale in SPSS) take on numericalvalues for which mathematical operations (like +, ÷)make senseHas unit of measurement.

ExampleQuantitative variables in the SPSS data: height (in cm)

Quantitative data generallyhas units

ExampleHeight is quantitative. You mustindicate if it is measured in inches,metres, or cm.

Quantitative data generallyhas units

ExampleHeight is quantitative. You mustindicate if it is measured in inches,metres, or cm.

Types of data: Categorical data

Categorical variable: (Nominal in SPSS) values definecategories

ExampleCategorical variables in the SPSS data: gender (values‘Male’ and ‘Female’), faculty (of enrolment)

Categorical variable: (Nominal in SPSS) values definecategories

ExampleCategorical variables in the SPSS data: gender (values‘Male’ and ‘Female’), faculty (of enrolment)

Categorical (Nominal in SPSS) data is usually codedfor use in SPSS

ExampleConsider gender: Males may be coded as 1; females as2. Or females coded as 0; males as 1.

Careful: Categorical data may look quantitative if thecategories are given numerical codes

Types of data in the dataset

The variable ‘faculty’

The variable ‘Faculty’ iscategorical, with levelsdefined numericallyWe can see thesedefinitions using‘Variable Views’

Types of data: Ordinal data

Data is ordinal if it is between categorical andquantitative

ExampleResponses such as ‘Disagree’, ‘Neutral’ and ‘Agree’ areordinal: they can be placed in a natural order, but are notquantitative

Example‘How often do you smoke? Never; Sometimes; Often;Regularly’. This variable is also ordinal.

Understanding dataSB §1.2

Who: information about the casesWhat, and in what units: The meaning of thevariablesWhenWhereWhyHow

Understanding data: The SPSS data setThere’s no point having data if you don’t understand it

Who: students attending the first STA2300 lectureWhat: various: height (in cm), gender, etc.When: Semester, YearWhere: L209 (ie. on-campus students only whocame)Why: To generate some data for use in lecturesHow: A quick paper survey

Bar chartsPie chartsContingency tables

Outline

Distributions and graphsSB §1.3

The distribution of a variable tells us what values thevariable takes and how often it takes them

ExampleThe distribution of gender tells us how many Males andFemales are in the dataset.

Different graphs are used for different reasons anddifferent data types

Different graphs for displaying one variable

Categorical variables Quantitative variables

Bar chart Stem-and-leaf plotPie chart Histogram

Boxplot

Which of these options we use depends on the data. . .

Different graphs for displaying one variable

Categorical variables Quantitative variables

Bar chart Stem-and-leaf plotPie chart Histogram

Boxplot

Which of these options we use depends on the data. . .

One categorical variable: bar chart

Categorical variable on the horizontal axisCount or percentage on the vertical axisTitles and labels essential!Bars don’t touchCan order bars alphabetically, from largest tosmallest, etc.Don’t add an artificial third dimension

Example barchartSPSS Exercise 5 explains how to draw barcharts

The bars could beordered:

alphabeticallyby sizeby my preferenceor any way I like

since the variable graphedis categorical

Get the little things right!We look for these things when we mark assignments

Variable names onaxesTitleScale on axesGaps between bars

The good and bad

Good things about bar charts:used for any categorical variablesimple to construct

Bad things about barcharts:not so easy to see what fraction of the whole group aparticular category is

The good and bad

Good things about bar charts:used for any categorical variablesimple to construct

Bad things about barcharts:not so easy to see what fraction of the whole group aparticular category is

One categorical variable: pie chart

Circle divided into areas of the appropriate sizePie charts need all categories (must add to 100%)

Not all categorical data can be graphed with a piechart

Don’t add an artificial third dimension

The good and bad

Good things about pie charts:used for showing parts of a whole

Bad things about pie charts:Pie charts are hard for the brain to understandHard to compare the sizes of pie segmentsAdding an artificial third dimension makes them verymisleadingCan’t always use a pie chart

The good and bad

Good things about pie charts:used for showing parts of a whole

Bad things about pie charts:Pie charts are hard for the brain to understandHard to compare the sizes of pie segmentsAdding an artificial third dimension makes them verymisleadingCan’t always use a pie chart

An example pie chartSPSS Exercise 5 explains how to draw barcharts

This is one place wherethe pie chart can bedrawn for the dataNotice it is hard tocompare the sizes of thesegments

A bad pie chart

The third dimension isunnecessaryThe third dimension ismisleadingEven harder tocompare the sizes ofthe segments

Two categorical vars: Contingency tables

When we look at two categorical variables, use acontingency tableContingency tables are also called two-way tables, orcross-tabulations (cross-tabs)Can examine contingency tables in many ways:

joint distributionsmarginal distributionsconditional distributions

Consider an exampleSPSS Exercise 4 explains how to construct contingency tables

ExampleAll 722 members of a senior class at the Uni. of Illinoiswere asked which business major they had chosen. Hereare the data of those who responded:

Female Male TotalAccounting 68 56 124Administration 91 40 131Economics 5 6 11Finance 61 59 120Total 225 161 386

Understanding the table

There are two categorical variables:1 Gender of the student (with values ‘Female’ and

‘Male’)2 The chosen business major (with values ‘Accounting’,

‘Administration’, etc.)

This is a 4 × 2 table: four rows and two columns(don’t count the Total row or column)

Questions

What proportion of students are male Finance majors?

Questions

What proportion of students are female Economicsmajors?

Questions

What proportion of students are female?

Questions

What proportion of Accounting majors are male?

The joint distribution

Female Male Total

Accounting 68386 × 100 56

386 × 100

Administration 91386 × 100 40

386 × 100

Economics 5386 × 100 6

386 × 100

Finance 61386 × 100 59

386 × 100

Total 100%

Female Male Total

Accounting 17.6% 14.5%

Administration 23.6% 10.4%

Economics 1.3% 1.6%

Finance 15.8% 15.3%

Total 100%

15.3% of students are male finance majors.1.3% of students are female economics majors.

Female Male Total

Economics 1.3% 1.6%

Finance 15.8% 15.3%

Total 100%

Female Male Total

Economics 1.3% 1.6%

Finance 15.8% 15.3%

Total 100%

The marginal distribution by rows

Female Male Total

Accounting 124386 × 100

Administration 131386 × 100

Economics 11386 × 100

Finance 120386 × 100

Total 100%

Female Male Total

Accounting 32.1%

Administration 33.9%

Economics 2.8%

Finance 31.1%

Total 100%

33.9% of students are administration majors

Female Male Total

Accounting 32.1%

Administration 33.9%

Economics 2.8%

Finance 31.1%

Total 100%

33.9% of students are administration majors

Can draw a bar chart of major

Accnt. Admin. Econ. Fin.

Bar plot of choice of majors (n=386)

The marginal distribution by column

Female Male Total

Accounting

Administration

Economics

Finance

Total 225386 × 100 161

386 × 100 100%

Female Male Total

Accounting

Administration

Economics

Finance

Total 58.3% 41.7% 100%

58.3% of students are female

Female Male Total

Accounting

Administration

Economics

Finance

Total 58.3% 41.7% 100%

58.3% of students are female

Conditional distributions

What proportion of the Accounting majors are males?

Of the 124 Accounting majors,

Of the 124 Accounting majors, 56 are male.

The answer is56

124× 100 = 45.2%

The conditional distribution by rows

Female Male Total

124 × 100 100%

131 × 100 100%

11 × 100 100%

Finance 61120 × 100 59

120 × 100 100%

Female Male Total

Accounting 54.8% 45.2% 100%

Administration 69.5% 30.5% 100%

Economics 45.5% 54.5% 100%

Finance 50.8% 49.2% 100%

Female Male Total

Accounting 54.8% 45.2% 100%

Economics 45.5% 54.5% 100%

Finance 50.8% 49.2% 100%

The male–female ratio is similar for all majors, exceptAdmin.

Female Male Total

Accounting 54.8% 45.2% 100%

Economics 45.5% 54.5% 100%

Finance 50.8% 49.2% 100%

45.2% of accounting majors are male.

Female Male Total

Accounting 54.8% 45.2% 100%

Economics 45.5% 54.5% 100%

Finance 50.8% 49.2% 100%

45.2% of accounting majors are male.

Female Male Total

Accounting 54.8% 45.2% 100%

Economics 45.5% 54.5% 100%

Finance 50.8% 49.2% 100%

50.8% of finance majors are female.

Female Male Total

Accounting 54.8% 45.2% 100%

Economics 45.5% 54.5% 100%

Finance 50.8% 49.2% 100%

50.8% of finance majors are female.

Can draw a stacked bar chart

The conditional distribution by column

Female Male Total

161 × 100 124386 × 100

161 × 100 131386 × 100

161 × 100 11386 × 100

Finance 61225 × 100 59

161 × 100 120386 × 100

Total 100% 100%

Female Male

Economics 2.2% 3.7%

Finance 27.1% 36.6%

Total 100% 100%

Female Male

Economics 2.2% 3.7%

Finance 27.1% 36.6%

Total 100% 100%

Females divide into majors in a similar way to the males,apart from Administration.

Female Male

Economics 2.2% 3.7%

Finance 27.1% 36.6%

Total 100% 100%

30.2% of females study accounting.

Female Male

Economics 2.2% 3.7%

Finance 27.1% 36.6%

Total 100% 100%

30.2% of females study accounting.

Female Male

Economics 2.2% 3.7%

Finance 27.1% 36.6%

Total 100% 100%

24.8% of males study administration.

Female Male

Economics 2.2% 3.7%

Finance 27.1% 36.6%

Total 100% 100%

24.8% of males study administration.

About contingency tables

The marginal distribution of the row variable comesfrom the row totalsThe marginal distribution of the column variablecomes from the column totalsThe cell counts give rise to the joint distribution of therow and column variables

Each row of counts produces a conditionaldistributionEach column of counts produces a conditionaldistributionThe conditional distributions provide evidence for oragainst an association between the variables

Associations between variables

ExampleIs there an association between gender and major?Yes—the row conditional distributions are not the same.The female–male split is similar for all majors except forAdministration.

Female Male Total

Accounting 54.8% 45.2% 100%

Economics 45.5% 54.5% 100%

Finance 50.8% 49.2% 100%Professor Shahjahan Khan, PhD Lecture 1

Associations between variables

ExampleIs there an association between gender and major?Yes—the row conditional distributions are not the same.The female–male split is similar for all majors except forAdministration.

Female Male Total

Accounting 54.8% 45.2% 100%

Economics 45.5% 54.5% 100%

Finance 50.8% 49.2% 100%Professor Shahjahan Khan, PhD Lecture 1

Keeping up

Material covered today: §Module 1 (Study Book)Before next week, read §Module 2 (Study Book)Tutorials commence this week:

bring textbook; study book (or Module 1) with tutorialquestions; calculator

Assignment 1 is due next weekRemember to check the The Learning Centre websitefor additional assistance

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