Lecture 1

Math 132ALecture 1: 

Math 132A Lecture 1 Class Introduction Chapter 1

Agenda: 

Agenda Syllabus Chapter 1 Percentages/Fractions/Decimal Worksheet

Introductions: 

Introductions Meghan Cherry Master of Public Policy Master of Industrial Engineering Employment in Applied Statistical Analysis Barclays Capital University of Michigan Hospital Operations University of Michigan Hospital Government Relations

Availability: 

Availability Office Hours: 10:30 to 12:20 T & TH Location: SW 248 Feel free to schedule alternative meeting times Email mcherry@svsu.edu Expect day delay in answering emails Phone Cell: 989-413-9004 Call between 10:00 a.m. and 8:00 p.m. Expect day delay in answering voicemail SVSU Weather Line (989) 964-4477

Materials: 

Materials Textbook: Elementary Statistics 10th Edition Basic Scientific Calculator Software: Minitab Available in computer labs Free 30 day trial http://www.minitab.com/products/minitab/14/demo/

Tests: 

Tests 3 Tests 100 pts Each Non-cumulative During Class Final Exam 200 pts Cumulative Dec 10th 8:30 (MW class) or Dec 11th 8:30 (TTH class) Formula Sheets Will be provided for review before each test or exam Copies will be provided on each test or exam day The results of some in-class activities will be given to you on your exam day

Homework: 

Homework 13 Assignments 30 pts each (3% of grade each) Best 10 homeworks will be used to calculate grade Please included all work and problem methodology in answers for partial credit PUT A BOX AROUND FINAL ANSWER Grade for each problem is 20% answer and 80% methodology Homework should be completed individually Guideline: If two students find themselves looking at each-others homework papers then collaboration is too extensive. Collaboration and conversations should be limited to general methodology.

Computer Assignments: 

Computer Assignments Basic analysis of real data sets using Minitab software. Answer critical-thinking questions about the data analysis Students may collaborate when using Minitab but must turn in assignments individually

Honor Code: 

Honor Code As a student at Saginaw Valley State University: I am committed to upholding a high standard of academic integrity in all of my work, inside and outside of the classroom. Out of respect for my peers, professors, institution, and self, I will complete all tasks honestly and to the best of my ability. I am guided by my conscience as I work toward my educational and personal goals, and I expect my fellow students to practice that same moral judgment. I take pride in my academic accomplishments and therefore will not give or receive unauthorized assistance on any assignment, project, exam or other university requirement. I seek to maintain the honor of a Saginaw Valley State University degree, and I will preserve its value throughout my professional career. Don’t cheat- It isn’t worth it!

Learning Associations: 

Learning Associations Your brain recalls information by association with experiences, ideas, objects, people, etc. Build a variety of associations through learning in multiple ways Lecture Homework Group work Tricks to help you remember Organizing information Memorization Repeated recall of information

Types of Memory: 

Types of Memory Short term or working memory Temporary neural connections Short lived Long term Memories from short term are repeatedly rehearsed and associated Each rehearsal and association potentates (strengthens) neural connections Can last for decades

Techniques for Increasing Learning: 

Techniques for Increasing Learning Use and reuse information Work problems in class, homework and exam review Use information in multiple ways- solve specific problems and make general theoretical rules Introduce material at many points in time

Studying to Learn: 

Studying to Learn Read before class for general understanding Highlight questions you have on the reading by section Complete reading portion of the homework Attend class As each section is covered, ask yourself if your questions have been answered or whether new questions are generated Take notes Try to work problems in class, check answers and get help as needed Be able to explain the reason for each step in your solution After class, create flashcards for memorization After class, do your homework checking questions with answers Visit office hours if you have trouble completing any of the above steps

Studying to Learn- Exams: 

Studying to Learn- Exams Reread material working examples without reading the solutions Review any missed homework questions Outline material or create a review sheet including directions on how to approach problems and solve them in your own words Take mid-chapter tests and chapter tests in book ASK FOR HELP BEFORE THE TEST IF YOU THINK YOU NEED IT

“Play it Again Sam”…”Or didn’t you already say that 50 times?”: 

“Play it Again Sam”…”Or didn’t you already say that 50 times?” Ask for help as soon as you need it! Not later Not tomorrow Not in the morning Not when the cows come home

Course Schedule: 

Course Schedule Tentative and subject to change based on class progress

Course Goals: 

Course Goals Learn statistical terminology and methodologies Show real-life applications of statistics Develop critical thinking and reasoning skills Use statistics to substantial or refute arguments

General Education Goals: 

General Education Goals To understand and manipulate numerical data; to respond to arguments and positions based on numbers and statistics.

Questions?: 

Questions?

Chapter 1: 

Chapter 1 Overview Types of Data Critical Thinking Design of Experiments

1-1 Overview: 

1-1 Overview Data: are observations that have been collected Statistics: are a collection of methods to collect data and then organize, summarize, present, analyze, interpret and draw conclusions Population: is the complete collection of all elements studied Sample: is a subcollection of members collected from a population

Population vs. Sample: 

Population vs. Sample Population: All candy collected on Halloween Sample: Three of the pieces of candy collected on Halloween

1-2 Types of Data: 

1-2 Types of Data Parameter: Numerical measurement describing some characteristic of a population Statistic: Numerical measurement describing some characteristic of a sample

Parameter vs. Statistic: 

Parameter vs. Statistic Population: All People Parameter: 5 of 15 or 33% wear glasses Sample: 3 Randomly Selected People Statistic: 0 of 3 or 0% wear glasses

The United States Census: 

The United States Census Every 10 Years the Census Bureau attempts to count and survey all citizens of the United States Number of US Representatives in each state are determined by the census The amount of Federal funds each state receives depends on the census (over $185 billion each year) Approximately 275 million residents Requires 860,000 employees to conduct the census All households receive a short-form questionnaire and 1 in 6 receive a long-form questionnaire that takes about 40 minutes to complete

Census Methodology: 

Census Methodology The census is used to calculate population parameters Is the census successful? Should the census be conducted through sampling?

Quantitative vs. Qualitative Data: 

Quantitative vs. Qualitative Data Quantitative Data: consists of numbers representing counts or measurements Qualitative Data: can be separated into categories based on nonnumeric characteristics Discussion in groups: Consider a bag of M&Ms…. Name some qualitative characteristics Name some quantitative characteristics

Discrete vs. Continuous Data: 

Discrete vs. Continuous Data Discrete: Number of possible values is a either finite or countable number Continuous: Infinitely many possible values that correspond to a continuous scale that covers a range of values without gaps interruptions or jumps.

Examples: 

Examples Discrete Number of rainy days Pant size Continuous Volume of liquid Distance to a destination Tricky Examples Number of stars is infinite but countable (discrete) The set of numbers between zero and one – finite scale but infinite number of values ie, .5, .567777, etc. (continuous)

Levels of Measurement: 

Levels of Measurement Nominal: data consisting of names and labels (i.e.. Color) Ordinal: data can be arranged in order but differences between data values are meaningless (i.e.. Rating systems) Interval: data that can be arranged in order with meaningful differences between data points but no natural zero. (i.e.. Years) Ratio: data that has the properties of interval data with a natural zero (i.e.. Weight)

Name the Level of Measurement: 

Name the Level of Measurement Consumer reports magazine ratings of “best buy”, “recommended” and “not recommended” Number of yes responses when 500 students are asked if they have ever engaged in binge drinking Temperature in New York

1-3 Critical Thinking: 

1-3 Critical Thinking “Some people use statistics as a drunken man uses lampposts- for support rather than illumination” Bad statistics lead to bad conclusions Use common sense

Common Sample Problems: 

Common Sample Problems Sample too small Sample Biased Voluntary response sample – respondents themselves decide whether to be included Combat bias by randomized sampling Non-response Refusing to answer a survey People who answer and do not answer are different Missing Data

Common Study Problems: 

Common Study Problems Loaded questions Would you vote for Mr. President if you knew he had gone to prison? (push-polling) Order of questions Would you say traffic contributes more to air pollution than industry? (45% traffic, 27% ind.) Would you say industry contributes more to pollution than traffic? (24% traffic, 57% ind.)

Common Problems Presenting Results: 

Common Problems Presenting Results Misleading Graphs Pictographs Percentages Partial Pictures

Misleading Graphs: 

Misleading Graphs

More Misleading Graphs: 

More Misleading Graphs http://www.bbc.co.uk/schools/gcsebitesize/maths/datahandlingfi/representingdatarev4.shtml

Misleading Pictograms: 

Misleading Pictograms http://www.bbc.co.uk/schools/gcsebitesize/maths/datahandlingfi/representingdatarev4.shtml

Misleading Percentages: 

Misleading Percentages Example: Privatizing Social Security Presidential plan says 2 percent of Social security taxes will be ‘diverted’ into private accounts. Common interpretation: If you pay $100 into social security, $2 will be diverted Actual interpretation: 6.2% of the average American’s income goes to social security. Under the privatization plan, 4.2% would go to social security and 2% to private accounts. So, if one pays $100 into social security, $32 would be diverted- a big difference! (ABC News) http://abcnews.go.com/Technology/WhosCounting/story?id=300038&page=1

Correct Percentile Use: 

Correct Percentile Use Find Percentage of an Amount 2% of 200 hundred = (2/100) * 200 = 4 Convert Fraction to a Percentage (4/200)*100% = 2% Convert a Decimal to a Percentage .02 * (100%) = 2% Convert a Percentage to a Decimal 2%/100% = .02 Note the similarity to other calculations used when changing units such as changing a measurement in inches to a measurement in feet

Problems with Methodology: 

Problems with Methodology Correlation vs. Causality Tall men, on average wear long pants Bad conclusion: long pants cause men to grow tall Self-Interest Study Consumer products Precise Numbers 57.5% survey participants responded ‘yes’ 5% margin of error The level of precision does not imply accuracy

1-4 Design of Experiments: 

1-4 Design of Experiments If sample data is not collected appropriately, data may be completely useless Two Primary Types of Studies Observational Study: Observe and measure characteristics but do not modify objects being studied Experiment: Apply a treatment and observe effects on the subjects

Types of Observational Studies: 

Types of Observational Studies Cross-Sectional Study: Data are observed, measured and collected at one point in time Retrospective Study: Data are collected from the past, going back in time Prospective Study: Data are collected in the future from groups sharing common factors.

Example Observational Studies: 

Example Observational Studies Retrospective Study: Collect data about a group of drivers that died in car crashes and a group that did not. Prospective Study: Follow two groups of drivers- those who used cell phones and those who didn’t and see how many die in car crashes in the future

Confounding Variables: 

Confounding Variables Confounding occurs when your are not able to distinguish between the effects of different variables Often happens when important variables are excluded from a study

Confounding Discussion Question: 

Confounding Discussion Question A study is conducted to answer the question “Which School, Anderson High or Belman High, has a more successful reading curriculum?” In order to answer the question, researchers collect data on the reading level of all graduating seniors at both high schools. Will the researcher’s study answer the question posed? What potential confounding variables may occur?

Controlling Effects of Variables: 

Controlling Effects of Variables Blind experiment: some subjects receive a treatment and some subjects receive a placebo which looks identical to the treatment but does not contain active ingredients Placebo effect: untreated subjects report improvements that are real or imagined when receiving a placebo

Controlling Effects (2): 

Controlling Effects (2) Double-blind: both experimenters and subjects are unaware of which patients receive the placebo and treatment Hawthorne Effect: subjects respond differently simply because they are part of an experiment Rosenthall Effect: Researchers unintentionally influence study subjects

Types of Experiment Design: 

Types of Experiment Design Rigorously Controlled Design: Subjects carefully chosen so that subjects in each treatment group are similar in ways important to the experiment Often used when large sample sizes are difficult to obtain Randomized Block Design: Form blocks of subjects with similar characteristics Randomly assign treatments to subjects within each block Used in agricultural experimentation Completely Randomized Design: Subjects are assigned to treatment groups through random selection Most popular experiment type

Random Sampling: 

Random Sampling Random sample: each individual member of a population has an equal chance of being selected Simple random sample: n subjects are selected in such a way that every sample of size n has an equal probability of being selected Probability sample: each member of a population has a known, though not necessarily equal chance of being selected

Types of Semi-Random Sampling: 

Types of Semi-Random Sampling Systematic Sampling: Randomly select a starting point and then select every kth element in a population Convenience Sampling: Use results easiest to get Stratified Sampling: Subdivide population into at least two subgroups then draw a sample from each subgroup Cluster Sampling: Divide population into clusters then randomly select a subset of clusters and choose all members of selected clusters Multi-stage sampling design: uses different methods of sampling at different stages in an experiment This class will primarily study simple random samples

Slide52: 

Systematic Sampling Select some starting point and then select every k th element in the population

Slide53: 

Convenience Sampling use results that are easy to get

Slide54: 

Stratified Sampling subdivide the population into at least two different subgroups that share the same characteristics, then draw a sample from each subgroup (or stratum)

Slide55: 

Cluster Sampling divide the population into sections (or clusters); randomly select some of those clusters; choose all members from selected clusters

Sampling Error: 

Sampling Error Sample Error: Difference between sample result and true population result Non-Sample Error: Difference caused by data that has been incorrectly collected, recorded or analyzed

Worksheet Answers: 

Worksheet Answers Answers: 1) 65% 2) 75% 3) 25% 4) 727% 5) 26% 6) 41% 7) 51% 8) 51% 9) 50 10) 100 11) 500 12) 33.3% 13) 152% 14) 9 15) 51% 16) 81 17) 100% 18) 26 19) 310 20) 105 21) 9.5% 22) 16% 23) 255

For Next Class: 

For Next Class Read Chapter 2 Read Minitab Project Complete Homework 1 Covered Material 1-2: pg 10-11 #5-27 1-3: pg 18-21 #5-27 1-4: pg 31-33 #5-30, 33 Reading 2-2: pg 48 #1 2-3: pg 54 #1-2 2-4: #1