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UK STA 291 - STA 291 Lecture 2

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1STA 291 - Lecture 2 1STA 291Lecture 2 • Course web page: Updated: Office hour of Lab instructor.• Statistics is the Science involving Data• Example of data:STA 291 - Lecture 2 2Item Name Price In Stock? # in stockSilver cane 43.50 Yes 3Top hat 29.99 No 0Red shoes 35.00 No 0Blue T-shirt 5.99 Yes 15…… …… …… …• More complicated data (time series): many of those tables over time….every quarter company have their financial report.• A single variable value over time: Stock price over the time period of 20 years.STA 291 - Lecture 2 32STA 291 - Lecture 2 4Basic Terminology• Variable– a characteristic of a unit that can vary among subjects in the population/sample– Examples: gender, nationality, age, income, hair colour, height, disease status, grade in STA 291, state of residence, voting preference, weight, etc….There are 4 variables displayed in the table on previous slideSTA 291 - Lecture 2 5Type of variables• Categorical/Qualitative and • Quantitative/numerical• Recall: – A Variable is a characteristic of a unit that can vary among subjects in the data• Within numerical variables: continuous or discrete.• Within categorical variables: nominal or ordinal.• Examples (ordinal): very satisfied, satisfied, unsatisfied…..STA 291 - Lecture 2 63STA 291 - Lecture 2 7Qualitative Variables(=Categorical Variables)Nominalor Ordinal• Nominal: gender, nationality, hair color, state of residence• Nominal variables have a scale of unordered categories• It does not make sense to say, for example, that green hair is greater/higher/better than orange hairSTA 291 - Lecture 2 8• Ordinal:Disease status, company rating, grade in STA 291. (best, good, fair, poor)• Ordinal variables have a scale of ordered categories. They are often treated in a quantitative manner (GPA: A=4.0, B=3.0,…)Qualitative (Categorical) VariablesNominal or OrdinalSTA 291 - Lecture 2 9Quantitative Variables(=numerical variables)• Quantitative: age, income, height, price• Quantitative variables are measured numerically, that is, for each subject, a number is observed4STA 291 - Lecture 2 10Example 1• Vigild (1988) “Oral hygiene and periodontal conditions among 201 institutionalized elderly”, Gerodontics, 4:140-145• Variables measured– Nominal: Requires Assistance from Staff?Yes / No– Ordinal: Plaque ScoreNo Visible Plaque - Small Amounts of Plaque -Moderate Amounts of Plaque - Abundant Plaque– Quantitative: Number of Teeth (discrete)STA 291 - Lecture 2 11Example 2• The following data are collected on newborns as part of a birth registry database• Ethnic background: African-American, Hispanic, Native American, Caucasian, Other • Infant’s Condition: Excellent, Good, Fair, Poor• Birthweight: in grams• Number of prenatal visitsSTA 291 - Lecture 2 12Why is it important to distinguish between different types of data?• Some statistical methods only work for quantitative variables, others are designed for qualitative variables.5STA 291 - Lecture 2 13You can treat variables in a less quantitative manner.(but lose information/accuracy….sometimes for security reason).• Examples include income, [20k or less, 20k to 40k, 40k to 60k, 60k and above] and– Height: Quantitative variable, continuous variable, measured in cm (or ft/in)– Can be treated as ordinal: short, average, tall– Can even be treated as nominal180cm-200cm, all othersSTA 291 - Lecture 2 14Sometimes, ordinal variables are treated as quantitative: the quality of the photo prints rated by human with a score from 1 to 10.STA 291 - Lecture 2 15Discrete and Continuous• A variable is discrete if it can take on a finite number of values• Examples: gender, nationality, hair color, disease status, company rating, grade in STA 291, state of residence• Qualitative (categorical) variables are always discrete• Quantitative variables can be discrete or continuous6STA 291 - Lecture 2 16Discrete and Continuous• Continuous variables can take an infinite continuum of possible real number values• Example: time spent on STA 291 homework– can be 63 min. or 85 min.or 27.358 min. or 27.35769 min. or ...– can be subdivided– therefore continuousSTA 291 - Lecture 2 17Discrete or Continuous• Another example: number of children• can be 0, 1, 2, 3, …• can not be 1.5 or 2.768• can not be subdivided• therefore not continuous but discrete• Data are increasingly getting larger. A few gigabyte is considered large 5 years ago• Microsoft Excel often not enough. (64k rows by 256 columns)• Data base software SQL etc.• Data miningSTA 291 - Lecture 2 187STA 291 - Lecture 2 19Where do data come from?• Two types of data collection method covered in this course: (1) experiments (2) pollsSecond hand, from internet…..STA 291 - Lecture 2 20Simple Random Sampling• Each possible sample has the same probability of being selected. [no discrimination, no favoritism.]• The sample size is usually denoted by n.STA 291 - Lecture 2 21Example: Simple Random Sampling• Population of 4 students: Adam, Bob, Christina, Dana• Select a simple random sample (SRS) of size n=2 to ask them about their smoking habits• 6 possible samples of size n=2: (1) A B, (2) A C, (3) A D(4) B C, (5) B D, (6) C D8STA 291 - Lecture 2 22How to choose a SRS?• Each of the six possible samples has to have the same probability of being selected• For example, roll a die (or use a computer-generated random number) and choose the respective sample• Online Sampling AppletSTA 291 - Lecture 2 23How not to choose a SRS?• Ask Adam and Dana because they are in your office anyway– “convenience sample”• Ask who wants to take part in the survey and take the first two who volunteer– “volunteer sampling”STA 291 - Lecture 2 24Problems with Volunteer Samples• The sample will poorly represent the population • Misleading conclusions• BIAS• Examples: Mall interview, Street corner interview9STA 291 - Lecture 2 25Homework 1• Due Jan 28,11 PM.• homework assignment:Log on to MyStatLab and create an account for this course. Complete one question with several multiple choices.STA 291 - Lecture 2 26Attendance Survey Question• On a 4”x6” index card (or little piece of paper)–write down your Nameand 291 Section number–Today’s Question: (regarding prereq.) You have takenA. MA123, B. MA113, C. both, D.


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