exploring and collection data basics

10 basic knowledge for business statistic including differences between population and sample, probability versus statistic....

10 basic knowledge

• I. population and sample
  • population
    • definition: set of all items of interst
    • symbol: population size: N
    • example：all of uoft students
  • parameter
    • defintion: number descriping a population
    • symbol: population mean= μ
  • sample
    • defintion: subset of population
    • symbol: statistic size: n
    • example: random sampling 1000 uoft students
  • statistic
    • defintion: number descriping a sample
    • symbol: sample mean:¯x¯
• II. statistic
  • descriptive statistic
    • describe a sample
  • inferential statistics
    • definition: make inference about a population and its parameter using sample data
• III. probability versus statistic
  • probability
    • know everything, know population
      • calculate probability of an event occurs
  • statistic
    • unknown population
      • take sample dataand calculate sample statistic
        • infer parameter
• IV. sampling and nonsampling error
  • Sampling Error
    • characteristics
      • it is not a mistake
        • cause the sample is a random subset of the population
      • as sample size rizes, sampling error tends to fall
  • Non-sampling Error
    • 4 categories
      • biased estimate
        • definition: systematically higher or lower than the population parameter
        • reason: sample is too samll
      • systematic lying
        • reason: due to poor survey design
        • example: There is a survey about humanity and some passerbys could give money to homeless dogs under moral pressure if lots of people arrounded him.
      • non-response bias
        • reason: low response rate where non-responders differ from responders
        • example: If students can write report letter to the headmaster email which decide whether teachers leave or stay, it could appear a situation that letters are almost bad letters to teachers.
      • sampling frame differs from target population
        • reason: the list from which units are drawn for the sample is wrong.
        • example: if a investiagator plan to make a survey of meansalary of uoft students, but he asks parents of uoft students. (cause students could lie to their parents.)
• V. What are data
  • definition: data are recorded information, whether numbers of labels together with its context
  • 3 types
    • cross sectional data
      • definition: same variables in same time period measured for different units
    • time series data
      • definition: same variables for same unit measured a different time period
    • panel
      • definition: same variables measured for a range of units and time periods.
• VI. What is variable
  • definition: A variable holds information about the data.
  • Quantitative variable数字变量
    • definition: a variable in which the numbers are values of measured quantities
      • Discrete variable
        • definition: a finite or countable list of values 结果有限
        • example: number of heads in 4 tosses of a coin
      • continuous variable
        • definition: any value possible in an interval(uncountable)结果无限
        • example: after tax income
  • categorical variable类别变量
    • defiinition: a variable that labels the category of the measured unit
      • discrete variable only
  • 4 types
    • Quantitative variable
      • Interval
        • numerical measurements which allow for degree of difference between values
        • distance is consistent but ratios are meaningless
        • Does not have a true 0 measure
        • Ex: dates
      • Ratio
        • numerical measurements which allow for degree of difference between values
        • ratios are meaningful-sensible to carry out multiplication/division
        • Ex: temperature, length,time duration
    • Categorical variable
      • Nominal
        • categorize units into distinct classes
        • unordered categories
        • Ex: gender, program of study, favorite color
      • Ordinal
        • ordered categories without natural units / distance metric.
        • natural ordering to the categories; not just the names of the categories differ
        • Ex: letter grades, income, professional rank
• VII. Frequency tabulation
  • definition: Lists all unique values in data & relative frequency
  • Interval or nominal data
• VIII. Bar chart vs. Histogram
  • Bar chart: used for limited outcomes
    • Ex:head or tail
      • discrete
  • Histogram: used for unlimited outcomes
    • Ex: 10,000 people after tax income and outcome is unlimited
• IX. Cross Tablution
  • = contigency table = two-way table
  • measures frequency that two variables take each possible pair of values (freq tab: one variable)
• X. Simpson's paradox/ Composition effect
  • same data look alone is diiferent to overall
  • solution: do more experiences.
• • believe ability, choose b
  • believe luck, choose a
• Two cross-tabs
• • 70: 70 female watch 129 powerad
  • 17: 17 female remember powerad
  • 43: 43 people remember powerad
• Ex
• • 165: 254 total, 164 attendences forgot
  • 64.96: 64.96% attendences forgot
• • 254: total 254 attendances
  • 123: 123 attendences are male
  • 48.43:48.83% attendences are male
• • 254: total 254 ads
  • 129: 254 total, 129 power ads
  • 50.79: 50.79% power ads
• • A company wanted to know whether its ads would be remembered by customers. Then, they found some attendences who donot know the test context to do a quiz. Investigators let these units to watch TVs about 2 hours and released a car ad. some audience would watch the horsepower ad, and some other people would watch the safety ad. After they finished TV, investigators would ask them whether remember some details of ads
  • Goal: compare ads "Power": emphasizes horsepower "Safety": emphasizes safety features Participants watch TV alone for 2 hours. Insert one ad at random with other ads. Give "quiz" about car
• • Histogram
• • Bar Chart
• • Bat Chart to summarize tabulation
  • NSSE 2006, U of T seniors: if you could start again, would you go to the same instituition you are now attending? 1=definitely yes 2= probably yes 3= probably no 4= definitely no
• • tables meaning: a variable, the number of occurrences of different outcomes.
  • 992 tosses, 286 for 1
  • 992 tosses, 28.3% for 1
  • 68.15 means the probability of occurrences of 1 and 2
• • # of variables: 2
    • I. exclude sequence
  • # of observations: 3
    • # of units
  • categorical
    • nominal
      • unordered
    • ordinal
      • ordered
  • quantitative
    • interval
      • discrete
    • ratio
      • continuous
• Q：
  • Q1: Consider data on 257 people who tasted a new snack product at loblaws. Each was asked: how likely is it that you will purchase this product in the future? which kind of data are these: a. Cross sectional data b. Time series c. Panel data
    • answer: a
  • Q2: Price of the textbook each year for the past decade and the percent of students that had a copy. which kind of data are these? a. Cross sectional data b. Time series c. Panel data
    • answer: b