Sampling Techniques and Misuses of Statistics

Statistics is a field of Mathematics interested in data.
- Collection
- Organization
- Analysis
- Interpretation
- Presentation
This field has skyrocketed recently
- Data driven decision making
- Data analytic
- Data science
Statistics is the art and science of gathering, analyzing, and making inferences from numerical information obtained in an experiment.
An experiment is a controlled operation that yields a set of results.
Descriptive statistics is concerned with collecting, organizing, and analyzing data.
Inferential statistics is concerned with making generalization or predictions from the data collected.
A statistician is interested in describing a population based on a sampling.
- A population is the universal set for a given study.
- A sample is a subset of the population, hopefully representative of the population.
Sampling
- There are a number of reasons we can not examine an entire population
  - It might not be possible:
    - I would like to know what percent of the stars in the universe are larger than our sun.
  - It might be possible but very expensive
    - I would like to know what portion of the tick population in Erie County are infected with the bacteria that causes Lyme Disease
    - Can I collect and test all of them?
  - It might destroy the thing I want to know about
    - I would like to know what portion of the bags of potato chips at a factory contain a burnt chip.
    - If I open every bag, I won't have anything left to sell.
- The goal is sampling is to obtain an unbiased sample
  - This is a sample where every item in the population has an equally likely chance of being selected.
Sampling Techniques
- I would like to build a new Student Activity Center
  - I want students to vote to pay a fee to fund this center.
  - It will be filled with game opportunities
    - Laser Tag
    - Escape Rooms
    - Computer Game Center
  - To support this, I want to do a study of interest by conducting a poll.
- Biased Sampling
  - Find the items to prove your point and select these.
  - Absolutely worthless
  - For my activity center, I will find 100 students who support this and ask their opinions on the center.
- Random Sampling
  - Select items randomly from a population.
    - Assign each a random id number
    - Select from those id numbers.
  - For my activity center, I will select 100 ids at random from the list of all active student id numbers..
  - This is the gold standard of sampling.
- Systematic Sampling
  - Start at some random point and select every n^th item
  - Probably best in some type of assembly line situation
    - Select every 50^th bag of potato chips and test for burnt chips.
    - Can be problematic if I have 5 machines that bag chips. Why?
  - For my activity center, I will:
    
    List the student population by banner id in order
    Divide the student population by 100 -> k
    Select a value between 1 and k to start
    Select ids at k, 2k, 3k, ... (there will be 100)
- Cluster Sampling or Area Sampling
  - Divide an area into groups or sections.
    - Usually based on physical proximity.
  - Select a number of these groups
  - Sample the selected groups, either fully or using another technique.
  - Example 1: Select a number of cases of potato chips produced on a given day, then randomly sample 5 bags from each to see how many contain burnt chips.
  - Example 2: Select 100 city blocks at random in Erie then survey every household in those selected blocks.
  - For my activity center, I will:
    
    Select 10 classrooms from all classrooms in use at 2:00 on Monday.
    Select 10 people at random to survey
- Stratified Sampling
  - When you know the population is broken into different categories
  - Select a representative sample from each strata.
  - Erie County PA has the following political mix
    - 55% Democrat
    - 34% Republican
    - 11% Other
  - So conduct a poll and ask an opinion of the correct percentage of each group.
  - For my activity center, I will:
    
    Divide the list of students at Edinboro into class rank.
    Find the percentage of each.
    Select that percent of students from each group to survey.
- Convenience Sampling
  - Pick whoever is handy.
  - Ask the first 100 people you encounter
    - In the Student Center Lower Level
    - In the Library
    - In McComb Field House
    - In the Science and Health Professions Living Learning Floor
    - In the parking lot.
Misuse of statistics
- Make sure you know the sampling technique involved.
- Look out for biased experiments
  - Are you still cheating on your exams?
- Look out for poorly constructed experiments
  - Ambiguous terms: who is the biggest store?
Misuse of Graphs
- Look how great the stock marked did Friday
- Or how poorly it did last week
- Or the last five years
In general with graphs
- Show the full extent of the y axis.
- Make sure circle graphs sum to 100% only
- As you double 2d items, area is x4.
- As you double 3d items, volume is x8.