Stat

• Statistics refers to a set of mathematical procedures that deals with the collection, organization, presentation, analysis, and interpretation of data in order to make a decision
• Data is the set of individual values associated with a variable
• Variable is a characteristic of an item or individual that can change or take different values
• Descriptive procedures involve collecting, presenting, and describing data
• Inferential procedures involve drawing conclusions and/or making decisions concerning a population based only on sample data
• Goal of statistics: Convert data into meaningful information
• Levels of Measurements:

  • Nominal Scale: Classifies data into distinct categories
  • Ordinal Scale: Classifies data into distinct categories with ranking implied
  • Interval Scale: Ordered scale where the difference between measurements is meaningful but lacks a true zero point
  • Ratio Scale: Ordered scale where the difference between measurements is meaningful and has a true zero point
• Sources of Data:

  • Primary Sources: Data collected from surveys, experiments, or observations
  • Secondary Sources: Data analyzed by someone other than the data collector, such as census data or data from print journals
• Sampling Frame is a listing of items that make up the population, such as population lists, directories, or maps
• Probability Sampling involves random selection, allowing for strong statistical inferences about the whole group

  • Simple Random Sampling: Every possible sample of a given size has an equal chance of being selected
  • Stratified Random Sampling: Divides the population into subgroups and ensures every subgroup is properly represented in the sample
  • Systematic Random Sampling: Selects every kth individual after randomly selecting the first individual
  • Cluster Sampling: Divides the population into clusters and randomly selects entire clusters
• Non-probability Sampling involves non-random selection based on convenience or other criteria

  • Convenience Sampling: Sample selected based on ease, cost, or convenience
  • Voluntary Response Sampling: Participants volunteer themselves, leading to self-selection bias
  • Snowball Sampling: Participants recruit other participants
  • Purposive Sampling: Researcher selects a sample based on expertise and specific criteria
  • Quota Sampling: Non-random selection of a predetermined number or proportion of units called a quota
• Evaluating Survey Worthiness:

  • Consider the purpose of the survey
  • Check if the survey is based on a probability sample
  • Watch out for coverage error, nonresponse error, measurement error, and sampling error
• Data Cleaning is Necessary:

  • Identify and address irregularities in the data, such as typographical errors, missing values, and outliers
  • Recode variables to supplement or replace the original variable
• Things to Consider in Potential Sources of Data:

  • Structured data follows an organizing principle, while unstructured data does not
  • Electronic data formatting and encoding should be considered
• References:

  • Various textbooks on statistics
• Techniques for Inferential Procedures

  • Estimation e.g., Estimate the population mean weight

  using the sample mean weight

  • Hypothesis Testing e.g., Use sample evidence to test the claim that

  the population mean weight is 120 pounds
• Populations and Samples

  • A population is the entire collection of things under consideration

  and referred to as the frame

  • The sampling unit is each object or individual in the frame

  • A parameter is a summary measure computed to describe a

  characteristic of the population

  • A sample is a subset of the population selected for analysis

  • A statistic is a summary measure computed to describe a

  characteristic of the sample drawn from the population
• Why Sample?

  • Less time consuming than a census

  • Less costly to administer than a census

  • It is possible to obtain statistical results of a sufficiently high

  precision based on samples

  Strive for representative samples to reflect the population of interest accurately!