STAT 178 Chapter 1

• Statistics is concerned with the collection, organization, summarization, and analysis of data
• Statistics involves drawing inferences about a body of data when only a part of the data is observed
• The purpose of statistics is to investigate and evaluate the nature of numbers and the meaning of obtained information
• Sources of data:

  • Documented data: primary data documented by the primary source and secondary data documented by a secondary source
  • Survey: method of collecting data by asking people questions
  • Experiments: method of collecting data with direct human intervention on conditions
  • Observation: method of collecting data by recording observations
  • Other sources: internal data, registration, computer simulations
• Biostatistics is the application of statistical tools and concepts in the biological sciences and medicine
• Variables:

  • A variable is a characteristic that takes on different values in different persons, places, or things
  • Quantitative variables can be measured and convey information regarding amount
  • Qualitative variables cannot be measured and convey information regarding attribute
• Random variable:

  • A random variable is a result of change factors and cannot be exactly predicted in advance
  • Discrete random variable: characterized by gaps or interruptions in the values it can assume
  • Continuous random variable: does not possess gaps or interruptions, can assume any value within a specified interval
• Population: a collection of all units from which data is collected

  • Sample: a subset or representative part of the population
  • Measurement: assigning a number to a characteristic being measured
• Scales of measurement:

  • Nominal scale: possesses only the property of identity
  • Ordinal scale: possesses identity and order but not equality of scale
  • Interval scale: possesses identity, order, and equality of scale but not absolute zero
  • Ratio scale: possesses all properties of identity, order, equality of scale, and absolute zero
• Sampling methods:

  • Probability sampling: every element in the population has a non-zero chance of being chosen
  • Simple random sampling: all possible subsets have the same chances of selection
  • Systematic random sampling: selection of the first element is random and subsequent elements are taken at regular intervals
  • Stratified sampling: dividing the population into nonoverlapping subpopulations and selecting samples from each stratum
• Proportional allocation method assigns equal probabilities for all elements by allocating them proportionately to the sizes of the strata
• Cluster sampling divides the population into nonoverlapping groups or clusters, selects a sample of clusters, and includes all elements in the selected clusters
• Two-stage sampling identifies elements in the sample at the second stage, while three-stage sampling identifies elements at the third stage
• Multistage sampling is a natural extension of one-stage cluster sampling and is more cost-efficient when clusters are large and elements are homogeneous
• Nonprobability sampling methods do not use randomization and allow researchers to subjectively choose sampling units
• Haphazard or convenience sampling includes elements that are most accessible or easiest to contact, based solely on convenience
• Judgment or purposive sampling selects respondents based on the judgment or opinion of the researcher, leading to personal biases and exclusion of other units
• Quota sampling subdivides the population into subgroups, determines a quota for each stratum, and fills the quota using convenience or judgment sampling
• Snowball sampling starts with initial samples taken by SRS and expands through referrals, often done through social networks
• Advantages of nonprobability sampling include convenience and cost-effectiveness, but limitations include lack of representativeness, bias, and inability to determine sampling error
• Observation leads to the formulation of questions or uncertainties that can be answered scientifically
• Hypotheses are formulated to explain observations and make quantitative predictions of new observations, often generated after extensive background research and literature reviews
• Criteria for designing an experiment include accuracy and precision, where accuracy refers to the correctness of a measurement and precision refers to the consistency of a measurement