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NotesOn_StatisticsInANutshell_2ed.md

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Notes on Statistics in a Nutshell, 2nd Edition

By Sarah Boslaugh; O'Reilly Media, Nov. 2012

ISBN 9781449316822

Chapter 1: Basic Concepts of Measurement

  • Types of data
    • Nominal - unordered, non-arithmetic
    • Ordinal - ordered, non-arithmetic
    • Intervals - ordered, equal intervals between measurement points, non-arithmetic
    • Ratio - ordered, equal intervals, has a natural zero point, meaningfully divisible
    • Continuous - can take any value within a range (floats)
    • Discrete - can only take specific values (counts, integers)
  • Classical measurement theory conceives of any measurement or observed score as consisting of two parts: true score T and error E
  • X (observed measurement) = T + E
  • Random error is everywhere, and can be dealt with or assumed to cancel out
  • Systematic error:
    • has an observable pattern
    • is not due to chance
    • often has a cause or causes that can be identified and remedied
  • Methods of measurement have to be evaluated for reliability and validity
  • Reliability - how consistent and / or repeatable measurements are
    • Multiple-occasions reliability, or test-retest reliability, is how similarly a test or scale performs over repeated administration. Can be a measure of 'temporal stability.'
    • Multiple-forms reliability, or parallel-forms reliability, is how similarly different versions of a test or questionnaire perform in measuring the same entity
    • Internal consistency reliability is how well the items that make up an instrument reflect the same construct (how much they measure the same thing).
  • Validity - how well a test or rating scale measures what it is supposed to measure
    • Content validity - how well the process of measurement reflects the important content of the domain of interest
    • Face validity - whether it appears to a typical person to be a fair assessment of the qualities under study. Important for establishing credibility.
    • Concurrent validity - how well inferences drawn from a measurement can be used to predict some other behavior or performance that is measured at approximately the same time
    • Predictive validity - how well you can draw inferences about the future
  • Triangulation - using information from multiple sources to arrive at some accurate or more accurate output, or to adjust for error in one source
  • Measurement bias
    • Can enter studies in two primary ways:
      • during selection and retention of subjects
      • in the way information is collected about subjects
    • Selection bias - when some potential subjects are more likely than others to be selected for the study sample
    • Volunteer bias - people who volunteer for things aren't usually representative of the population as a whole
    • Nonresponse bias - people who decline to take part represent a portion of the population, but are not in the results
    • Informative censoring can create bias in any longitudinal study. The worst of that is when study participants drop out not at random but for reasons related to the study's purpose.
    • Information bias - enters through the data collection methodology
    • Interviewer bias - introduced by the knowledge or attitudes of the researcher
    • Recall bias - people with a life experience such as suffering from a serious disease are more likely to remember events that they believe are related to that experience
    • Detection bias - certain characteristics are more likely to be detected or reported in some people than in others.
    • Social desirability bias - people want to present themselves in a favorable light

Chapter 2: Probability

Definitions

  • Trials - experiments, observations, some event whose outcome is unknown
  • Sample space - set S of all possible outcomes of a trial
  • Event - E, the outcome of a trial, can consist of one outcome or a set of outcomes
  • Union - compound event that occurs if one or more of the events occur. EuF means "either E or F or both E and F"
  • Intersection - compound event that occurs if all the simple events occur. EnF means "both E and F"
  • Complement -