06 sep 2018

Inhoud

Reasoning in statistics

Statistical Literacy

  • Knowledge (Basic understanding of concepts)
    • Identify
    • Describe
  • Skils (Ability to work with statistical tools)
    • Translate
    • Interpret
    • Read
    • Compute

Statistical Reasoning

  • Understanding
    • Explain why
    • Explain how

Statistical thinking

  • Apply
    • What methods to use in a specific situation
  • Critique
    • Comment and reflect on work of others
  • Evaluate
    • Assigning value to work
  • Generalize
    • What does variation mean in the large scheme of life

Empirical Cycle

By Adriaan de Groot

The components

  • Observation
    • Idea for hypothesis
  • Induction
    • General rule
    • Hypothesis
  • Deduction
    • Expectation / Prediction
    • Operationalization
  • Testing
    • Test hypothesis
    • Compare data to prediction
  • Evaluation
    • Interpret results in terms of hypothesis

Explained by Annemarie Zandscholten

Null Hypothesis Statistical Significance Testing

Neyman-Pearson Paradigm

\(H_0\) and \(H_A\)

\(H_0\)

  • Skeptical point of view
  • No effect
  • No preference
  • No Correlation
  • No difference

\(H_A\)

  • Refute Skepticism
  • Effect
  • Preference
  • Correlation
  • Difference

Binomial \(H_0\) distribution

Binomial \(H_A\) distribution

Decision table

\(H_0\) = True \(H_0\) = False
Decide to
reject \(H_0\)
Type I error
Alpha \(\alpha\)
Correct
True positive = Power
Decide not
to reject \(H_0\)
Correct
True negative
Type II error
Beta \(\beta\)

Alpha \(\alpha\)

  • Type I error
  • False Positive
  • Criteria often 5%
  • Distribution depends on sample size

Power

  • True positive
  • Power equal to: 1 - Beta
    • Beta is Type II error
  • Criteria often 80%
  • Depends on sample size

Post-Hoc Power

  • Also known as: observed, retrospective, achieved, prospective and a priori power
  • Specificly meaning:

The power of a test assuming a population effect size equal to the observed effect size in the current sample.

Source: O'Keefe (2007)

1 - alpha

  • True negative

Beta

  • Type II error
  • False Negative
  • Criteria often 20%
  • Distribution depends on sample size