Chi-squared

Concepts behind tests of goodness-of-fit and association
  • observed counts -the no. of occurrences in each category observed in the sample
  • expected counts - the no. of occurrences in each category expected under the null hypothesis
  • χ2 - the test statistic represents the sum of the squared (and scaled) differences between observed and expected counts
  • degrees of freedom - determines the distribution’s shape and proportions
    • i.e. they are the number of values that are free to vary
  • goodness of fit test - tests whether a sample of frequency data came from a population with a specific, known distribution
  • continuous data - represents some measurement or score on a scale (e.g. reaction time)
    • answers question: how much?
  • categorical data - represents membership in a particular group or condition (e.g. control vs experimental group)
    • answers question: which one?
Interpret and report significance tests of χ2
  • ???
χ2 test of association
  • two variables → both categorical
  • data (in this context) - counts how many observations fall into each combinations of categories
  • use Fisher’s exact test (fisher.test()) - work under the assumption that for χ2 expected frequencies are greater than 5
    • statistical assumptions - a precondition that must be true for a statistical test to work as expected (if these assumptions are violated/not true, then the test may give inaccurate or misleading estimates or results)
  • association is not causation \n \n