Week 6: Non parametric analysis from dicho

• 2x2 contingency table

  • used to determine wether the distribution of one variable is conditionally dependent (contingent) on the other variable
• 2x2 table

  constructed with the outcome or dependent variable in the columns and the exposure in the rows
• Chi square tests

  Goodness-of-fit

  independence

  Homogeneity
• Chi square

  • Non-parametric
  • Asymmetric Distribution
  • Strictly categorical data
  • Same names but distinct tests
• When to use chi square?

  • Categorical only
  • measures how expectations vs actual observed data
  • test relationships between categorical variables
  • test hypothesis about a distribution of observations in different categories
  • estimate how distribution of a categorical closely matches an expected distribution, or wether two categorical variables are independent of one another
• Assumptions of chi square test:

  1. The data is discrete

  2. The data is independent

  3. The data is normally distributed

  • sampling method is simple random sampling
  • under categorical
  • at least 5 of expected number of sample observations in each level of variable
• Goodness of fit test (one sample chi-square)

  • categorical data from claimed discrete distribution or not
  • expansion of one-proportion z-test
  • 2 or more categories
• Formula for chi square

  
• Test of independence

  • associatatiom between categorical data for 2 independent variables
  • determine whether two categorical variables are associated with one another in the population
  • chi square test of association between 2 variables
• Test of Homogeneity

  • if the distribution of a categorical variable is the same for each of several populations or treatments
  • if the researchers want to know if 2 or more different population have the same proportions of some characteristics
  • separately random sampling each subgroup
  • two or more independent subgroups
• Test of homogeneity

  • determines if two or more subgroups of a population hare the same distribution of a single categorical variable
• expansions of two-proportion z-test

  • if response variable only has 2 categories as outcomes comparing 2 groups
• test of homogeneity

  • if response variable has several outcome categories and comparing two or more groups
• Chi square test for paired and matched data

  • Mcnemar test
• Mcnemar test if before and after comparisons

  • To compare before and after findings in the same indivi
  • 1 degree of freedom
• Formula of Mcnemar for paired and matched

  
• McNemar test of matched data

  • frequently used in case control studies, where the cases nd controls are matched
  • cases and controls are matched based on their characteristics then compared for the presence or absence of a specific risk factor
• Fisher exact probability test

  • used when one or more of the expected counts in a 2x2 table is small (less than 2)
  • tedious to manually compute
  • uses statistical software
• Properties of Chi square distribution

  • asymmetrical
  • cannot be negative
  • as the degree of freedom increases, the chi square distribution approches a normal distribution
• Summary of chi square