Statistical analysis

  • steps
    • Define hypothesis and plan research design
      • Define hypothesis
      • Research design
        • experimental design
          • directly influence variables
          • can assess a cause-and-effect relationship
        • correlational design
          • only measure variables
          • can explore relationships between variables
        • descriptive design
          • only measure variables
          • can study the characteristics of a population or phenomenon
    • Collect data from a sample
      • sampling type
        • probabilistic sampling for parametric testing
        • non-probabilistic sampling for non-parametric testing
      • create an appropriate sampling procedure
        • calculate sample size
          • significance level
          • statistcial power
          • expected effect size
    • Summarize data with descriptive statistics
      • data inspection
      • measure central tendency
      • measure variability
    • Test hypothesis or make estimates with inferential statistcis
      • point estimation
      • hypothesis testing
      • interval estimation
    • Interpret results and draw conclusions

Experimental design

  • experimental unit
    • the individual or group of individuals that are the subject of the experiment
  • experimental variable
    • the variable that is manipulated by the experimenter
  • control variable
    • the variable that is held constant by the experimenter
  • independent variable
    • the variable that is manipulated by the experimenter
  • dependent variable
    • the variable that is measured by the experimenter
  • experimental group
    • the group of individuals that are exposed to the experimental variable
  • control group

Sampling

  • calculate sample size - significance level - statistcial power - expected effect size

Hypothesis testing

  • one-group
    • z-test
    • t-test
  • two-group
    • z-test
    • t-test
    • Welch’s t-test
  • three-group
    • one-way ANOVA
    • two-way ANOVA
    • ANCOVA
      • to determine if there is a statistically significant difference between three or more independent groups after accounting for one or more covariates.
      • The covariate(s) and the factor variable(s) are independent
      • The covariate(s) are continuous
      • Homogeneity of variance
      • Independence of observations
      • No extreme outliers
      • Normal distribution of the dependent variable in each group
    • MANOVA: multivariate analysis of variance
      • identical to ANOVA except it uses two or more response variables
      • one-way
      • two-way
    • MANCOVA: multivariate analysis of covariance