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Updated: Apr 5 2022

Statistical Hypotheses and Error

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  • Hypotheses
    • Null hypothesis (H0)
      • hypothesis of no difference
        • e.g., there is no link between disease and risk factor
    • Alternative hypothesis (H1)
      • hypothesis of difference
        • e.g., there is a link between disease and risk factor
  • Type I Error (False Positive)
    • Stating there is an association when none exits
      • incorrectly rejecting null hypothesis
    • α = probability of type I error
    • p = probability that results as or more extreme than those of the study would be observed if the null hypothesis were true
      • general rule of thumb is that statistical significance is reached if p < 0.05
  • Type II Error (False Negative)
    • Stating there is no effect when an effect exists
      • incorrectly accepting null hypothesis
    • β = probability of type II error
  • Power (True Positive)
    • Probability of correctly rejecting null hypothesis
      • power = 1 - β
    • Power depends on
      • sample size
        • increasing sample size increases power
      • size of expected effect
        • increasing effect size increases power
  • True Negative
    • Probability of correctly accepting null hypothesis
  • Confidence Interval
    • Range of values associated with a confidence level indicating the likelihood that the true population value of a parameter falls within that range
      • usually done with 95% confidence interval (2 standard deviations from the mean)
      • e.g., based on our study data, we are 95% confident that the average salary of a teacher lies between $30,000-45,000/year
    • Confidence interval is calculated from statistics generated from the studied data
    • Smaller confidence intervals suggest better precision of the data
    • Larger confidence intervals suggest less precision of the data
    • If confidence intervals of 2 groups overlap, there is no statistically significant difference
  • A Priori Versus Post Hoc Analysis
    • A priori comparisons
      • comparisons planned prior to data analysis
      • planning dependent on knowledge researchers have prior to conducting statistical tests
    • Post hoc analysis
      • researcher decides additional comparisons to make after viewing data
      • choices dependent on knowledge researchers have gained after conducting statistical tests
        • e.g., a test is run that says there is a difference between groups A, B, and C
          • post hoc analysis would involve comparing group A to group B, B to C, and A to C to see between which groups the difference lies
      • one potential hazard is an increased likelihood of spurious statistical associations
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