Updated: 9/15/2019

Statistical Hypotheses and Error

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  • Hypotheses
    • Null Hypothesis (H0)
      • Hypothesis of no difference
        • i.e. There is no link between disease and risk factor
    • Alternative Hypothesis (H1)
      • Hypothesis of difference
        • i.e. 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

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(M2.OMB.18.1) In a study, 2 groups are placed on different statin medications, statin A and statin B. Baseline LDL levels are drawn for each group and are subsequently measured every 3 months for 1 year. Average baseline LDL levels for each group were identical. The group receiving statin A exhibited an 11 mg/dL greater reduction in LDL in comparison to the statin B group. Statistical analysis reports a p-value of 0.052. Which of the following best describes the meaning of this p-value?

QID: 210445

If 100 similar experiments were conducted, 5.2 of them would show similar results

5%

(1/20)

There is a 5.2% chance that A is more effective than B is due to chance

40%

(8/20)

There is a 94.8% chance that the difference observed reflects a real difference

15%

(3/20)

This is a statistically significant result

25%

(5/20)

Though A is more effective than B, there is a 5.2% chance the difference is due to a true effect

10%

(2/20)

M 5 C

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