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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Questions (1)

(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
1

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

6%

(1/16)

2

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

38%

(6/16)

3

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

19%

(3/16)

4

This is a statistically significant result

25%

(4/16)

5

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

12%

(2/16)

M 5 C

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