Type One and Type Two Error

ProfJameson Statistics 4 Comments

The purpose of inferential statistics is to predict differences between groups in the general population by measuring the difference in a small sample.

Examples

  • Blood pressure lowering of two drugs: Whocaresapine vs Lowpressure
  • The rate of venous thrombosis in knee replacements prophylaxed with Digabigatran vs Goldiloxaparin

As you know, a p value is the probability that the observed difference is due to random chance. However there are two main types of errors you can make.

So….

Type One Error in statistics
You detected a difference in the sample when there truly is no difference in the larger population (oops)

  • This is like a false positive (also known as an alpha error)
  • Associated with alpha / p-value
    • Alpha is the highest ACCEPTABLE probability that the measured outcome was due random chance
        Standard value for alpha is 0.05, or 0.025 for a two-tailed test
  • the p value is the MEASURED probability that your outcome is due to random chance
  • If your p-value (measured) is less than alpha (highest acceptable) then the difference is considered to be unlikely to have occurred due to chance.
  • A type I error can only occur when your p value is less than alpha. However, as your p-value increases towards alpha it is more likely that you are committing a type I error.
  • The probability of random chance producing a difference is additive with multiple comparisons. The more things you compare, the more likely you are to commit a type I error.

Let’s do a fun example:

  • A new drug (LowStress is coming to market. During the testing period, LowStress was shown to make people happier than placebo. On placebo 15 % of people were happy. On LowStress, 22% of people were happy. The alpha was set at 0.05, and the p-value that LowStress made more people happy versus placebo was 0.04. This indicates that there is a 4% chance that more people were happier due to random events not related to LowStress.
  • An alpha value of 0.05 means there is a 5% probability that more people would be happy due to random chance and not LowStress, which is the standard acceptable value. Because the p-value of 0.04 is less than alpha we are believe that the results seen with LowStress were not due to random chance.
  • Notice : There is still a 4% chance (1 out of 25) that this difference was, in fact, due to random chance. If it is due to random chance , we have committed a type I error.

Type Two Error
You fail to detect a difference in the Sample when there truly is a difference in the Population

AKA false negative or a beta error
  • Beta is directly related to power (1-beta = power).
    • Acceptable standard for power is 80% (see 1 minute genus on power), therefore the acceptable standard for beta is 20%.
    • This means that there is a 20% chance that you will detect a difference when there is no difference or you are 80% confident that you would have detected a difference in the sample if it exists in the population
  • As power increases your risk of committing a type II error decreases
  • If your p value is statistically significant <0.05) then you had enough power !!! Even if the number in the study was less than originally ESTIMATED. It was only an estimation.

    IF your p value is statistically insignificant (>0.05) THEN

    Eitherthere is really no difference OR you committed a type II error.

    Let’s revisit our fun example:

    You had drastic cuts made to your research budget and could only enroll 30 people in each group (LowStress vs Placebo). You found that 15% of people on placebo were happy and 22% of people on Lowstress were happy. But the p value is 0.34. You found no difference. However, you have probably committed a Type II error due to the small study size (inadequate power)

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