Type One and Type Two Error

admin — Tue, 23 Nov 2010 20:27:15 +0000

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….

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
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.

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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Absolute vs Relative Risk Reduction

admin — Wed, 19 Aug 2009 20:06:05 +0000

Albert and I developed an acute interest in risk reduction at about 3500 feet.

Examples:
Example 1A:

Consider the benefit of using Coumadin for Stroke prevention in Atrial Fibrillation. Moderate risk patients on placebo have 8% risk of stroke in ONE year
Coumadin decreases that to 3% risk of stroke in ONE year
Quick !! Instinctively, what is the risk reduction? ….. 5% , right? That’s absolute risk reduction, NOT relative to anything else.

Relative Risk Reduction is RELATIVE to the baseline 8% so… 0.05/0.08 or 5% reduction /8% baseline = .62 or 62% relative risk reduction

Example 1B:
OK, now consider if there was a very high baseline risk of 93%

Suppose Coumadin decreased the risk to 88%
Quick !! The absolute reduction is? …. You’re right! 5% (the same as the first example)

So which is the most important? Absolute reduction or Relative reduction. Well, they each give you different kinds of information. I prefer the absolute risk reduction, but both are important. See also the Number Needed To Treat

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Too Many Meds Professional » admin

Type One and Type Two Error

Examples

So….

There are many phrases that have brought people here, such as....

Absolute vs Relative Risk Reduction

There are many phrases that have brought people here, such as....