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
    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.

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

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)
The relative risk though is different. 5 / 93 = 5.3% relative risk reduction

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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