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

- Alpha is the highest
- 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**

**Either**there is really no difference **OR **you committed a type II error.

Letâ€™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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