**STATISTICS FOR BEGINNERS**

3rd session

ISABEL FLORES

IMM OCTOBER 2015

3rd session

ISABEL FLORES

IMM OCTOBER 2015

**What is an Hypothesis?**

When we test an hypothesis we are looking at accurate decisions.

Alpha

Power

**Error type**

**Inferential Statistics**

**What is a p-value?**

P Value - probability of the mean of the sample being so far from the null hypothesis that it would be very unlikely to have picked this sample by chance.

When we are testing hypothesis we are really anlyisng evidence to try and make a decision that has the highest probability of matching reality.

Threfore there is always some space for error, and our decision is always done within some confidence interval .

P-value was introduced in 1920 by Fisher, with the sole objective of observing if the results were consistent with a random experience or if there was something special to look at. It was not deterministic, and it was just an indicator among others.

Balance between error type 1 and error type 2

It is very common to listen to people saying P=,05 is too much mistake let's make it smaller

If we make P smaller it becomes harder to reject the null hypothesis.

Therefore we have a greater risk of not rejecting the null when in reality it does not hold

Type 2 error becomes more common.

It is the equivalent to telling the patient - no cancer when in reality the cancer is there

Power depends on Pvalue (we choose), on how far the real average is from the null hypothesis (effect size), on SD and on the size of the sample.

The power should be higher than 80%, and in some cases 90%.

Every study should report the power , the P-value and the effect size (d).

Use inferential statistics only when:

You have so much information that you need to reduce

You are quite sure your sample is a good representation of the population you are studying.

A good sample is only possible if:

Randomly collected

Cases are independent among each other

It is neither too small or too big

The best application for calculating the power is G*Power at

http://www.gpower.hhu.de/

Effect size is the distance in SE from the average of our control group to the average of the experimental group.

**Power Analysis**

http://jama.jamanetwork.com/article.aspx?articleid=1853165

Should we routinely prescribe Mamographies to every women as a routine exam?

What is the Probability of Cancer given a positive mamography? Knowing that the average probability of Cancer is 1,9% (i.e 19 women in 1000 develop breast cancer)