06 sep 2018

bit.ly/2j54A2U

## Emperical Cycle

• Observation Patiënt is showing post traumatic symptoms
• Induction Intherapy works
• Deduction $$H_0$$: P: fair coin → C: patiënt is balanced
• Deduction $$H_A$$: P: Unfair coin → C: patiënt is unbalanced
• Deduction $$H_A$$: P: data $$\neq$$ EV → C: is unbalanced
• Testing Choose $$\alpha$$ and Power
• Evaluation Make a decision

## Nul distribution

Let's analyse the null distribution of the results.

## Binomial distribution

${n\choose k}p^k(1-p)^{n-k} \\ {n\choose k} = \frac{n!}{k!(n-k)!}$

With values:

n = 10   # Sample size
k = 0:10 # Discrete probability space
p = .5   # Probability of head

## Testing

I landed 2 times head. Can we conclude that the therapy worked?

• As you can see from the distribution of healthy coins, we cannot conclude that by definition.

• What we can do is indicate how rare 2 is in a healthy population.

• We can see that a percentage of 5% is very rare.

## Testing

• Based on the null distribution we can see that the expected value (EV is 5.)
• We can now define the $$H_0$$ hypothesis: $$H_0 = 5$$
• What is the alternative hypothesis?
• The alternative hypothesis describes a situation where the therapy worked.
• We could say that the alternative hypothesis is not 5.
• $$H_A \ne 5$$
• We could also formulate our $$H_0$$ and $$H_A$$ more abstract:
• $$H_0:$$ the patient is balenced
• $$H_A:$$ the patient is unbalenced
• What criterium should we use to conclude that one would be unbalenced?
• In the social sciences this $$\alpha$$ criteria is often 5%.
• I tossed 2 times head. That is more frequent than 5%.
• Therefore, we conclude that our patient is probably healthy but we can never be sure.
• My coin could still be part of the unbalenced population.

## Alternative Distribution

But we have no clue of what this distribution could look like.

For now let's assume the probability of landing heads for my coin is .25

## $$H_0$$ and $$H_A$$ distribution

Not reject H0