06 sep 2018

Inhoud

Experiment

Heads

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

Probabilities

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

Power and more

End