Statistical Reasoning

Null Hypothesis Testisn

Klinkenberg

University of Amsterdam

2024-02-05

Course structure

Course parts

  • Lectures: On campus / Online / Video recording
  • Preparatory Assignment: Submit in Testvision and Reflection in canvas
  • Tutorials: For your support and in class assessment
  • Exam: Knowledge and skills

in class assessment

Grading

\[\text{Final grade} = 0.9 \times \text{exam grade} + 0.1 \times \text{credit points}\]

  • Exam
  • Credits for
    • Tutorial participation
    • Preparatory assignment

Credits

You get 10 at the start of the course.

Number of times missed Deduction for TU Deduction for PA
1x 0 0
2x 0 2
3x 2 3
4x 4 4
5x or more 5 5

See canvas for all the details.

Learning

Reasoning in statistics

Source: ARTIST

Statistical Literacy

  • Knowledge (Basic understanding of concepts)
    • Identify
    • Describe
  • Skils (Ability to work with statistical tools)
    • Translate
    • Interpret
    • Read
    • Compute

Statistical Reasoning

  • Understanding
    • Explain why
    • Explain how

Statistical thinking

  • Apply
    • What methods to use in a specific situation
  • Critique
    • Comment and reflect on work of others
  • Evaluate
    • Assigning value to work
  • Generalize
    • What does variation mean in the large scheme of life

Empirical Cycle

By Adriaan de Groot

The components

  • Observation
    • Idea for hypothesis
  • Induction
    • General rule
    • Hypothesis
  • Deduction
    • Expectation / Prediction
    • Operationalization
  • Testing
    • Test hypothesis
    • Compare data to prediction
  • Evaluation
    • Interpret results in terms of hypothesis

Explained by Annemarie Zandscholten

Experiment

Video registration

Heads

bit.ly/2j54A2U

Emperical Cycle

  • Observation Patiënt is showing post traumatic symptoms
  • Induction Can we diagnose PTSD
  • 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

Null distribution

Let’s analyse the null distribution of the results.

Google sheet

Distributions

What is the difference between

  • Population distribution
  • Sample distribution
  • Sampling distribution

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 PTSD?

  • 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.

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 PTSD is pressent.
  • 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.

Null distribution

End

Contact

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