Statistical Reasoning

Introduction to statistical reasoning

Klinkenberg

University of Amsterdam

2024-09-02

Statistical Reasoning

Course parts

Lectures: On campus / Online / Video recording
Preparatory Assignment: Submit and reflect 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	0
3x	2	2
4x	4	4
5x or more	5	5

See canvas for all the details.

Learning

Reasoning in statistics

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.

Null distribution

End

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