LECTURE 1: basic concepts in statistics

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# LECTURE 1: basic concepts in statistics
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## FANR 6750 (Experimental design)
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.author[
### Fall 2022
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# outline

#### 1) What is statistics?

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#### 2) Statistics and the scientific method

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#### 3) Experiments and causal inference

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# what is statistics?

> The study of the collection, analysis, interpretation, presentation, and organization of data (Dodge 2006)

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> The science of learning from data (various)

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# why do we need statistics?

### Common tasks 
- Estimate unknown parameters

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- Test hypotheses

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- Describe stochastic systems

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- Make predictions that account for uncertainty

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# stats and the scientific method

#### Ways of learnings

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**Inductive reasoning**

- Often attributed to Francis Bacon (and others)

- Consistent observations -> general principle

- Problem: "confirmatory" observations can't disprove theory

- Example: I've only seen birds that fly :: all birds can fly
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**Deductive reasoning**

- Formalized by Karl Popper

- Theory -> predictions -> observations

- Based on *falsification*

- Example: All birds can fly :: penguins are birds :: penguins can fly
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# stats and the scientific method

#### Ways of learnings (real world)

1) Pattern identification (i.e., exploratory studies)
- Anecdotes  
- Correlations/visual analysis  
- Exploratory modeling (i.e., fishing)
    
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# stats and the scientific method

#### Ways of learnings (real world)

1) Pattern identification (i.e., exploratory studies)

2) Hypothesis formation
- Formed from patterns  
- Should focus on mechanisms ("because", "controls", "adapted to") 
- Should be falsifiable  
- Ideally > 1 alternatives

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# stats and the scientific method

#### Ways of learnings (real world)

1) Pattern identification (i.e., exploratory studies)

2) Hypothesis formation

3) Predictions
- If the hypothesis is true, what do you expect to see?  
- Focus on things **we can measure**
- More = better
- "associated", "correlated", "greater/less than"

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# stats and the scientific method

#### Ways of learnings (real world)

1) Pattern identification (i.e., exploratory studies)

2) Hypothesis formation

3) Predictions

4) Data collection
- Can be observational but ideally manipulative experiment  
- Sampling must be *designed* to answer question

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# stats and the scientific method

#### Ways of learnings (real world)

1) Pattern identification (i.e., exploratory studies)

2) Hypothesis formation

3) Predictions

4) Data collection

5) Models and testing  
- Model is mathematical abstraction of hypothesis
- Model used to "confront" hypothesis with data (via predictions)
- Draw conclusions: Does data support hypothesis?

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# stats and the scientific method

#### Example
1) **Pattern**: Trees at higher elevations are shorter than at low elevations

2) **Hypotheses**

3) **Predictions**

4) **Data collection**1

5) **Models**1

.footnote[[1] We'll get to these!]

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# causal inference

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# causal inference

#### Often, we want to know whether `\(x\)` influences `\(y\)`

- In other words, if we change `\(x\)`, will `\(y\)` change also (and by how much)?

- Harder than it seems! Why?

- Generally restricted to *manipulative* experiments

+ Well-designed experiments ensure that "treatment assignment is independent of the potential outcomes" (Gelman et al. 2021)

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# looking ahead

### **Next time**: Princples of estimation

### **Reading**: Quinn chp. 2.1-2.3