Hypothesis Testing

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Hypothesis testing I
Kevin Soo

Outline
• • • • Theory and the research process What is a hypothesis? Hypothesis testing Statistical models

Theory and the research process

Theory
• A belief
– Can be true or false – P (belief)

• A proposed/possible explanation for something
– ‘Some students do poorly at statistics because they have less exposure to mathematics’ – ‘Women don’t date me because I’m ugly’ – ‘Manchester United lost the Premier League because they struggled with injury all season’

Theory
• How do we test a belief/theory?
– Collect evidence/data – How probable is the belief/theory to be true in light of the evidence we have? • P (belief | data)

‘It will rain today’
• P (rain)
– Let’s say 0.5 (50% chance, guessing)

• Test the belief
– Look for rain clouds

• P (rain | no clouds)
– < 0.5 – Decreases our confidence in the belief/theory

‘It will rain today’
• P (rain)
– Let’s say 0.5 (50% chance, guessing)

• Test the belief
– Look for rain clouds

• P (rain | dark clouds)
– > 0.5 – Increases our confidence in the belief/theory

Scientific theories
• Theories predict and explain what will happen under certain conditions – Observe/test what happens under those conditions to see if theory predicted correctly – Established and accepted theories are those that have evidence supporting them • Predicted correctly

– Bad theories will have little evidence supporting it and will be discarded • Predicted incorrectly

Research process
• Theories tested via research over and over again
– Repeated experiments/studies – If data from studies consistent with theory, it is strengthened

• If theory is accepted, it leads to more research
– Generalizations for slightly different conditions
Theory

Experiment/
Observation

Data/
Evidence

Refined theory

What is a hypothesis?

Hypotheses
• A prediction (‘educated guess’) based on the theory being tested – In experiment, the prediction is the pattern of results that should support the theory

• Requirements
1. Logically consistent with theory 2. Empirically testable/falsifiable • Can the hypothesis be shown to be false?

3. Related to variables in study
• Shows relation to pattern of data in study

Theory-hypothesis
• ‘Some students do poorly at statistics because they have less exposure to mathematics’ • Hypothesis – Psychology students will score lower than actuarial science students in a statistics examination

Theory-hypothesis
• ‘Women don’t date me because I’m ugly’ • Hypothesis – If person X is given a choice to date me or Ryan Gosling, she will choose Ryan Gosling.

Theory-hypothesis
• ‘Manchester United lost the Premier League because they struggled with injury all season’ • Hypothesis – In a season where Manchester United has fewer injured players, they will have more points in the league.

Theory
• Anchoring & adjustment heuristic
– When estimating quantities, people do not have the ability to make specific estimates. They take a given value and adjust their estimates ↑ or ↓ from this starting point.

Hypothesis
• Study 1
– When asked to estimate the number of countries in Asia + Africa in relation to their body weight, heavier students will give higher estimates.

• Study 2
– When asked to bid for items at a price relative to their birth date, students born later in the month will give higher bids.

Hypothesis testing

Types of hypotheses
• Null hypothesis (H0)
– The effect (predicted by theory) is absent – ‘No difference between groups…’ – ‘No relationship…’

• Alternative hypothesis (H1)

– The effect (predicted by theory) is present – ‘Group 1 scores _____ than group 2 in _____’ – ‘There is a relationship…’

• Opposite sides of a coin

Types of hypotheses
• Another distinction for H1
Directional

Alternative
Hypotheses Null

Nondirectional

– Directional
• ‘Group 1 will score higher than group 2’

– Non-directional
• ‘There will be a...
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