Hypothesis Testing
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
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