Transcript Tutorial 2a - hypothesis testing and coin toss

Data Handling & Analysis
BD7054
2012-2013
Andrew Jackson
Zoology, School of Natural Sciences
[email protected]
Introduction to Hypothesis
Testing
An Experiment Flipping coins
A simple experiment
• Question:
– Does adding weight to a coin make it unfair?
– Blu-tac added to head side
• Need to construct testable hypotheses
– The null hypothesis
Weighted coin toss
• Toss the coin 10 times
• What is the hypothesis about how you
think your system will behave?
– More likely to get heads
– Less likely to get heads
– Either more or less likely to get heads
• What are the corresponding null
hypotheses?
– That the coin is fair
Behaviour of a fair coin
0.15
0.10
0.05
0.00
Probability
– Toss an un-weighted
coin 10 times and repeat
0.20
• The model is a fair 50:50 coin
• How do we generate information about
how a fair coin behaves?
0
1
2
3
4
5
6
Number of Heads
7
8
9
10
Behaviour of weighted coin
• Compare the weighted coin against the
expected behaviour of a fair coin
• Question
– How likely is it that our observed coin is fair?
0.15
0.10
0.00
0.05
Probability
0.20
Behaviour of weighted coin
0
1
2
3
4
5
6
7
8
9
10
Number of Heads
0
1
2
3
4
5
6
7
8
9
10
0.001
0.01
0.04
0.12
0.21
0.25
0.21
0.12
0.04
0.01
0.001
Alternative hypotheses
• HA: coin is more likely to produce heads
– One-tailed test in right tail
• HA: coin is less likely to produce heads
– One-tailed test in left tail
• HA: coin is unfair (in either direction)
– Two-tailed test including both left and right
tails
P-values
• A p-value is the probability of your observed
data or more extreme being generated
according to the null hypothesis
• The less likely your data are, the less likely you
would accept the null hypothesis as being true
– We generally use a cut-off of p<0.05 to accept the
alternative hypothesis
• One or two tailed tests refer to where you
predict your alternative hypotheses to lie
before you do your experiment
Summary
• Science is about constructing experiments or
designing observations to test your ideas
about how the world works
• Hypotheses must be falsifiable
• Generally we construct null hypotheses
against which our alternative hypotheses can
be tested
• p-values tell us how likely it is our data came
from the null hypothesis and therefore allow
us to accept or reject it (H0)