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Data Handling & Analysis BD7054 2012-2013

Data Handling & Analysis BD7054 2012-2013. Andrew Jackson Zoology, School of Natural Sciences a.jackson@tcd.ie. 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

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Data Handling & Analysis BD7054 2012-2013

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  1. Data Handling & AnalysisBD70542012-2013 Andrew Jackson Zoology, School of Natural Sciences a.jackson@tcd.ie

  2. Introduction to Hypothesis Testing An Experiment Flipping coins

  3. 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

  4. 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

  5. Behaviour of a fair coin • The model is a fair 50:50 coin • How do we generate information about how a fair coin behaves? • Toss an un-weighted coin 10 times and repeat

  6. 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?

  7. Behaviour of weighted coin

  8. 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

  9. 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

  10. 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)

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