Maximum Likelihood

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Maximum Likelihood

• Lhypothesis data Prdata hypothesis
• Allows you to solve problems and test hypotheses
  that would be extremely difficult in any other way

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Example

• What proportion of this class has shoplifted an
  item worth more than 10?
• Flip a coin
• Dont tell ANYONE the result
• If heads, answer heads
• If tails, answer heads if youve shoplifted
  something, tails otherwise

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Pseudoreplication

• The error that occurs when samples are not
  independent, but are treated as though they are

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Example The transylvania effect
A study of 130,000 calls for police assistance
in 1980 found that they were more likely than
chance to occur during a full moon.
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Example The transylvania effect
A study of 130,000 calls for police assistance
in 1980 found that they were more likely than
chance to occur during a full moon.
Problem There may have been 130,000 calls in
the data set, but there were only 13 full moons
in 1980. These data are not independent.
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Pseudoreplication

• We are making a false claim about the number of
  independent samples in our data
• Very common mistake in biology
• Easiest solution use the average of all the
  pseudoreplicates

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Very small samples and assumptions

• Question from the class
• Say there's a test which you desire to carry
  out which is expensive and therefore you can
  afford only 2 treatments, each with two
  replicates. How would we go about analysing any
  difference, because are sample would be so small
  that we wouldn't be able to know if our data
  followed a normal distribution, right? and would
  these tests be worth carrying out since they
  would have pretty low power?
• Answer most scientists will just proceed with
  the test
• Interpret the results as if our assumptions are
  true (and we have no idea), then

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Very small samples and assumptions

• Example does the Earth have more species of
  living things than other planets in the solar
  system?
• Data Earth10,000,000-100,000,000
• Mercury, Venus, Mars, Jupiter, Saturn, Uranus,
  Neptune0 (as far as we know)

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Hypothesis testing

• Null hypothesis are usually very simple, and
  often known beforehand to be false
• You will eventually reject them if you have a big
  enough sample size

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Example

• Study on logging
• Ho The density of large trees is greater in
  unlogged versus logged areas

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Fewer trees
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Statistical significance ? Biological importance

• Statistically significant means P lt 0.05
• But it does not necessarily mean important!
• Likewise, nonsignificant results can be
  biologically important
• Its always useful to estimate a parameter or
  effect size, with a confidence interval

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Examples

• Some studies of thousands of children have found
  statistically significant associations of IQ with
  birth order
• These differences are on the order of 1-2 IQ
  points
• Such differences are not biologically important
  for individuals, and cant explain why your
  sister is smarter than you!

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Examples

• Large study of hormone replacement therapy showed
  no significant benefit of HRT to post-menopausal
  women
• Confidence interval for the effect size suggested
  that any possible undetected effect is likely to
  be extremely small

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Correlation does not require causation
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Correlation and Causation
Ice cream
Violent crime
Hot weather
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Data for many countries
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Confounding variables

• Variables that mask or distort the association
  between measured variables in a study
• Two approaches
• Try to measure them all
• Do an experiment

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Make a Plan

• Develop a clear statement of the question
• List possible outcomes
• Develop an experimental plan
• Keep the design as simple as possible
• Check for common design problems
• Is sample size big enough?
• Discuss with other people!

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The importance of controls

• Placebo effect - an improvement in a medical
  condition that results from the psychological
  effects of medical treatment
• Most people get better over time
• Humans like to please others, including their
  doctors
• Benefits of doctors beyond drugs
• Direct psychological effects on health

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The importance of controls

• Well-documented for pain relief
• Up to 40 of people report improvement in pain
  when given sugar pills
• Drugs and treatments must be analyzed in this
  context

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Head On stick of wax
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Im addicted to placebos. I could quit but it
wouldnt matter.
Steven Wright
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Mistakes

• Two types of mistakes
• Experimental mistakes
• Statistical mistakes (Type III error)

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Mistakes

• Two types of mistakes
• Experimental mistakes
• Statistical mistakes (Type III error)

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Experimental Mistakes
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Mistakes

• Two types of mistakes
• Experimental mistakes
• Statistical mistakes (Type III error)

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Statistical Mistakes

• 1/3 to 1/2 of scientific papers that use
  statistics make at lease minor mistakes
• 8 major mistakes - enough to alter the
  conclusions of the paper
• Be careful when reading papers
• Be careful with your own work!

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Data dredging

• The process of carrying out statistical tests on
  your data until you come up with a statistically
  significant result.

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P 0.05
second digit
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Beware multiple comparisons
Probability of a Type I error in N tests
1-(1-a)N
For 20 tests, the probability of at least one
Type I error is 65.
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Example - ESP
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Six or more correct answers you have ESP!
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Bonferroni correction
Anyone in the class have 8 or more correct?
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Garbage-in, garbage-out

• Small P-values do not rescue a poor measurement
• Example IQ test bias

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Aboriginal-based IQ Test

• 1.What number comes next in the sequence, one,
  two, three, __________?

MANY
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Aboriginal-based IQ Test

• 2. As wallaby is to animal so cigarette is to
  __________

TREE
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Aboriginal-based IQ Test

• 3. Three of the following items may be classified
  with salt-water crocodile. Which are they?
• marine turtle brolga
• frilled lizard black snake

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Fraud happens
Original
Haeckel's copy
(echidna embryos)
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Recent Fraud Example

• Woo Sek Hwang, human cloning
• Much of the data suspected to be fabricated

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Regression to the mean

• When repeated measurements are taken over time
• Individuals with extreme values for the first
  measurement tend to be nearer to the mean for the
  second measurement

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Regression to the Mean
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Regression to the Mean
The sophomore slump
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Publication bias
Papers are more likely to be published if Plt0.05
This causes a bias in the science reported in the
literature.
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Meta-analysis

• Compiles all known scientific studies testing the
  same null hypothesis and quantitavely combines
  them to give an overall estimate of the effect
  and its statistical properties
• This is a GREAT honours project