Quotes of the day

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Quotes of the day

• Prediction is very difficult, especially about
  the future.
• Niels BohrDanish physicist (1885 - 1962)
• When a distinguished but elderly scientist states
  that something is possible, he is almost
  certainly right. When he states that something is
  impossible, he is very probably wrong.
• Arthur C. Clarke, Clarke's first lawEnglish
  physicist science fiction author (1917 - )

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What is hypothesis testing?

• Hypothesis-driven research
• A good hypothesis is one that can be tested
• A good experiment is one that unequivocally tests
  an hypothesis
• Most experiments are based on quantitative data.
  These require statistics for analysis

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Biologists and Statistics

• The drunk and the lamp post
• Suspicion How to lie with statistics
• Misuse gives stats a bad name
• Misuse of stats inappropriate test gives
  invalid answers
• Strategic planning in retrospect
• Statistical analysis should be part of
  experimental design.

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Why statistics some definitions

• Populations vs samples
• We rarely have the opportunity to assess a
  parameter in the entire population
• We sample the population and try to infer from
  the sample what would happen in the population.
• Example Interleukin 12 response in virus
  infected mice. We cant measure the response in
  all mice, so we sample the population.
• Eventually we try to extrapolate to relevant
  species.

The fundamental question How do we know if an
unknown sample is part of the population or if it
is part of a different population?
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Population parameters
N 5
8
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The sums of the differences between individual
observations and the mean is always 0.
How can we come up with a number that estimates
how variable the data are?
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The miracle of the square.
Variance
Standard Deviation
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Now lets sample that population
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Random sampling involves error in estimating the
population
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Population terms
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Quotes of the Day

• He can compress the most words into the smallest
  ideas of any man I ever met.
• Abraham Lincoln16th president of US (1809 -
  1865)
• Politics is not the art of the possible. It
  consists in choosing between the disastrous and
  the unpalatable.
• John Kenneth GalbraithUS (Canadian-born)
  administrator economist (1908 - 2006)

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What is an experiment?

• Types of studies
• Descriptive No experiment observation
• Correlation May need experiment
• Causality Always requires experiment
• To design an experiment, first need research
  hypothesis.
• This is different from statistical hypothesis

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Variables

• Types
• Independent
• Dependent
• Extraneous (nuisance) variables
• Classifications of variables
• Measurement variables
• Continuous
• Discontinuous
• Ranked variables (e.g. development stages)
• Attributes or nominal variables
• Typically collected as a frequency of occurrence.

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Sampling a population

• Problems with generalization
• Sampling procedure Random sampling and
  allocation
• Statistical analysis assumes random sampling
• Must distribute nuisance variables randomly among
  groups- avoid systematic error.

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Basic structure of experimental designs

• Between subjects
• Within Subjects
• Factorial

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Statistical hypothesis testing

• The null hypothesis
• States that groups are sampled from the same
  population
• Statistical analysis either accepts or rejects
  the null hypothesis.
• What do we mean by p lt 0.05?
• One tail vs. 2 tail hypotheses

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Types of error

• Type I reject a true null hypothesis
• Type II accept a false null hypothesis

Reject H0 Probability a Probability 1 - ß
Accept H0 Probablility 1-a Probability ß
H0 is true H0 is false
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Statistical power

• Probability of a type II error depends on the
  sample size and standard deviation.
• Common error accept null hypothesis based on
  under powered test.
• Solution more N
• Infinite N will not create significance. It will
  only make probability of Type II error smaller.
• More on power later.

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Experimental Designs

• Correlation studies
• Seeks to establish whether two or more variables
  are related to each other.
• Does not imply causality.
• Synaptic delay and 100 meter world record.
• Can provide a good initial observation to lead to
  mechanistic hypotheses.

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Experiments

• Independent and dependent variable
• Random assignment of individuals to groups.
• Experiment is designed to test an hypothesis.

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Planning an experiment

• Idea hypothesis and basic plan for experiment
• Variables
• Independent vs. dependent (how many of each?)
• Derived variables- be careful of self fulfilling
  prophecy.

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Planning an experiment

• Sampling
• Randomness of the sample unknown nuisance
  variables eg, animal vendor, season, time of
  day, etc
• Random assignment
• Matching
• Independence and degrees of freedom
• N vs replicates

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Experimental designs

• Between subjects design
• Each observation is independent of all other
  observations
• Within subjects design
• Each subject receives each treatment
• Advantage with inter-subject variability

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Experimental designs

• Factorial Designs
• Two or more factors
• Each factor may have multiple levels
• Main effects vs. interaction
• Mixed factorial designs
• Both between and within subjects factors