Hypotheses
•Basic components of scientific theories
•Formulated as universal statements (concerning all objects of a given class)
•E.g. All mammals are viviparous, All plants contain chlorophyll
•Informative about the members of the given class (even without knowledge of a specific case): A
lion is a mammal -> it is also viviparous (
•Must be falsifiable = sensitive to empirical observations, which may demonstrate it is false
•A single contradictory observation can be used to reject a hypothesis no matter how many
observations support it
•Empirical singular statement – not informative beyond the
•No hypothesis can be demonstrated universally true
•Science is a process of rejecting old hypotheses and replacing them with new ones which explain
reality better
•
Obsah obrázku obraz, savec, skica, kresba Popis byl vytvořen automaticky
Platypus is an oviparous mammal.
Obsah obrázku venku, květina, červená, území Popis byl vytvořen automaticky
Rafflesia arnoldii and Lathraea squamaria are parasitic plants containing no chlorophyll.

Statistical hypothesis testing
•Empirical evidence mostly comes from measurements of quantitative data
•Statistics quantifies the disagreement between a null hypothesis (H0) and empirical observations
•Measured by a test statistic
•E.g. χ2, t, F-ratio
•Test statistics have a known probability distribution
•Allows computing the p-value  = Type I Error probability (probability of making an error if
rejecting the H0)
•Acceptable error typically 0.05 (5%)
•Shape of the distribution depends also on the degrees of freedom
•These depend on the complexity of the system and/or number of observations
•
•
•
•
Reality
H0 is true
H0 is false
Our Decision
Reject H0
Type I Error
Ok
Not reject H0
Ok
Type II Error
Possible outcomes of hypothesis testing by statistical tests. H0 = null hypothesis
•Classical biostatistics quantifies precisely only the Type I Error
•Hypotheses cannot be confirmed!
•A non-significant test means that empirical evidence is not sufficient to reject the H0

Pattern detection
•Special cases when H0 = 0 (no effect, independence)
•Generic null hypotheses can be converted to pattern detection problems by subtracting hypothesis
expectations from observed data
•Generally easy to compute
•Biology is still largely exploratory science
•many biological problems have the pattern-detection nature
•

Goodness of fit test