Sub-topic 2: A framework for testing models Flashcards
Week 1
MODEL (i.e. an idea about e.g. pattern/process/cause/effects in the world)
• Starting point in developing the framework to rigorously test this idea
• Derived from observation, theory, previous studies etc.
Yes.
ALTERNATE (Experimental) HYPOTHESIS (HA) • An effect/difference/change exists between observed groups/parameters etc. • Philosophically, impossible to prove a hypothesis ∴ logically can only disprove (falsify) HO
Yes.
NULL HYPOTHESIS (HO) • There is NO difference/effect/ change that supports the proposed model • “Falsificationist” in that we falsify this equivalence i.e. if we falsify HO, by inference, we must accept HA
Yes.
Example 1 Model: Bacteria causes meat to rot Hypothesis: Meat in a sterile jar will rot slower than meat in an open jar
Example 1 Model: Bacteria causes meat to rot Null Hypothesis: Meat in a sterile jar will NOT rot slower than meat in an open jar
Yes.
We need statistical tests because We can’t do our experiments (or collect our observations) in all places at all times The results of a study may vary from place to place and time to time (chance events, error, change over time) The results may depend on the particular sites or times or organisms sampled
Yes.
We use statistical tests To determine the probability that the results we got, could have occurred by chance alone If our results could have been found by chance, there is no reason to believe that anything else has happened Accept the null hypothesis If our results were unlikely to have occurred by chance, we have evidence of a biological process Reject the null hypothesis
Yes.
Rejecting the null hypothesis when it is true - The 5% significance level is set by convention - A 5% level means that a Type I error will occur in 5% of all tests when the null hypothesis is true - Altering the significance level alters the likelihood of making this type of error • A stricter level (α = 0.01) makes Type I errors less likely but Type II errors more likely • A looser level (α = 0.10) makes Type I errors more likely but Type II errors less likely
Yes.
Accepting the null hypothesis when it is false Definition • β = probability of accepting H0 when it is false; that is, concluding there is no effect when there actually is • (1 – β) = probability of rejecting H0 when it is false; that is, concluding correctly that there is an effect • (1 – β) = power Power is influenced by • Sample unit size • Sample unit arrangement Sample unit number
Yes.
Recap: Take home messages
• Estimation or hypothesis (model) testing or both!
- Estimate e.g. estimate size of stock, mean yield per hectare
- Model test e.g. does nitrogen affect plant growth? Does rainfall
influence breeding success?
• Using a methodical and iterative framework
- makes the process of testing ideas (models) methodical and clear
- is iterative and repeatable, with each iteration adding to previous
knowledge
• We need and use statistical tests because:
- Need them because we can’t observe everything all the time
- We use them to determine if what we see is by chance alone, or if
the effect is real/observable/detectable
• Incorrect decisions can be made (Type I and Type II errors)
- Type I (α) – the “false positive”
- Type II (β) – the “false negative”
Yes.
An idea about some aspect of the world, e.g. pattern/process/cause/effect The alternate/experimental hypothesis – i.e. a significant difference exists, thus supporting our proposed model The null hypothesis – i.e. no significant difference exists therefore we cannot support our model Reject HO – evidence exists to reject HO therefore model is deemed to be correct and proposed prediction is supported
Yes.
