Lecture 6 Flashcards
What do frequentists think probabilities are?
Long run behaviour of random processes (relative frequency with which an event occurs)
Frequentists believe chance should not be banned from research, but used, who had this insight and give two examples in which this is used today
Ronald Fisher
Random assignment and random sampling
What is the consequence of using random sampling?
You know what the sampling distribution of your statistic is
What does P(D!H) mean in the context of frequentist ideas? Not just the definition, the idea behind it
Prob of a data D occuring given the truth of hypothesis H. Aka, relative frequency with which D would be observed if H were true and we repeatedly drew samples of the same size
What do frequentists believe about P(H!D)
It is not a true and real probability (it is simply a yes or no, and not a long run probability)
Also, P(D!H) does not equal the probability that the H0 is true
What can one use P(D!H) for (frequentists)?
Quantify uncertainty and thus control the probability of Type I and Type II errors
What are advantages of the null hypothesis? (3)
Can be constructed for virtually all research designs.
p-value always has the same interpretation,
correct execution of test gaurantees 5% of Type I errors at most
How does one interpret the p-value?
If H0 is true than the probability of observing this or a larger deviation from the null would be X probability
Bayesian is subjective, however what is the argument used to highlight that subjective does not equal arbitrary?
Many things in science are subjective (i.e. developing a theory, proposing predictions, designing an informative experiment)
What are the practical benefits of Bayesian?
Learning from prediction errors
Quantifying evidence (over time)
Adjusting knowledge on the fly
Obtaining answers to meaningful questions
What do bayesians think probability is?
Reasonable expectations representing a state of knowledge or a quantification of personal belief
