Lecture 6

Question 1

data, phenomena en theory bij diffusion model

Answer 1

data = response time, accuracy
phenomena = global slowing (in elderly)
theory = diffusion model says it is caution

Question 2

frequentism can be a useful tool for a particular set of data, limited purposes. but their purpose is fine. bayesian approach does not observe the limits of its territory because it claims too much. this is also a tool.

Answer 2

oke

Question 3

the concept of probability was obscure in history, only in the …

Answer 3

17-18th century -> people gained insight that it has lawfullness, in the long run!

Question 4

probability =

Answer 4

the relative frequency in which an event occurs

Question 5

wat dacht fisher

Answer 5

the insight that chance/probability should not be banned from research design, but used:
- random assignment (letting change allocate subjects to conditions)
- random sampling (letting change choose which elements from the population will be in your sample)

Question 6

if you use random sampling, then…

Answer 6

you know what the sampling distribution of your statistic is

= lawfull behaviour because you use probability

Question 7

wat zegt p(D|H) bijvoorbeeld

Answer 7

the probability of a data (D) occuring given that hypothesis (H) is true. this equals the relative frequency with which D would be observed if H were true and we repeatedly drew samples of the same size as the original one

Question 8

is p(D|H) real?

Answer 8

yes! it is real! not an opinion. therefore frequentist laws are not opinions. in that sense, frequentism is objective, it definitely has a value.

Question 9

wat doe je bij statistical inference

Answer 9

bij using p(D|H) judiciously, one can quantify uncertainty.
-> probability of observing data at least as extreme as d given that H is true. -> control the probability of type 1 and type 2 errors.

Question 10

wat is de standard null hypothesis

Answer 10

guarantees at most 5% of type 1 errors if you do this many times (at most, in 5% of the times you will incorrectly conclude that something works when it does not)

Question 11

advantages of the null hypothesis test

Answer 11

• null hypothesis tests can be constructed for ALL research designs
• the p-value always has the same interpretation
• correct execution of tests guarantees 5% type 1 errors at most

Question 12

p-value interpretation

Answer 12

how likely it is that your data would have occurred by random chance (i.e. if the null hypothesis is true).

if we were to repeat the experiment and the null hypothesis were true, then we would find such extreme deviations in a% of the cases.

Question 13

wat is een voorwaarde aan het gebruiken van de p waarde

Answer 13

wat je doet met het resultaat, ligt aan jou. jij moet een reden bedenken waarom jouw experiment geslaagd is (of niet) en waarom jouw alpha level rechtvaardigt is. je moet er echt over nadenken!

Question 14

wat is het verschil met de incorrecte interpretatie

Answer 14

the p value is the probability of finding these extreme kinds of data. it is not the probability that the null hypothesis is true!!!

Question 15

wat is de probability that the null hypothesis is true?

Answer 15

that probability does not exist. because probabiltiy is a long run frequency in a chance experiment, and the truth of hypotheses is not a function of a change experiment. an hypothesis is either correct, or not correct. it is not true one day and then false another (that is what probability is: on what side of the coin will it fall?)

Question 16

what do bayesians claim

Answer 16

they claim that they can actually distill p(H) from the data.

Question 17

what is the price of deriving p(H) from the data

Answer 17

you have to drop the objective frequentist definition of probability

Question 18

how do the bayesians do this (which formula)

Answer 18

p(H|data) = P(Data|H) * P(H)

Question 19

what does p(H) mean in Bayesian terms

Answer 19

the degree of belief one ought to attach to H

dus hoeveel je wil geloven in p(H)

Question 20

wat is kritiek op bayesian

Answer 20

wat bedoelen ze met the degree of belief one ought to attach to H? what does that mean? idk how to do that?

Question 21

dus wat is conclusie van frequentism

Answer 21

• p value has some downsides, waaronder de misinterpretatie
• frequentist tools are limited, but useful in some situation. bayesian tools are also limited and useful.
• bayesian results are at least as complicated: will they not generate the same problems?
• bayesian techniques are tools among other tools!
• human nature is the problem, not frequentism (ppl love magic bullets). bayesian statistics are often sold as remedies for poor use of statistical tools. (silly) -> we need to teach people how to reason with probabilities

Question 22

when should you choose bayes according to bayesians

Answer 22

• if you want to learn efficiently
• if you want to adjust plausibility assessments for hypotheses or parameters according to predictive performance

Question 23

is bayesian statistics subjective

Answer 23

yes, existing knowledge is applied to ask meaningful questions.
but it is not arbitraty: every bayesian with the same backgroun knowledge draws an identical conclusion

Question 24

waarom is het niet erg dat bayesian subjective is

Answer 24

alles in onderzoek is subjective; developing a theory,proposing predictions, designing an experiment

-> science is inherently subjective, but it is not arbitrary!

Question 25

statement wagenmakers

Answer 25

one statistical analysis must not rule them all!

Question 26

what are benefits from bayesian statistics

Answer 26

• Learning from prediction errors;
• Quantifying evidence, also in favor of H0;
• Adjusting knowledge on the go;
• Obtaining answers to meaningful questions.

Question 27

the current state of affairs

Answer 27

• The Bayesian paradigm is now mainstream.
• Psychology curricula lag modern statistics by decades.
• Philosophical discussions about chance are misused to hide the fact that teachers are too lazy to introduce Bayes into the curriculum.

Question 28

what is the conclusion of bayesian

Answer 28

• The Bayesian framework offers concrete, practical advantages, and this is increasingly being recognized.
• It is a missed opportunity that the Bayesian framework is undervalued in your statistical training.

Question 29

definition of p value: frequentism vs bayesian

Answer 29

fr = probability of observing the same or more extreme data assuming the the null hypothesis is true

ba= the probability of the null hypothesis (p(H))

Question 30

large samples needed: frequentism vs bayesian

Answer 30

fr= usually needed, when normal theory based methods are used

ba = not necessarily needed

Question 31

inclusion of prior knowledge possible? frequentism vs bayesian

Answer 31

fr = no
ba= yes

Question 32

nature of parameters in the model? frequentism vs bayesian

Answer 32

fr= unknown but fixed
ba = unknown and therefore random

Question 33

population parameter: frequentism vs bayesian

Answer 33

fr = one true value

ba = unknown and therefore random

Question 34

uncertainty is defined by: frequentism vs bayesian

Answer 34

fr = the sampling distribution based on the idea of infinite repeated sampling

ba = the probability distribution for the population parameter

Question 35

estimated interval: frequentism vs bayesian

Answer 35

fr= confidence interval, over an infinity of samples taken from the population, 95% of these contain the true population value

ba= credibility interval, a 95% probability that the population value is within the limits of the interval