6. Statistics

Question 1

What is ‘Lying with statistics’?

Answer 1

The intentional misapplication of statistical methods.

Question 2

What is statistical methodology?

Answer 2

Justification of the choice of using a particular statistical method.

Question 3

What is descriptive statistics?

Answer 3

In descriptive statistics, one aims to display data and conclusions accurately.

Question 4

What is inferential statistics?

Answer 4

In inferential statistics, one aims to draw a justified conclusion from data.

Question 5

What is a stochastic hypothesis?

Answer 5

A hypothesis whose implications come in the form of a probability distribution.

Question 6

What is a deterministic hypothesis?

Answer 6

A hypothesis all of whose implications are certain.

Question 7

What is a quantitative measure of measurement error?

Answer 7

The likelihood of a measurement error being made, presented on a quantitative scale.

Question 8

What are error based statistics?

Answer 8

Determining the probability of an observation given that a certain hypothesis is true.

Question 9

What does confidence in a hypothesis refer to?

Answer 9

The subjective estimation of the probability of a hypothesis.

Question 10

What is Fisher’s significance testing?

Answer 10

A method of statistical hypothesis testing developed by Ronald Fisher.

Question 11

What are test statistics?

Answer 11

Any quantity, computed from values in a sample, that is considered for a statistical purpose.

Question 12

What is a sampling distribution?

Answer 12

A distribution over the possible outcomes of the test statistic.

Question 13

What is a p-value?

Answer 13

The probability of observing an outcome at least as extreme as the observed outcome.

Question 14

What is a significance level?

Answer 14

A conventionally set level of p-values, below which the associated hypothesis should be rejected.

Question 15

What is p-value abuse?

Answer 15

Changing test setup, statistical method, or sample in order to make the p-value either higher or lower than the significance level, depending on the desired result.

Question 16

What is Neyman-Pearson hypothesis testing?

Answer 16

A method of hypothesis testing developed by Jerzy Neyman and Karl Pearson.

Question 17

What is the original hypothesis denoted as?

Answer 17

Hi - Some claim that you are interested in.

Question 18

What is the alternative hypothesis denoted as?

Answer 18

Ha - A hypothesis that due to logical necessity has to be true if the original hypothesis is false and vice versa.

Question 19

What is a Type I error?

Answer 19

Wrongly rejecting a true hypothesis Hi.

Question 20

What is a Type II error?

Answer 20

Wrongly accepting a false hypothesis Hi.

Question 21

What is the power of a test?

Answer 21

The probability of correctly rejecting a false hypothesis Hi.

Question 22

What is Bayesian statistics?

Answer 22

Posterior probability of a hypothesis is calculated based on the prior probabilities for the hypothesis together with the observed outcome, using Bayes theorem.

Question 23

What is prior probability?

Answer 23

The (estimated) probability of the hypothesis being true before the application of Bayes theorem.

Question 24

What are subjective degrees of belief?

Answer 24

The Bayesian view of what is meant by ‘probability’ - that probability is the subjective estimation of likelihood rather than a property belonging to the world.

Question 25

What is posterior probability?

Answer 25

The (calculated) probability of the hypothesis being true after the application of Bayes theorem.

Question 26

What is the problem of priors?

Answer 26

Bayesianism does not offer a clear way to determine prior probabilities.

Question 27

What is the principle principle?

Answer 27

A subject’s prior probability should be assigned on the basis of objective probability, if it is known.

Question 28

What is the principle of indifference?

Answer 28

A subject’s prior probabilities should be assigned equally to the possible outcomes, if there is no information about the objective probabilities.

Question 29

What is the problem of slow convergence?

Answer 29

If two subjects assign sufficiently different prior probabilities to the same hypothesis, it is possible that their respective posterior probabilities will not converge even though Bayes theorem has been applied to large amounts of data.

Question 30

What is the problem of old evidence?

Answer 30

The problem of determining what evidence that has been previously used to determine posterior probabilities.

Question 31

What is the problem of uncertain evidence?

Answer 31

Bayesianism does not take uncertainty about evidence into account.