Part 6: Statistics

Question 1

Lying with statistics:

Answer 1

The intentional misapplication of statistical tools.

Question 2

Statistical methodology:

Answer 2

Justification of the choice between statistical methods.

Question 3

Descriptive statistics:

Answer 3

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

Question 4

Inferential statistics:

Answer 4

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

Question 5

Stochastic hypothesis:

Answer 5

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

Question 6

Deterministic hypothesis:

Answer 6

A hypothesis all of whose implications are certain.

Question 7

Quantitative measure of measurement error:

Answer 7

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

Question 8

Error based statistics:

Answer 8

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

Question 9

Confidence in a hypothesis

Answer 9

The subjective estimation of the probability of a hypothesis.

Question 10

Fisher’s significance testing:

Answer 10

In other words, we have made a bunch of observations and we want to find out whether we should reject a certain hypothesis based on the data or not. For this, we calculate how probable the observed data would be if – i.e. under the assumption that – the hypothesis was true. If it is very improbable, then we should reject the hypothesis.

Question 11

Test statistic:

Answer 11

All possible outcomes of a test, and their respective probabilities.

Question 12

Sampling distribution:

Answer 12

A distribution over the possible outcomes of the test statistic.

Question 13

p-value:

Answer 13

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

Question 14

Significance level:

Answer 14

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

Question 15

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 what result is desired).

Question 16

Neyman-Pearson hypothesis testing:

Answer 16

The test begins by formulating two hypotheses that are mutually exclusive and jointly exhaustive. That is, one is the negation of the other. For example, we might set the H0 as the claim that the coin is not fair and the Ha, the alternative hypothesis, as the claim that it is fair. Either of them might be true, hence accepting one or the other might yield one of four possible outcomes. You either correctly accept the true H0, or correctly reject a false H0.

Question 17

Null hypothesis (H0):

Answer 17

The negation of the test hypothesis.

Question 18

Alternative hypothesis (Ha):

Answer 18

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

Question 19

Type I error:

Answer 19

Wrongly rejecting a true null hypothesis

Question 20

Type II error:

Answer 20

Wrongly accepting a false null hypothesis.

Question 21

Power of a test:

Answer 21

The probability of correctly rejecting a false null hypothesis.

Question 22

Bayesian statistics:

Answer 22

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

Question 23

Prior probability:

Answer 23

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

Question 24

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

Posterior probability:

Answer 25

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

Question 26

The problem of priors:

Answer 26

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

Question 27

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

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

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

The problem of old evidence:

Answer 30

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

Question 31

The problem of uncertain evidence:

Answer 31

Bayesianism does not take uncertainty about evidence into account.