Understanding Psychology as a Science

Question 1

Distinguish objective and subjective probability

Answer 1

Objective probability is the long run relative-frequency; the frequency of an event that you expect to get in the long run, subjective probabilities is the degree of conviction in a belief

Question 2

What do objective probabilities apply to? (what they don’t apply to also)

Answer 2

They apply to collectives, not singular events (so not hypotheses)

Question 3

If we symbolise data by D and a hypothesis by H, how is the probability of obtaining some data given a hypothesis written as?

Answer 3

P(D/H)

Question 4

What is a common misconception regarding the hypothesis and P(D/H)

Answer 4

P(D/H) is not the same as P(H/D) there is not probability of the hypothesis because it is simply true or false.

Question 5

What is the reasoning behind the Neyman and Pearson approach to hypothesis testing?

Answer 5

Statistics can’t tell us how much to believe a certain hypothesis. Thus, Neyman and Pearson set up decision rules for accepting or rejecting hypothesis in such a way that we will not often be wrong in the long-run.

Question 6

What is meant by the rejection region?

Answer 6

values of t so extreme (or more extreme) that the probability of obtaining a t in that region is equal to α, if H0 is true. If our obtained t falls in this region, we reject H0.

Question 7

What is meant by the alpha? (a)

Answer 7

the level of significance that is set in advance. It is the probability of obtaining a t value in the rejection region

Question 8

What is meant by the beta? (b)

Answer 8

the proportion of times we accept H0 when it is in fact false: p(accepting H0|H0 false).

Question 9

What is meant by power and how do we calculate it?

Answer 9

(1-b)

It is the sensitivity- the chances that we will find an effect given that H1 is true

Question 10

Why do larger sample sizes have more power?

Answer 10

Larger sample sizes have more power because they are better approximations of the population.

Question 11

What is specifity and how do we calculate it?

Answer 11

(1-a)

the probability of finding that there is no effect given that there is none: p(accept H0|H0)

Question 12

What is meant by stopping rules?

Answer 12

conditions under which you will stop collecting data for a study.

Question 13

Give a common rule for stopping rules

Answer 13

A common rule is to run as many participants as is traditional in that area. Some studies use the rule of collecting data until a significant result is found, this results in an alpha of 1.

Question 14

When doing three tests at a significance level of 0.05, what should the P level be lower than for each test?

Answer 14

0.05/3= 0.017

Question 15

Name 5 common misconceptions in NHST

Answer 15

• You have absolutely disproved H0 when p < α or absolutely proved it when p > α.
• You have found the probability of H0 being true.
• You can deduce the probability of HA being true.
• A 95% confidence interval has a 95% probability of containing the population value.
• You know the probability that you make the wrong decision if you decide to reject H0.

Question 16

What does the Duhem-quine problem state?

Answer 16

it is not possible to test a single hypothesis in isolation as every hypothesis relies on several other hypotheses, theories and assumptions about the world.

Question 17

What is meant by observations are theory-laden?

Answer 17

Expectations and assumptions about the world influence observations. Observations, in turn, influence hypotheses.

Question 18

In this regard of observations being theory laden, what does a good theory contain?

Answer 18

A good theory makes these expectations and assumptions visible.

Question 19

What is meant by the substantive hypothesis?

Answer 19

the hypothesis based on the previous research

Question 20

What is wrong with research and statistical hypothesis?

Answer 20

They are often not aligned with the substantive hypothesis

Question 21

What is required in order to connect scientific findings?

Answer 21

Theory

Question 22

What is the effect of a precise theory on falsification?

Answer 22

More precise theories require fewer data to be falsified.

Question 23

When are null hypotheses useful and how do they influence the hypothesis?

Answer 23

A null hypothesis is only useful for simple hypothesis testing and this influences hypotheses being formulated in such a way to fit null hypothesis testing.

Question 24

What form of faulty argument texhnique is this? Explain

Answer 24

Straw-man; No difference between experimental designs is very unlikely given that the test has enough power. Therefore, accepting a theory on the basis of rejecting a null is not a stringent theory.

Question 25

What is meant by Abduction?

Answer 25

Abduction is inference to the best explanation.

Question 26

What are the three forms of circle reasoning?

Answer 26

1. Repeating the premise.
2. The premise presupposes the truth of the conclusion.
3. The premise is logically or semantically equal to the conclusion.

Question 27

What is meant by equivocation?

Answer 27

This is putting forward a conclusion using vague or ambiguous terms.

Question 28

If the null hypothesis is true, then the p-values drift randomly, and can produce a significant result. how is this different to bayesian statistics?

Answer 28

In Bayesian statistics, the Bayes factor does not drift randomly but drifts towards the correct decision.

Question 29

In classical studies what three influences are there on the conclusion which is not the case for bayesian statistics?

Answer 29

the stopping rules (1), the timing of explanations (posthoc test or not) (2) and multiple tests influence the conclusion.

Question 30

Why can probability be assigned to a single hypothesis in bayesian statistics?

Answer 30

Bayesian statistics is a method of learning from prediction errors. It assumes that probability does not exist but only uncertainty, which has to be quantified in a principled manner.

Question 31

Why can bayesian statistics investigate P(H/D) rather than P(D/H)?

Answer 31

The data drive an update from prior knowledge to posterior knowledge.

Question 32

What can the bayes factor be seen as?

Answer 32

The Bayes factor can also be seen as the predictive
updating factor for the posterior belief. It is the ratio of likelihood where the likelihood refers to the probability of obtaining the data given the hypothesis

Question 33

Give bayes rule as an equation

Answer 33

P(H\D)=P(D\H)*P(H)\P(D)

Question 34

Does a high predictive updating factor in favour of the alternate hypothesis mean that the alternative hypothesis is better? Explain

Answer 34

The prior distribution determines the posterior distribution, therefore, a high predictive updating factor in favour of the alternative hypothesis does not necessarily mean that the alternative hypothesis is better. It only predicts the dataset X times better than the null hypothesis in this case.

Question 35

Give the strength of evidence which corresponds to each range of bayes scores

Answer 35

1-3; Anecdotal
3-10; Moderate
10-30; Strong
30-100; Very strong 
>100; Extreme

Question 36

When is the posterior belief and the bayes factor the same?

Answer 36

The posterior belief and the Bayes factor are the same if the prior belief is that the distribution is 50/50.

Question 37

What does statistical evidence refer to?

Answer 37

Statistical evidence refers to a change in conviction concerning a hypothesis brought about by the data.

Question 38

It is easier to detect the _____ of something than the _____ of something

Answer 38

Presence; Absence

Question 39

What does a bayes factor smaller than 1 mean?

Answer 39

A Bayes factor small than 1, provides evidence for the null hypothesis over the alternative hypothesis.

Question 40

What does a bayes factor of approximately 1 indicate?

Answer 40

that the experiment was not sensitive enough to differentiate between the two hypotheses. This is how power is incorporated into Bayesian statistics.

Question 41

What does the liklihood principle state?

Answer 41

The likelihood principle states that all the information

relevant to inference contained in data is provided by the likelihood.

Question 42

What does a hypothesis having the highest likelihood mean?

Answer 42

A hypothesis having the highest likelihood does not mean that the hypothesis has the highest probability of being true, it means that the data support the hypothesis the most.

Question 43

Distinguish between the p-value and likelihood in relation to a graph

Answer 43

In a distribution, the p-value is the area under the curve, whereas the likelihood is the height of the distribution at a certain point.

Question 44

Give three advantages to the Bayes factor

Answer 44

1. The Bayes factor provides a continuous degree of evidence without requiring an all-or-none decision (p-value).
2. The Bayes factor allows evidence to be monitored during data collection.
3. The Bayes factor differentiates between support for the null hypothesis (evidence for absence of an effect) and non-informative data (absence of evidence).

Question 45

Name 4 advantages to frequentist statistics

Answer 45

1. The p-value is objective as the probability of the data given the null hypothesis (P(data | hypothesis) is an objective probability.
2. Frequentist statistics also allows to control for Type I and Type II error rates.
3. Frequentist statistics are very practical as almost all research designs can use null hypothesis
   testing.
4. The p-value always has the same interpretation.

Question 46

Comment on the view of frequentists on the probability of a single event.

Answer 46

The probability of a single event (e.g. P(hypothesis)) does not exist according to frequentists.

Question 47

Name four practical advantages to bayesian statistics

Answer 47

1. Bayesian statistics allows for learning from prediction errors.
2. Bayesian statistics allows quantifying evidence in favour of a hypothesis.
3. Bayesian statistics allows adjusting knowledge while conducting research.
4. Bayesian statistics allows to obtain answers to meaningful questions (e.g. P(hypothesis|data)).

Question 48

What are the three types of distributions in bayesian statistics?

Answer 48

1. Uniform distribution
   This is a distribution where every value is equally likely.
2. Normal distribution
   This is a distribution where one value is most likely with the values on both sides of this value being equally likely as the distribution is symmetrical.
3. Half-normal distribution
   This is a distribution which is centred on zero with only one tail (e.g. positive or negative).