L3

Question 1

What are the 2 main features of a random binominal distribution?

Answer 1

1. The outcomes are independent - random independent error variables
2. They have a constant probability (coin flip has a constant probability of .5)
   * But you need a large enough sample to generate this probability accurately*

Question 2

What is the law of large numbers?

Answer 2

With many instances, chance evens out.

Events converge on their average probability.

Question 3

What is the law of small numbers?

Answer 3

With few instances, chance is lumpy. In the short run, anything can happen.

Question 4

The chance of getting all heads is much larger for

Larger or Smaller sample sizes?

Answer 4

Smaller

Question 5

The bigger the sample size, the more accurately you can estimate the actual probability you are interested in.

What law is this?

Answer 5

Law of large numbers

Question 6

What is the gamblers fallacy?

Answer 6

If something happens more frequently than normally in a short amount of time, the odds are that it should happen less frequently in the future (and vice versa)

Question 7

What is the “regression to the mean”?

Answer 7

If a variable is extreme on its first measurement, it will tend to be closer to average on its second measurement

and if it is extreme on its second measurement, it will tend to have been closer to average on its first

It is a regression to mediocrity

Question 8

Why should we be careful of jumping to causal conclusions when judging behaviour?

Answer 8

Regression to the mean and the law of large numbers mean that we need to be careful of attributing causal or systematic explanations for single observations

An increase or decrease in performance might simply be an example of regression to the mean

Question 9

What are random independent variables?

Answer 9

Variables are independent if knowing the value of one of them does not change the probabilities for the other one

• Many things influence measurement besides the variable of interest.*
• These are nearly always independent of one another*

Question 10

What is measurement error?

Answer 10

Regression is greatest with less precise measurement - where there is more variance

Question 11

What are the two types of experiments in regards to participants?

Answer 11

Between-Subjects and Within-Subjects

Question 12

Which experiment is “stronger”

Between-Subjects or Within-Subjects

Why?

Answer 12

Within Subjects

You can control for the random error that is introduced simply through the individuals differences when you assign people to different groups

Question 13

What is a Between-Subjects design?

Answer 13

Different participants are assigned to different levels of the IV

• Participants are “nested” in the different conditions of your experiment*
• (e.g., treatment, placebo, or control)*

Question 14

What is a Within-Subjects design?

Answer 14

The same participants are repeated in every level of your IV

Participants are ‘crossed’ with the different conditions of your experiment (e.g. fingerprints, faces and scrambled images)

Question 15

Why is within-subject designs ideal in experimental designs?

Answer 15

Eliminates random error variance due to using different subjects in different conditions

Question 16

Should you always try to manipulate IV in experimental designs?

Answer 16

Its almost always best to manipulate the independent variable if it is ethical to do so to remove randomness

Question 17

What is a matched-pairs design?

Answer 17

You match participants on particular variables across key conditions in the experiments

• e.g. comparing experts of novices in a particular domain*
• They might be paired on age, or level of education or each pair of expert and novice. Each expert is paried with a novice and are compared across each condition. You match the pairs based on variables that might explain the outcome*

Question 18

Why might you use a matched pairs design?

Answer 18

If you are not able to manipulate the IV of interest or do a within-subjects design

Question 19

What is the advantage of using a matched pairs design?

Answer 19

Allows us to control for random error variance

Potential differences in the population that might explain the results

Question 20

Potential disadvantages of Matched-Pairs Designs?

Answer 20

Might be difficult to find matched samples of participants (time consuming and resource intensive)

Question 21

What is the pre-post design?

Answer 21

We are measuring something in different points of time and seeing if there is a difference between those measurements

Question 22

When would we use a pre-post design?

Answer 22

When we don’t have complete control over the variable of interest

e.g. measuring participants knowledge before and after completing a course

Question 23

What is the weakness of the pre-post design?

Answer 23

No control group

no comparison that we can say “it is because of the original reason that the results happened”

Question 24

How do you account for the weakness of the pre-post design?

Answer 24

Have a control group or more than one control (important to have a placebo for example and a control which has no treatment)

Question 25

What are the two best types of experiments for **reducing random chance explanations**?

Answer 25

**Within-subjects design** and if that is not possible **paired-samples design.**

Question 26

*Measuring differences* How might you measure the difference between two groups when running an experiment?

Answer 26

Comparing to a mean

Question 27

How might you compare one mean to a theoretical number? (2 ways)

Answer 27

**One sample t-test** or **one-sample wilcoxon rank sum test**

Question 28

What are the assumptions made in a **one-sample t-test?**

Answer 28

Question 29

What are the assumptions of a **one-sample wilcoxon rank sum test?**

Answer 29

The observations are independent of one another Lower power (higher Type 2 error rate)

Question 30

What two types of analysis could we use to compare **two means?**

Answer 30

**Independent samples t-test** and **Mann-Whitney U test**

Question 31

What are the assumptions of the **independent samples t-test?**

Answer 31

Question 32

What are the assumptions of the **Mann-Whitney U test?**

Answer 32

1. **Independence**: you need two independent, categorical groupos that represent your independent variable 2. **Continuous or ordinal scales**

Question 33

Why would you use a Mann-Whitney U test?

Answer 33

Makes less assumptions about the data *Assumption about the scale we are using is more relaxed (can be continuous or ordinal)*

Question 34

What analysis should you use for a matched-pairs design or a within subjects design when you want to compare two means?

Answer 34

**Paired samples t-test** or **Wilcoxon signed rank test**

Question 35

What are the assumptions of a **paired-samples t-test?**

Answer 35

Question 36

What are the assumptions of the Wilcoxon Signed Rank Test?

Answer 36

1. **Dependence**: The independent variable consists of two categorical, 'related groups' or 'matched pairs'. ## Footnote **2. Continuous or Ordinal scales**

Question 37

What does the **normality assumption** mean for paired samples t-tests?

Answer 37

the **difference** between the scores of the paired groups are normally distributed

Question 38

Why would you use the **Wilcoxon signed rank test**?

Answer 38

It makes fewer assumptions than the paired samples t-test

Question 39

What is the final alternative to the t-test / wilcoxon test?

Answer 39

**Permutation test**

Question 40

What is a **permutation test**?

Answer 40

Resampling observed data without replacement many times in order to determine a p-value for our test Assuming our distributional nature of our data (assuming normality) we are actually building or estimating our distribution by shuffling our data around

Question 41

Describe the *p*-value in relation to the null hypothesis?

Answer 41

P-value: the probability of observing that data or more extreme when the null is true.