Statistics

Question 1

Contextual info

Demo slide

[Marks/Points required

Topic/Week

Question 2

What is Cohen’s d

Statistics 6

Answer 2

– A measure of distance between two condition means which takes variability into account

Question 3

How do you assess difference between 2 conditons.

Statistics 6

Answer 3

• Calculate and compare descriptive statistics
  – Means, medians, s.d.’s, confidence intervals
• Calculate “effect size” using Cohen’s d
• Use some kind of inferential test based on known probability distributions

Question 4

What is the range of Cohens d and what can be infered from the value

Statistics 6

Answer 4

0 - 1
* 0.2 = small effect size (around 85% overlap)
* 0.5 = medium effect size (around 67% overlap)
* 0.8 = large effect size (around 53%)

Question 5

What are we trying to do when we are hypothesis testin for 2 population means

Statistics 6

Answer 5

figuring out if they have significantly different means

Question 6

How do you calculate sample mean difference

Statistics 6

Answer 6

D = Ma - Mb
Difference = Sample mean A - sample mean B

Question 7

What would the result be for sample mean difference Assuming the null is true.

statistics 6

Answer 7

The difference between the two means is 0.

Question 8

There is a population of left handed people and right handed people.

In a task involving throwing darts, what would be a hypothesis that favours left handed people in an independent t-test testing the difference between means in 2 conditions.

S6

Answer 8

Left-handed people will be more accurate in a task involving left-handed dart throwing at a target than right handed people doing the same task

S6

Question 9

What are the two types of 2 sample T tests and when are they used

s6

Answer 9

– Related (or paired or repeated measures) t-test * Use when participants take part in both conditions WITHIN PARTICIPANTS DESIGN
– Independent t-test * Use when participants perform in only one of the two conditions BETWEEN PARTICIPANTS DESIGN

Question 10

What is the trick for converting Two paired samples means into one sample

S6

Answer 10

Taking the difference between the paired data

Question 11

Imagine you have reason to believe that attainment in some school district varies w/ left/right handedness and decide to test this idea.

Data for left:
Mean = 24.00
S.d = 12.20
n = 30

Data for right:
mean = 16.5
s.d = 11.8
n = 30

Decided on hypotheses youre testing against, Work out whether you are using the T or Z score and, and reach a conclusion on your decided hypotheses.

4 mark qustion , do the question

S6

Answer 11

• Unpaired T-test
• root (esea^2 + eseb^2)
• T = 2.42
• as N = 30 for both samples and 2 sample test –> 2N -2 = 58
• 2.42 > 2.392 therefore significant evidence for difference between levels of attainment between lefts & rights

You need to use the table Obvs

Question 12

What is Correlation

Statistics 7 - Correlation & Pearsons R

Answer 12

relationship between 2 variables

Question 13

Are correlated variables independent or non-independent

S7

Answer 13

Non-independent

Question 14

How can causality be inferred from correlation?

S7

Answer 14

Trick question - you cant infer causality from correlation

Question 15

What is covariance

S7

Answer 15

A measure of how much two variables vary together

Question 16

What do High covariance and low covariance indicate?

S7

Answer 16

High covariance = scores for one variable change, other variable will also change in a predictable manner
Low covariance = changes in one variable are not accompanied by a predictable change in the other variable

Question 17

What does positive covariance indicate?

S7

Answer 17

higher than average values of one variable tend to be paired with higher than average values of the other variable

Question 18

What does negative covariance indicate?

S7

Answer 18

that higher than average values of one variable tend to be paired with lower than average values of the other variable.

Question 19

What does zero covariance indicate?

S7

Answer 19

if the two random variables are independent, the covariance will be zero
- does not necessarily mean variables are independent, could just be indicative of a non-linear relationship

Question 20

What is pearsons R

S7

Answer 20

Shared variance/ total variance

Question 21

what do the scores of pearsons r indicate

Answer 21

0 < r < 1 = imperfect positive correlation
-1 < r < 0 = imperfect negative correlation
R ~ 0 = low correlation

Question 22

What are the steps of using Null Hypothesis significance testing for pearsons R

S7

Answer 22

1- Formulate hypothesis
Null - no correlation
Research 1 - (1 tailed) there is a positive correlation
Research 2 (1 tailed) there is a negative correlation
Research 3 (2 tailed) there is a correlation (does not commit to a direction)
2 - get data
3 calculate P value
4 - reject null

Question 23

What does the P value of pearsons R tell you?

S7

Answer 23

the probability that the correlation coefficient could arise by chance assuming the null is true

Question 24

What are some of the limitations of an extreme Pearsons R?

S7

Answer 24

not tell you there is necessarily a correlation between your variables, it could be really really really unlikely but still occur

Question 25

What is the difference between a parametrci and non-parametric tests

Statistics 8 - Non parametric hypothesis tests

Answer 25

• Parametric tests make certain important assumptions about populations from which data are sampled
• Non-parametric tests make far fewer assumptions about populations from which data are sampled

Question 26

What are some of the common testing assumptions of parametric testing.

S8

Answer 26

– Populations from which samples are drawn should be normally distributed
– Variances (s.ds) of the populations should be approximately equal
– No extreme scores (since these have a big impact on the estimated sample statistics)

Question 27

What are the benefits of using parametric testing if it features so many assumptions

S8

Answer 27

• ## Typically more powerful than other other approaches

Question 28

Why use non-parametric testsing if its less powerful

S8

Answer 28

– Because sometimes the assumptions of parametric testing are violated
– In this case we can almost always at least try a non- parametric alternative

Question 29

What are some exmaples of non -parametric tests

S8

Answer 29

• mann- whitney U test
• Wilcoxon signed rank test
• Spearmans Rho
• 2x2 chi square test
• 1 variable chi square test

Question 30

What is the Mann-Whitney U test

S8

Answer 30

a Non-parametric alternative for the independent t-test

Question 31

How would one conduct a Mann-whitney U test

S8

Answer 31

• create a research hypothesis
  have an independent groups design
• calculate the smallest possible sum of ranks,
• calculate the actual sum of ranks
• subtract the smallest possible sum of ranks from the actual sum of ranks,
• the Mann -w hitney U is the smaller of the two (if you have to variables)
• compare P value to 0.05, accept/reject null, conclusive statement

Question 32

What is the wilcoxon signed rank test

S8

Answer 32

a Non-parametric alternative for the paired/related test

Question 33

What is Spearmans Rho

S8

Answer 33

A non-parametric alternative to Pearsons R
Used when the assumptions required for pearson’s r have not been met

Question 34

What would you have to do in order to conduct a spearmans rho test

s8

Answer 34

• Convert scores to ranks
• Calculate difference in ranks
• Square the difference
• Calculate spearman’s rho using formula

Question 35

If the ranks are inversly related, what value of Spearmans rho would you get

S8

Answer 35

-1

Question 36

If the ranks are perfectly related what value of pearsons R would you get

S8

Answer 36

1

Question 37

What are some limitations of Spearmans Rho

S8

Answer 37

The given formula fails whenever we have tied ranks

Question 38

What is a 1-variable chi square test used for

S8

Answer 38

Can be used to assess whether observed frequencies in categories are different from what might be expected
Might expect equal distribution or pattern in frequencies