Non parametric tests

Question 1

Parametric tests

Answer 1

makes assumptions about parameters of population distribution from which data is drawn:

Question 2

Features of parametric tests

Answer 2

Fixed parameters - normal distributions
Data is interval/ratio
Sample sizes must be sufficient (relative to design) because otherwise cannot tell if its normally distributed
Should not have significant outliers nor too many outliers

Question 3

Features of nonparametric tests

Answer 3

Has fewer assumptions
Data can be any level of measurement
Data can have non normal distributions
Sample size can be very small
And uneven

Question 4

Can parametric tests be robust enough even with moderate skew?

Answer 4

Yes if the sample size is large enough

Question 5

Parametric tests examples

Answer 5

Independent samples t test
Paired samples t test

Question 6

When is independent samples t test used

Answer 6

If we fit the criteria for doing a parametric test and:
We have a between-subjects design

Question 7

When is a paired samples t test used

Answer 7

If we fit the criteria for doing a parametric test and:
We have a within-subjects design

Question 8

non parametric test examples

Answer 8

Mann-whitney u
Wilcoxon signed ranks

Question 9

When do we use a mann whitney u test

Answer 9

If we do not fit the criteria for parametric test
And have between subjects design

Question 10

When do we use a wilcoxon signed ranks

Answer 10

If we do not fit the criteria for parametric test
And have within subjects design

Question 11

Non parametric tests are 95% Power efficient

Answer 11

95/100 goes where a non parametric test is ran (despite meeting criteria for parametric) you observe a statistically significant difference

Compared to if we had run a parametric equivalent

Question 12

Problem with non parametric tests

Answer 12

More likely to commit a type 2 error (falsely reject the null hypothesis when we shouldnt have rejected it)
Because of the 95% power efficient: we want to observe 100% a statistically significant difference
In that 5%: no significance meaning we reject it??

Question 13

What do all non parametric tests involve

Answer 13

Ranking the data from smallest to largest

Question 14

Steps of a mann whitney test

Answer 14

Across the whole data set (inc conditions) , every number is ranked
Calculate the U statistic for each independent group
Choose thr lowest one
Compare this U value to a table of critical values:
Obtain a threshold U value we need to beat based on sample size and also the alpha level

Question 15

Rules of ranking

Answer 15

smallest data gets value of 1
Work way up
If multiple data entries are the same, they share a midpoint of this rank

Question 16

U statistic

Answer 16

U for a singular group equals
R - [ n(n+1) ] /2
Where R = sum of every rank
n = number of participants of that singular group

Question 17

Obtaining threshold value for U

Answer 17

The table we get this value from is specific for level of significance e.g. the alpha

Question 18

How do we know if the U we obtained is significant?

Answer 18

If calculated U is less than or equal to threshold U we got from table at specific alpha level

Question 19

Mann whitney u test: when we reject the null/

Answer 19

If we obtain a U value from the table at our alpha that is from sample sizes
And the lowest, calculated U value is equal to or below it

Question 20

What does null assume ?

Answer 20

Medians will be the same because the populations are identical

Question 21

Wilcoxon signed ranks test stages

Answer 21

Calculate the difference between each participants score
RANK THE DIFFERENCE ignoring if pos or neg
and IGNORE if 0 difference
Sum up all POSITIVE DIFFERENCE’S ranks
Sum up all NEGATIVE DIFFERENCE’S ranks
Choose the lowest value = Calculated T statistic

Question 22

How to obtain a threshold for T statistic

Answer 22

Based on one/two tailed test:
And sample size, look up in table to obtain threshold

Question 23

When do we reject the null in wilcoxon signed ranks

Answer 23

If the calculated T statistic is lower than threshold T statistic