lecture 10 - wilcoxon rank- sum test Flashcards

1
Q

when do we use a wilcoxon rank-sum test?

A

between-subjects tests of difference for two condition experiments with ordinal data

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2
Q

Within-subjects versus between-subjects tests

A

within-subjects tests
Each participant does both conditions in the experiment
e.g. measure reading comprehension while listening to Taylor Swift (the experimental condition) or in silence (the control condition) based on a test with 100 questions.
More generally paired data points are assumed to be related to each other
e.g. measure relationship happiness judged on a scale from 0 to 100 for each partner in a relationship where one partner is randomly assigned to go to loving kindness meditation classes and the other to kickboxing classes.
between-subjects tests
Participants in one condition are different than the other
E.g. measure relationship strength in terms of amount of time spent together for couples who have a dog versus couples who don’t.
E.g. Compare course satisfaction for psychology students versus engineering students

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3
Q

Why do within-subjects designs?

A

They control some noisy variability in terms of individual differences between participants
e.g. for the reading comprehension experiment, some people love Taylor Swift , but some can’t stand her….
Why not always do within-subjects designs?
Sometimes what happens in one condition fundamentally changes the person’s behaviour in the other (carry-over effects)
e.g. if listening to Taylor Swift makes you feel ill….
The frying pan effect

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4
Q

detecting outliers

A

this is important for t-tests as they are based on means and means are very susceptible to the impact of very extreme outliers

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5
Q

wilcoxon rank-sum test step 1

A

you take the data and find the number in the data that’s closest to zero - ignore minuses
eg 9 and replace that with a rank of 1

then next smallest is 13 but there are two in the data - you figure out what ranks they would have been if they were different (2 and 3) and take the average of those ranks = 2.5 and they would both be ranked 2.5

eg if you have 3 x 23s you find the average of their ranks they would be and that’s what rank they each have

you find the sum of each group of datas rank
and work out the number of data points for each group = N1 and N2
if groups have different numbers of participants in you make N1 the group with the smaller no of ptps

Ws is the sum of ranks for the smaller group - if the groups are same it doesn’t matter which one you pick

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6
Q

wilcoxon rank-sum test step 2

A

use a wilcoxon rank-sum test critical value table (p<0.05) to find if the Ws value is significant

use the N1 and N2 values to find the critcial value in the table

SPSS output is in notes - the value comes out under Mann-whitney test - conclusions of Mann-whitney u are similar to wilcoxon

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7
Q

non-parametric tests

A

solution to reducing bias when you have a small sample and can’t rely on the central limit theorem.

they make fewer assumptions than the linear model. they don’t assume a Normal distribution

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8
Q

how to find mean ws

A

w-bar s = n1 (n1 + n2 + 1)/ 2

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9
Q

how to find standard error of this test statistic

A

SEW-bar s = √n1n2 (n1 + n2 + 1 ) /12

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10
Q

calculating an effect size

A

we can calculate approximate effect sizes easily from the z-score for the test-statistic. The equation to convert a z-score into the effect size estimate (from Rosenthal, 1991), r, is as follow

r = z / √ N

in which z is the z-score that SPSS produces and N is the size of the study (i.e., the number of total observations) on which z is based

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11
Q

writing results of Mann-whitney u test

A

U = 35.50, z = -1.11, p= 0.280, r = -0.25

U = 35.50 = the test statistic
P = exact value of P
z = z score
r = effect size

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12
Q

summary

A

The Mann–Whitney test and Wilcoxon rank-sum test compare two conditions when different participants take part in each condition and the resulting data have unusual cases or violate any assumption.
Look at the row labelled Asymptotic Sig. or Exact Sig. (if your sample is small). If the value is less than 0.05 then the two groups are significantly different.
The values of the mean ranks tell you how the groups differ (the group with the highest scores will have the highest mean rank).
Report the U-statistic (or Ws if you prefer), the corresponding z and the significance value. Also report the medians and their corresponding ranges (or draw a boxplot).
Calculate the effect size and report this too

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