Term 2 L6: Non parametric tests

Question 1

when do you use a NPT?

Answer 1

the assumption of normality is not met; or

• the dependent variable is nominal or ordinal

Question 2

What is the NPT equivalent for a independent sample T-test?

Answer 2

Mann Whitney U

Question 3

What is the NPT for a repeated measures T-test?

Answer 3

Wilcoxon Signed Ranks test

Question 4

How you you NP measure independent samples?

Answer 4

Mann-Whitney U

Question 5

Why would you use a Mann-Whitney U?

Answer 5

the dependent variable is ordinal, or

if the dependent variable is interval/ratio but assumptions of the t-test for independent samples are not met.

Question 6

which assumptions need to be violated to do a MWU?

where in the SPSS output do you look to check?

Answer 6

Equality of variances

The “equality of variances” assumption does not seem to be met. It looks unlikely that the two samples have come from populations with the same variances.

Normality
There is slight skew in the Treatment as Usual group, and the values for kurtosis suggest non-normality in both groups.
(The sample sizes are too small to ensure a normal sampling distribution of the mean in the case that the population distributions are not normal).

Question 7

The MWU test is based on _______ scores

Answer 7

ranked

Question 8

What is the H0 and H1 for a MWU

Answer 8

The distribution of the dependent variables is the same for both groups

the distribution of the dependent variable is different for the two groups

Question 9

Ranking data - what happens when you get ties?

Answer 9

If two or more values are the same ties ranks are assigned where the tied rank is the average of the rank positions occupies by the tied values

Question 10

If the two groups have the same distribution, their ____ ____ should be roughly the same (or, if group sizes are very different, rank sums should be roughly proportional to group size).

If the two groups do not have the same distribution, their ____ ____ should be ____ ____ from one another.

Answer 10

rank sums

rank sums very different

median: if the medians of two samples differ
(considerably) , the population distributions of the two samples are unlikely to be the same.

Often, the difference between two distributions of ranks can be seen in the
However, it is possible for two distributions to be different despite
having the same (or very similar) medians…

Question 11

What is the MWU statistic called?

Answer 11

U

Question 12

THe logic of the WSRT:

If the treatment is effective, we expect most differences to be….

In this case, T+ would be…..

and the T– would be……

Hence the statistic T would be…..

a X T is evidence XX

If treatment has no effect….

in this case T+ and T- would be….

Answer 12

positive (i.e. we expect to observe weight gain in most girls).

large,

small.
large.

large T is therefore evidence against H0 .

we expect positive and negative differences to be approximately equal in number, and to be similar in size.

close together and relatively small.
A small T would therefore tend to lead us to retain H0. We evaluate T against its distribution under H0.

Question 13

Comparing two matched samples:

Answer 13

Wilcoxon Signed Ranks Test

Question 14

When to use the WSRT

Answer 14

alternative to the t-test for
matched samples. This test is appropriate if:
• the dependent variable is ordinal, or
• if it is interval/ratio but assumptions, for example normality, are
not met

Question 15

What is a typical H0 and H1 for a WSRT?

Answer 15

The Wilcoxon Signed Ranks Test tests the null hypothesis that the
distribution of difference scores is symmetric around the value 0.

The alternative hypothesis is that the distribution of difference scores
is not symmetric, and/or that it has a median that is different from zero.

Question 16

The WSRT is based on

Answer 16

The test is based on the ranks of difference scores.

Question 17

The difference scores are ranked……

Answer 17

The difference scores are ranked irrespective of their sign. Then the ranks of the
positive and negative difference scores are recorded separately.
Sum of positive Ranks: T+ = 108.5
Sum of negative Ranks: T– = – 44.5
SPSS takes the Wilcoxon T statistic to be the larger absolute value of
T+ and T–
. In this case, Wilcoxon T = 108.5.

Question 18

If the treatment is effective, we expect most differences to be X
T+ would be X, and T– would be X.
Hence the statistic T would be X. A X T is therefore evidence against H0
.
If the treatment has no effect, we expect positive and negative differences to be _________ _____ in number, and to be SIS .

In this case, T+ and T– would be ct and rs. A X T would therefore tend to lead us to retain H0
.
We evaluate T against its distribution under H0
. The larger the sample,
the closer that distribution is to the normal distribution (irrespective of
the distribution of difference scores). Using this normal approximation, we can compute an “asymptotic p-value” (called “Asymptotic Sig.” in
SPSS)

Answer 18

positive 
large 
small 
large 
large 
relatively equal 
close together 
relatively small

Question 19

Strengths and Lims of NPTs

CTR
SP

Answer 19

Non-parametric statistics “buy” freedom from assumptions, but at
the price of loss of information: when we convert exact
measurements to ranks, we are discarding information about specific
differences between individuals.

Non-parametric tests and statistical power:
• When the assumptions underlying parametric tests are met, then
parametric tests are usually more powerful than their nonparametric counterparts.
• When the parametric assumptions are not met, non-parametric
tests may be more powerful than their parametric counterparts.

Question 20

Comparing two matched samples:

Answer 20

Wilcoxon Signed Ranks Test

Question 21

Wilcoxon Signed Ranks Test is an alternative to the t-test for

Answer 21

matched samples.

Question 22

This WSRT test is appropriate if

Answer 22

• the dependent variable is ordinal, or
• if it is interval/ratio but assumptions, for example normality, are
not met.

Question 23

The WSRT is based on:

Answer 23

the ranks of difference scores

Question 24

How is WSRT ranked?

Answer 24

difference scores

The difference scores are ranked irrespective of their sign. Then the ranks of the positive and negative difference scores are recorded separately.

Note: two scores of ±1.0 are tied for ranks 2 & 3, so both get assigned the rank 2.5

Question 25

THe logic of the WSRT:

If the treatment is effective, we expect most differences to be….

In this case, T+ would be…..

and the T– would be……

Hence the statistic T would be…..

a X T is evidence XX

If treatment has no effect….

in this case T+ and T- would be….

Answer 25

positive (i.e. we expect to observe weight gain in most girls).

large,

small.
large.

large T is therefore evidence against H0 .

we expect positive and negative differences to be approximately equal in number, and to be similar in size.

close together and relatively small.
A small T would therefore tend to lead us to retain H0. We evaluate T against its distribution under H0.

The larger the sample, the closer that distribution is to the normal distribution (irrespective of the distribution of difference scores). Using this normal approximation,
we can compute an “asymptotic p-value” (called “Asymptotic Sig.” in SPSS).

Question 26

The larger the sample, the closer that distribution is…….

Answer 26

to the normal distribution (irrespective of the distribution of difference scores).
Using this normal approximation, we can compute an “asymptotic p-value” (called “Asymptotic Sig.” in SPSS).

Question 27

When we are in doubt whether the assumptions underlying parametric tests are met, we may want to….

Non-parametric statistics “buy” freedom from assumptions, but at the price of…..(loi)

Answer 27

use a non-parametric alternative instead.

loss of information: when we convert exact
measurements to ranks, we are discarding information about specific
differences between individuals.

Question 28

When the assumptions underlying parametric tests are met, then parametric tests are usually more _______ than their nonparametric counterparts.

• When the parametric assumptions are not met, ____________ may be more powerful than their parametric counterparts.
• It is important to base the decision about which test to use on a careful review of…..

Answer 28

powerful

non parametric tests

test assumptions