Term 2 L6: Non parametric tests Flashcards
when do you use a NPT?
the assumption of normality is not met; or
• the dependent variable is nominal or ordinal
What is the NPT equivalent for a independent sample T-test?
Mann Whitney U
What is the NPT for a repeated measures T-test?
Wilcoxon Signed Ranks test
How you you NP measure independent samples?
Mann-Whitney U
Why would you use a Mann-Whitney U?
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.
which assumptions need to be violated to do a MWU?
where in the SPSS output do you look to check?
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).
The MWU test is based on _______ scores
ranked
What is the H0 and H1 for a MWU
The distribution of the dependent variables is the same for both groups
the distribution of the dependent variable is different for the two groups
Ranking data - what happens when you get ties?
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
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.
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…
What is the MWU statistic called?
U
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….
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.
Comparing two matched samples:
Wilcoxon Signed Ranks Test
When to use the WSRT
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
What is a typical H0 and H1 for a WSRT?
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.
The WSRT is based on
The test is based on the ranks of difference scores.
The difference scores are ranked……
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.
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)
positive large small large large relatively equal close together relatively small
Strengths and Lims of NPTs
CTR
SP
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.
Comparing two matched samples:
Wilcoxon Signed Ranks Test
Wilcoxon Signed Ranks Test is an alternative to the t-test for
matched samples.
This WSRT test is appropriate if
• the dependent variable is ordinal, or
• if it is interval/ratio but assumptions, for example normality, are
not met.
The WSRT is based on:
the ranks of difference scores
How is WSRT ranked?
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
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….
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).
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).
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)
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.
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…..
powerful
non parametric tests
test assumptions
