5. Parametric and Non-Parametric Data

Question 1

Parametric data:

Answer 1

These are quantitative data that have a normal (Gaussian) distribution.

In such a distribution the mean (average of all the results), the median (the
value above and below which contains equal numbers of results) and the mode (the
most frequently occurring value) are all the same

The variation around the mean is given by the variance,
σ2, the square root of which is the standard deviation (SD), σ.

Question 2

Non-parametric data:

Answer 2

these do not have a normal distribution and the typical bellshaped
curve is replaced by one which may, for example, be skewed in either
direction or may be bimodal (with two peaks). The data can sometimes be transformed
mathematically so that they assume a normal distribution and can be
analyzed by parametric tests. This may be desirable because parametric statistical
tests are more powerful than non-parametric.

Question 3

SD:

Answer 3

this provides a convenient way of describing the spread around the mean, with
68% of a population falling within 1 SD, 96% within 2 SD, and 99% within 3 SD
of the mean.

Question 4

Standard error of the mean (SEM):

Answer 4

this is used to determine whether the mean of the sample
reflects the mean of the population.

It is calculated by dividing the standard deviation by the square root of the degrees of freedom (SEM = SD/√n).

Question 5

Confidence intervals

Answer 5

Concept is linked to the SEM.

A sample mean will lie beyond 1.96 SEs only 5% of the time,
and so we can be 95% confident that the sample
mean does reflect the population mean

They have the advantage that they are expressed in the same units as the measurements,
rather than as a probability value.

Question 6

Parametric tests

Answer 6

these include Student’s t-test and analysis of variance (ANOVA).

ANOVA and not the t-test should be used if there are more than two groups. The
data are considered paired if they derive from the same patient

For example, blood
pressure measurements before and after laryngoscopy would be analyzed using a
paired t-test

Question 7

Non-parametric tests

Answer 7

these are applied to quantitative data which do not have a normal distribution.

These include the Wilcoxon signed rank test for paired data and
the Mann–Whitney U test for unpaired data. If there are more than two groups, then
the corresponding tests are the Friedman (paired) and Kruskal–Wallis (unpaired).

Question 8

Qualitative data:

Answer 8

these data (for example, ASA grades, pain scores, operation type) are usually analyzed using the Chi-squared test

Question 9

You may be asked what statistical tests you might use in a particular trial, for example,
in a comparison of two anti-hypertensive agents

Answer 9

These are quantitative not qualitative data, and are likely to be normally distributed

The data may be unpaired if two groups of patients are being studied, but will be
paired if the anti-hypertensive drugs are being given sequentially to the same
individuals.

An appropriate test, therefore, would be Student’s t-test (paired or unpaired as
discussed), or ANOVA (also paired or unpaired).

A P value of less than 0.05 may be the level at which the null hypothesis is disproved
(i.e. confirming that there is a difference between the treatments), but this means
nevertheless that there is up to a 5% probability that this observed difference could
have arisen entirely by chance. This is the type I or alpha error (false positive).

Question 10

Levels of evidence

Answer 10

I:
Evidence from at least one review of multiple randomized controlled trials (RCTs).

II: evidence from at least one well-designed RCT.

— III: evidence from well-designed trials without randomization or matched
controls.

IV: evidence from well-designed non-experimental studies from more than
one group.

V: opinions based on clinical evidence, on descriptive studies or on the reports of
expert committees.