Biostatistics%20in%20Research%20Practice:%20Non-parametric%20tests

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Biostatistics in Research Practice
Non-parametric tests

• Dr Victoria Allgar

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What is a non-parametric test ?

• Methods of analysis that do not assume a
  particular family of distributions for the data.

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When to use a non-parametric test

• Non-parametrics are distribution free
• Data may be rank ordered (Ordinal data)
• Data may be from small samples
• There may be non-normal distribution of the
  variables (Skewed data)
• Outliers may be present

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Non-parametric v Parametric tests

• Usually only perform one analysis of a data set
  choosing between parametric and non-parametric
  methods.
• It is usual to use a parametric method, unless
  there is a clear indication that it is not valid.
• It is important to realise that if we apply
  different tests to the same data then we do not
  expect them to give the same answer, but in
  general two valid methods will give similar
  answers.
• Non-parametric tests are less powerful than the
  equivalent parametric test (especially in small
  samples) and will tend to give a less significant
  (larger) p-value

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Dealing with ordinal data

• Non-parametric tests are usually based on Order
  Statistics and Ranks
• ORDER STATISTICS the observations arranged in
  increasing order of size.
• RANKS their places in this order

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Ordering data
Data 7 9 10 12 12 9 12 11 -13
Ordered
Ranked
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Ordering data
Data 7 9 10 12 12 9 12 11 -13
Ordered -13 7 9 9 10 11 12 12 12
Ranked
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Ordering data
Data 7 9 10 12 12 9 12 11 -13
Ordered -13 7 9 9 10 11 12 12 12
Ranked 1 2 3.5 3.5 5 6 8 8 8
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Wilcoxon Signed Rank Test

• Non-parametric equivalent for testing or
  estimating location for a one sample problem
  (equivalent to one sample t-test) OR for paired
  samples (equivalent to the paired t-test)
• Assumptions
• A random sample of n independent observations OR
  independent random pairs are taken.
• The variable of interest is the difference (d)
• For the one sample problem d Observed value -
  Hypothesised value
• For paired data d X - Y - where X is value at
  time 1 and Y is value at time 2.
• The level of measurement is at least ordinal.

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Examples

• Anxiety levels pre and post operation
• Pain levels pre and post operation
• Yorkshires fruit and veg consumption vs
  recommended 5 a day
• BP pre and post exercise

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Friedman Test

• The assumption that the residuals have a Normal
  distribution cannot be assessed before fitting
  the model.
• Sometimes, however, it can be seen from the raw
  data that the model will not fit well. In
  particular, wide variation in the standard
  deviations for each row and column will suggest
  problems with the parametric two-way ANOVA.
• Therefore, we have a non-parametric equivalent of
  the two way ANOVA that can be used for data sets
  which do not fulfill the assumptions of the
  parametric method.
• The method, which is sometimes known as
  Friedmans two way analysis of variance, is
  purely a hypothesis test.

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Examples

• Time periods
• Pre op, post op and 12 months
• Baseline, week 2, week 12

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Mann Whitney U test

• Non-parametric equivalent of two sample t-test.
• The Mann-Whitney test is used to compare two sets
  of data from independent groups.
• It is the most commonly used alternative to the
  independent samples t-test.
• The values from both samples are combined and
  then the data is ranked from smallest to largest.
  The rank of 1 is assigned to the smallest value,
  2 to the next smallest and so on. If the ranks
  are tied, then the average rank is used.
• Assumptions
• There are two independent random variables (X and
  Y), of size n and m.
• The variable of interest is a continuous random
  variable.
• The two populations differ only with respect to
  location.

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Examples

• Comparing two groups e.g.
• Anxiety between men and women
• Control group and an intervention group

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Kruskal Wallis Test

• Just as the one way analysis of variance is a
  more general form of the t-test, there is a one
  for the non-parametric Mann-Whitney test.
• The Kruskal-Wallis test is an obvious
  mathematical extension of the Mann-Whitney test.
• Assumptions
• There are three or more independent random
  variables (X1 , X2, X3.Xn, ), of size n1 ,n2,
  n3.nn
• The variable of interest is ordinal or a
  continuous random variable which is non-normal.
• The populations differ only with respect to
  location.

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Examples

• Comparing more than 2 groups, e.g.
• Contol group and two intervention groups
  Satisfaction with procedure
• Age groups 18-30 30-50, 50
• Social class groups

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Choosing an appropriate method of analysis

• Number of groups of observations
• Independent or dependent groups of observations
• The type of data
• The distribution of data
• The objective of the analysis

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Choice of Test