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Exploring data
Dr Janelle YorkeUniversity of Salford
& Professor Carol Haigh
Manchester Metropolitan University
Background & Aims
• Based upon our joint reviewing experience• Differing degrees of irritation regarding application of statistical tests.
• Seemed to be much confusion about test to be used
• Was it just us?
Making the terms clear…
Nominal Data
• A set of data is said to be nominal if the values / observations belonging to it can be assigned a code in the form of a number where the numbers are simply labels. You can count but not order or measure nominal data. For example -
• In this example yes could be coded as 1, No as 2
Are you a Bon Jovi Fan?
Yes No
Categorical data• A categorical variable is for mutual exclusive, but not ordered, categories. For example, A Likert scale;
• You can code the five categories with numbers if you want, but the order is arbitrary and any calculations (for example, computing an average) would be meaningless.
Bon Jovi are the worlds greatest rock band
Strongly Agree Agree Uncertain Disagree Strongly Disagree
Ordinal data• A ordinal variable, is one where the
order matters but not the difference between values. For example, Pain Scales
• Patients are asked to express the amount of pain they are feeling on a scale of 1 to 10. A score of 7 means more pain that a score of 5, and that is more than a score of 3. But the difference between the 7 and the 5 may not be the same as that between 5 and 3. The values simply express an order
Interval data
• A interval variable is a measurement where the difference between two values is meaningful. The difference between a temperature of 100 degrees and 90 degrees is the same difference as between 90 degrees and 80 degrees
Ratio Data
• A ratio variable, has all the properties of an interval variable, and also has a clear definition of 0.0. When the variable equals 0.0, there is none of that variable
In summary….
OK to compute...
Nominal Categorical Ordinal Interval Ratio
frequency distribution Yes Yes Yes Yes Yes
median and percentiles. No No Yes Yes Yes
add or subtract. No No No Yes Yes
mean, standard deviation, standard error of the mean.
No No No Yes Yes
ratio, or coefficient of variation.
No No No No Yes
Know your tests
Non-parametric tests
• Nonparametric tests are often when certain assumptions about the underlying population are questionable.
• For example, when comparing two independent sample non-parametric tests do not assume that the difference between the samples is normally distributed whereas parametric tests do
• Nonparametric tests may be more powerful in detecting population differences when certain assumptions are not satisfied.
• All tests involving ranked data, i.e. data that can be put in order, are nonparametric.
Parametric tests
• Parametric statistics allow you to assume the data come from a type of probability distribution and make inferences about the parameters of the distribution.
• Generally speaking parametric methods make more assumptions than non-parametric methods.
• If those extra assumptions are correct, parametric methods can produce more accurate and precise estimates.
• They are said to have more statistical power.
Which test for what sort of data?
Test Parametric Non-parametric
Correlation test Pearson Spearman
Independent measures, 2 groups
Independent-measures t-test
Mann-Whitney test
Independent measures, >2 groups
One-way, independent-measures ANOVA
Kruskal-Wallis test
Repeated measures, 2 conditions
Matched-pair t-test Wilcoxon test
Repeated measures, >2 conditions
One-way, repeated measures ANOVA
Friedman's test
Thank you for your attention