Ordinal data

Ordinal data is rank order data. Ordinal means that the data is ordered in some fashion. For example, rankings from best to worst, highest to lowest, or poor, fair, good, etc., would be considered ordinal data. A safety manager could use this type of data to evaluate safety practices. For example, a survey that asked employees, How often do you use protective gloves when handling chemicals and offered almost always, often, seldom, and almost never as choices would be an example of ordinal data. 

Common examples of ordinal data are Likert scales.When a person is asked to select a number on a Likert scale (for example, evaluate the safety program from 1 to 5), it is 

Interval data is a form of continuous data. Continuous means that all points along the line of data are possible (including fractional values). Interval data also has zero as a placeholder on the scale. An example of a scale that is interval is the Fahrenheit thermometer. Examples of interval data that a safety professional may use include temperature readings, job analysis scales, and environmental monitoring readings. 

An interval scale is divided into equal measurements. In other words, the difference between 20 and 10 degrees Fahrenheit is the same as between 30 and 20 degrees Fahrenheit. However, it is not accurate to say that 20 degrees is twice as hot as 10 degrees Fahrenheit. When ratio comparisons like this cannot be made, the scale is said to not have magnitude. Magnitude is an ability to make comparisons between the values of a scale. 

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There is a hierarchy of usefulness of data, according to how well it can be statistically manipulated. The accepted order is continuous data > ordinal data > nominal data. 

Only a limited number of chemicals evoke a local quantifiable pharmacodynamic response, for example, the concentration-dependent vasoconstriction effect of corticosteroids. In these experiments, resulting skin blanching is scored visually by one or more qualified investigators, using an ordinal data scale. The lack of instrumentation has been criticized, because of possible subjective errors [25], However, approaches using the Chromameter device, although recommended by the FDA, have failed to return the desired precision [26, 27],... 

Once an entry of interest in the Cambridge X-ray file has been located by one of the search programs, its crystal sequence number can be used to retrieve the appropriate literature reference, structure, or co-ordinate data or both. 

The simplest form of qualitative data is binary data in which there are only two possible values, for example, death/survival or success/failure each of which needs to be defined within a specified time interval has pain relief been achieved within two hours of treatment, success - or not, failure. This form of data is extremely common in medical research and yet it ignores the possibility of gradation, success may not be total but only partial and yet not be total failure. These considerations lead naturally to the concept of ordered categorical or ordinal data. 

Ordinal data arises in many situations. In oncology (solid tumours) the RECIST criteria record outcome in one of 4 response categories (National Cancer Institute, WWW. cancer, gov) ... 

As we shall see later the data type to a large extent determines the class of statistical tests that we undertake. Commonly for continuous data we use the t-tests and their extensions analysis of variance and analysis of covariance. For binary, categorical and ordinal data we use the class of chi-square tests (Pearson chi-square for categorical data and the Mantel-Haenszel chi-square for ordinal data) and their extension, logistic regression. 

There are further links across the data types. For example, from time to time we group continuous, score or count data into ordered categories and analyse using techniques for ordinal data. For example, in a smoking cessation study we may reduce the basic data on cigarette consumption to just four groups (Table 1.2). accepting that there is little reliable information beyond that. 

The calculation of mean and standard deviation only really makes sense when we are dealing with continuous, score or count data. These quantities have little relevance when we are looking at binary or ordinal data. In these situations we would tend to use proportions in the various categories as our summary statistics and population parameters of interest. 

As with binary and categorical data, is there an issue with small sample sizes Well, in fact, no, there is not. The MH test is a different kind of chi-square test and is not built around expected frequencies. As a consequence it is not affected by small expected frequencies and can be used in all cases for ordinal data. There are some pathological cases where it will break down but these should not concern us in practical settings. 

Measures of treatment benefit for categorical and ordinal data... 

In this section we will discuss the extension of the t-tests for continuous data and the chi-square tests for binary, categorical and ordinal data to deal with more than two treatment arms. 

For binary, categorical and ordinal data there is also an approach which is a further form of the Mantel-Haenszel chi-square test. You will recall that the MH test is used for ordinal responses comparing two treatments. Well, this procedure generalises to allow ordering across the treatment groups in addition, for each of... 

For binary data in multi-centre trials we will have a series of 2 x 2 tables, one for each of the centres. For categorical and ordinal data with c categories, we will have a series of 2 x c tables. The CMH test in the first instance provides a single p-value for the main effect of treatment. 

We saw in the previous chapter how to account for centre in treatment comparisons using two-way ANOVA for continuous data and the CMH test for binary, categorical and ordinal data. These are examples of so-called adjusted analyses, we have adjusted for centre differences in the analysis. 

There are also connections between the Cochran—Mantel—Haenszel procedures and logistic regression for binary and ordinal data, but these issues are beyond the scope of this text. 

In Chapter 6 we covered methods for adjusted analyses and analysis of covariance in relation to continuous (ANOVA and ANCOVA) and binary and ordinal data (CMH tests and logistic regression). Similar methods exist for survival data. As with these earlier methods, particularly in relation to binary and ordinal data, there are numerous advantages in accounting for such factors in the analysis. If the randomisation has been stratified, then such factors should be incorporated into the analysis in order to preserve the properties of the resultant p-values. 

A characteristic of biological systems is variability, with most values of a variable clustered around the middle of the range of observed values, and fewer at the extremes of the range. The measure of location or central tendency gives an indication where the distribution is centred, while a measure of dispersion indicates the degree of scatter or spread in the distribution. The most widely used measure of central tendency is the arithmetic mean or average of the observed values, i.e, the sum of all variable values divided by the number of observations. Another measure of central tendency is the median, the middle measurement in the data (if n is odd) or the average of the two middle values (if n is even). The median is the appropriate measure of central tendency for ordinal data. 

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