Levels of measurement - what you can and can't do arithmetically

# 9. Resources

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### Glossary

TermDefinition
incidence density

The rate at which new cases occur in a population. Expressed in person days (or years), where the denominator is the sum of all the periods each individual has been at risk.

Average

The mean (or average) of a set of numbers is the total of all the values divided by the number of values in the list

Bayes' Theorem

A formula for calculating the posterior odds of X given its prior odds and the outcome of some kind of diagnostic event.

Central obesity

A waist-hip ratio of 0.95 and over in men and 0.85 and over in women. Common among adults in England. Around 28% of men and 20% of women have central obesity

Cumulative risk

The rate at which new cases occur in a population. Expressed in person days (or years), where the denominator is the sum of all the periods each individual has been at risk. Also known as 'incidence density'

False negative

A diagnostic test suggests absence of a disease when it is present.

False Positive

A diagnostic test suggests presence of a disease when it is absent.

Frequency

The number of times an event occurs over a given period of time.

Frequency distribution

The numbers of cases in a sample which have each possible value on a measure. When divided by the sample size this effectively gives a probability distribution. The shape of the distribution can be useful in statistical analys

High risk

A probability that is greater than in the background rate for a given age. A risk of 1 in 100 can be a high risk if the risk would normally be 1 in 1000.

Hypothesis

A supposition assumed or theory to be proved (or disproved) by observation and analysis of the facts.

Incidence

The number of cases of a disease occurrence over a defined time period in a given population.

Incidence rate

The rate at which new cases occur in a population. Expressed in person days (or years), where the denominator is the sum of all the periods each individual has been at risk. Also known as 'incidence density'

Incidence risk

The probability that any member of a group will develop the disease in a known period. Also known as 'cumulative risk'

Interval value

A level of measurement where the attributes are ordered and the intervals between them are also interpretable

Likelihood

The chances or probability of something occurring (see probability).

Likelihood ratio

Used in Bayes' theorem, it is the probability of a positive test result given that the disease is present (sensitivity) divided by the probability of a positive test result if the disease is absent (the false alarm rate).

Mean

The mean (or average) of a set of numbers is the total of all the values divided by the number of values in the list

Median

The median of a set of numbers is the central value in the list once they have been put in increasing order of size (and if there is an odd number of values in the list). If there are an even number of values in the list there will be two mid

Mode

The mode of a set of numbers is the most frequently occuring value in the list

Nominal value

A level of measurement where no ordering of cases is implied. ie. a footballer wearing a number 8 shirt is certainly not twice the value of the player wearing number 4

Odds

The odds of something occurring is the ratio of the number of times you would expect it to occur in the long run versus the number of times you would expect it not to occur. For example, if the odds of having breast cancer having tested positive on a mammogram are 1 in 2 (1/2 or 1:2), for every person who has breast cancer in that situation there are 2 who do not. Odds are not exactly the same as probability. If the odds are 1 in 2 the probability is 1/3 (0.33). This is because the probability is the number of times you would expect it to occur out of all the cases you come across. Odds can go from minus infinity to plus infinity.

Ordinal value

A level of measurement where the attributes are ordered but where the intervals between them are uninterpretable

Predictive value of a negative test result

The chances of a disease being present given that a diagnostic test has come out negative (i.e. in favour of the disease being absent)

Predictive value of a positive test result

The chances of a disease being present given that a diagnostic test has come out positive (i.e. in favour of the disease being present)

Prevalence

The percentage of a given population who have a particular disease in a given population at a given point in time or over a particular time period. Not to be confused with incidence.

Probability

The expected proportion of times you expect something to occur in the long run in a defined set of circumstances. It must be between 0 and 1. It is not the same as odds.

Ratio value

A level of measurement where the attributes are ordered, where the intervals between them are interpretable and where there is a meaningful absolute zero.

ROC analysis

'Receiver Operating Characteristic' analysis. This refers to a statistical process for evaluating a diagnostic test. For a quantitative marker (e.g. GGT as a marker of alcohol dependence), a graph is plotted of the True Positive rate against the False Positive rate when the threshold is set at different points. The area under this curve indicates how well the test performs as a whole in discriminating true cases from non-cases. The shape of the curve together with information on prevalence and the costs associated with misses versus false alarms is used to determine the optimum threshold.

Sensitivity

The 'true positive rate' or 'hit' rate. The chances of detecting the disease if it is actually present, usually expressed as a percentage.

Specificity

The 'true negative rate'. The chances of correctly coming up negative when the disease is absent. Expressed as a probability it is one minus the 'false alarm' rate. It is usually expressed as a percentage.

### Resources

ResourceResource Description
Mastering Statistics: A Guide for Health Service Professionals and Researchers

Authors: Kelvin Jordan, Bie Nio Ong, Peter Croft, Publication Date: 1998, Publisher: Stanley Thornes (Publishers) Limited, ISBN: 0748733256

Levels of Measurement RLO

To understand the different levels of measurement and the arithmetic operations that can be performed on them

### Learning outcomes

By completing this resource you will be able to:

You will be able to explain what arithmetic processes can be used on different levels of data measurement.

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Universities' Collaboration in eLearning (UCEL)

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