Fundamentals of Measurement by

Michael Everton (mxe06u)

Fundamentals of Measurement

• Is part of many fields and subject areas.• My example is based on ‘Measurement’ in conjunction with

statistics.• The presentation will cover:

--A brief explanation of measurement and how it is used.

--A explanation of statistics.

--How measurement data is broken down into several types or scales of measurement.

--The rules used to establish a consistent understanding of measurement.

Measurement?

The word ‘Measurement’ as used in daily life, implies the assignment of an exact and quantitative number to an object, such as £2, 4 metres, 5 amps or 70 MPH. These quantitative terms by themselves are of limited use.After measurements are taken they need to be made meaningful by relating them to other variables.

Measurement:

Scientists use words and numbers to communicate the results of their research. Statistics are numbers and results of tests conducted on sets of numbers.

Statistics:

• The term statistics is used to describe numerical data used in research, reports or presentations Examples: -The number of clients served in a

space of time e.g. an hour, day, week, month. -Performance ratios. -Age and gender of a village population etc...

• Statistics are also used to define many mathematical techniques and procedures used to collect, describe, analyse and interpret data

Statistics:

• In general statistics can be considered as both numerical data and a variety of tools and techniques used to process raw data to make it more meaningful.

• There are two types of Statistics: Descriptive statistics: used to summarise a larger

set of numbers called a dataset. Inferential statistics: these are measurements of

a smaller group that are used to make assumptions of a larger group of interest.

Statistics:

• The numerical values in statistics are measurements taken with some kind of scale or device.

• These scales provide different levels of information, based upon the type of data they intend to capture.

• The four types or levels of data:Nominal, Ordinal, Interval and Ratio.

Each type has a body of tests appropriate for that level.

Fundamentals of Measurement

• The key to ensure that everyone understands the Measurements.

• Measurement and data.

• Variables.

• Data types also known as ‘scales of measurement’.

• Each level has one or more rules.

Nominal Data• Nominal data is the least powerful • Of the four types.

It is only concerned with one rule.The Rule states that “Different numbers must mean different things”. In Nominal level data, numbers or labels are used to differentiate between things. Once a number has been assigned to a certain category all other items with the same characteristics must receive the same number.

Typical examples of Nominal or categorical scales are:

• The values of “1” and “2” assigned to the categories of Female and male.

• The count of times a head is shown when a coin is tossed up.• Numbers used to denote different types of occupations, university

years etc...

Ordinal Data

• Two rules apply to Ordinal data: 1)“Different numbers must mean different things”. 2)The second rule which states that “The things being measured can be ranked or ordered along some dimension”. Ordinal data can also be referred to as “Ranked data”.

• When things are ordered they are arranged in some logical sequence, they may have ‘more or less’ of a particular characteristic than others in a set.

• The primary limitation with Ordinal measurements is that the numbers seldom state how much ‘more or less’ the difference exists in two or more collections of data.

• A typical use of Ordinal data is to measure people’s preferences or rankings for candidates (Political polls).

Interval Data• The third class of measurement data is

‘equidistant interval’ or more simply known as “Interval”.Three rules apply to Interval scale 1)“Different numbers must mean different things“.2)“ The things being measured can be ranked or ordered along some dimension”.3)The third rule states that: “The differences between adjacent levels on a scale are to be equal”. The key requirement is that a single unit change always measures the same amount of change in whatever is being measured.The unit gradations within the scale must be as broad or as fine as needs be.

• For example on a five point scale the distance between “3” and “4” or “4” and “5” might be measured in tenths , hundreds, thousands or even finer but they must apply to every part of the scale equally.

• There are limitations to the information provided by Interval data. • For example we cannot say that 100 degrees Fahrenheit is exactly twice as warm as

50 degrees Fahrenheit, nor can we say that 35 degrees is half as warm as 70 degrees. We can only say that the differences between the two single points on the scale are equal.

Ratio Data

• Four rules apply to Ratio scales.1)Different numbers must still mean different things. 2)The data can be ranked or ordered along some dimension. 3)The intervals between adjacent points must be equal. 4)The fourth rule: “The measurement scale must have an absolute or fixed zero point”.

• Typical examples of Ratio scales are time, distance, mass or temperature.

References:

1. Downie, N.M “Fundamentals of

measurement” Second Edition Published by Oxford University press (1967) .

2. McNabb, D.E “Research methods for Political Science” Published by M.E Sharpe (2004).

Questions?