Measurement Scales

Hello. My name is Dominic Dwyer.

I am a professor in the school of psychology at Cardiff University,

and my research is mainly on animal learning and behaviour.

But I've been teaching on statistics since 2003.

In this lecture,

I'll be introducing the concepts of measurement and measurement scales,

but first, a little history.

Surprisingly,

in the 19 thirties and forties,

one of the key problems taxing the UK scientific community

was whether or not psychology involved measurement.

Why this was such a priority in the years leading up to World War Two.

And indeed, the early years of that war

is something I simply cannot guess that.

And

for a current student of psychology,

the conclusion

that they reached is perhaps even more surprising.

Their answer was no.

Psychology did not involve management,

but in doing so,

the committee might have taken on the wrong man.

The committee took one of its main examples as the

sone scale developed by Harvard psycho physicist Stanley Smith Stevens.

And oddly enough,

Stanley didn't agree with their conclusion.

1946

Stevens wrote what was essentially a reply to the committee,

arguing that their conclusion was based on misunderstanding measurement

and Stephen's paper

outlining measurement as he understood it,

has become the standard approach to measurement in psychology ever since.

Now I'll come to Stevens definition a minute,

but you might be wondering,

Why is it

that we need to even think about the concept of measurement at all?

Surely

we've been measuring things since the day we first picked up. A ruler

looked at a stopwatch,

picked up a scale in a kitchen.

And it's true,

we do measure all the time.

However,

psychological measurement

does seem to be something of a special case.

Were interested, possibly in intelligence or EQ,

in personality

in emotions,

things that you can't put on a scale or put next to a ruler or

measure with a stopwatch.

So,

in actual fact, the idea that the committee wanted to ask,

Does psychology involved?

Measurement

isn't so strange after all,

because psychological measurement

l seem

to be a bit different to the everyday measurements we make in the rest of our lives.

And that brings us back to Stevens.

What was his definition of measurement?

Well,

it is remarkably simple.

He defined measurement as

the assignment of numbers or numerals, two objects or events. According to rule,

this definition is so ubiquitous as to be

found in almost every textbook of psychology.

Indeed, often without direct attribution to Stevens,

we have internalised it within psychology to the degree

that we no longer often recognise its author.

However,

this simple definition

begs to critical questions.

What rule or rules should we use when assigning numbers to objects?

And why would we want to do this?

The answer to these two questions fit together.

We assign numbers to things in a way that reflects the properties of those things.

So the rule

is essentially

use numbers to represent properties of objects or events.

And we do this because mathematics offers a great

number of very useful tools for manipulating numbers.

So by using numbers

to reflect the properties of the things we are interested in,

then we can apply these mathematical tools to

the numbers that come out of our measurement

to help investigate those properties.

But again,

the idea of using numbers to reflect interesting properties of objects or events

is something of a generality

and only gets us so far.

What sort of properties would be interesting?

And how would we use numbers to reflect them.

Stevens answer was to set out four basic types of measurement

things he described as different measurement scales

nominal

orginal

interval and ratio.

And each of these scales reflected a critical question about the

properties of the object or event that were being measured.

Phenomenal scales. This question was, Are things the same

or are they different?

For orginal scales,

the question was, Is one thing bigger or smaller than another?

For interval scales?

The question was,

Is the difference between one pair of objects

the same as the difference between another pair of objects?

Or are those two differences

themselves different?

And finally,

for ratio scales? How much of something is there?

So

the answer to these questions

reflect the properties of the things being measured,

and therefore the scales relate to those sorts of answers.

Phenomenal scales. The question was, Are things the same or different?

And so this reflects identity or classification.

For example, hair colour

people have different colours of hair. Using a nominal scale

to reflect hair colour would mean that everyone with

the same colour hair gets the same number.

Everyone with different hair colours would get different hair, different numbers

for orginal. The question was, is one thing bigger than or smaller than another?

And so

the scale reflects, as the name suggests,

order.

A classic example is positions in a race

1st, 2nd, 3rd,

first person over the line gets a first gets 1st 2nd person over the line. 2nd,

3rd person. Third.

We don't care about how far ahead

first place was from second place.

They win the gold medal regardless,

and so

the numbers reflect the orginal

relationships between the events in the world

for interval scales. We're looking at the differences between things.

The classic example is temperature

be that measured in Celsius or Fahrenheit

and finally, the ratio scale. It asked the question. How much of something is there?

And so this reflects the amount

of something.

So for length, how far is something? How tall is someone

for weight? How much how heavy are they for time, how long a period has elapsed?

So those are the scales.

But there's one other critical thing that is

somewhat hidden in Steven's definition of measurement

and in the properties of the scale he talks about,

and that that hidden thing

is what we can or should usefully do

with the numbers that come out of measurement

in terms of applying mathematical or statistical tools to them.

Here,

Stevens provides a brief list of things that are sensible to do for each scale.

But

the underlying principle

is that the mathematical tools we apply

should preserve the information

in the properties that were being measured.

In other words,

we should only be drawing mathematically based conclusions

that would hold true

of the properties that were originally present in the objects themselves.

Now,

as I say, Stevens provided a small list of examples, and in this series of lectures,

that's exactly what I will do.

However,

this is a question that other mathematicians

and philosophers have debated at great length,

and it is genuinely a rather difficult thing to set out briefly.

Indeed,

perhaps the most comprehensive answer

to what should we do mathematically with the results of measurement

is given in a series of books called The Foundations of Measurement.

Those books,

all three of them,

took a total of 19 years to write by four authors.

Believe me, in this series of lectures, I will not be summarising them entirely,

so

that is very much

a broad overview

of measurement

measurement in psychology

and the way it is understood in terms of the four different scale types

nominal orginal interval and ratio

in the subsequent lectures in this series,

I will take each of these scale types in turn and consider them in a bit more detail.