# Levels of Measurement

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- We measure our dependent variables
- Different types are measured differently

# Types of Scales of Measurement

4 Fundamental Scales of Measurement:

- Nominal Scales
- Ordinal Scales
- Interval Scales
- Ratio Scales

## Nominal Scales

- Names or Categorizes
- Lowest level of measurement

- Examples

- Gender
- Handedness
- Favorite color
- Religion

## Ordinal Scales

Names or Categorizes and the order is meaningful

- Examples

- Consumer satisfaction ratings
- Military rank
- Class ranking

- Ordinal Scales are limited

- can't assume the differences between adjacent scale values are equal
- can't make this assumption even if the labels are numbers, not words

## Interval Scales

Names or Categorizes and the order is meaningful, and intervals have the same interpretation

- Examples

- Fahrenheit temperature scale - zero doesn't mean that the temperature doesn't exist

### No True Zero Point

- Ratios Do not make sense

Since an interval scale has no true zero point, it does not make sense to compute ratios of temperatures.

- Example

- There is no sense in which the ratio of 40 to 20 degrees Fahrenheit is the same as the ratio of 100 to 50 degrees;
- no interesting physical property is preserved across the two ratios.
- After all, if the "zero" label were applied at the temperature that Fahrenheit happens to label as 10 degrees, the two ratios would instead be 30 to 10 and 90 to 40, no longer the same!
- For this reason, it does not make sense to say that 80 degrees is "twice as hot" as 40 degrees.

## Ratio Scales

- highest and most informative scale
- contains the qualities of nominal, ordinal, and interval scales with the addition of an absolute zero point

- Examples

- amount of money - zero money indicates the absence of money

# Psychological Variables:

- Frequently use rating scales
- Rating scales are ordinal

- Example
- Memory experiment

What scale of measurement is number of item recalled? (ratio, interval or ordinal?)

Subject Easy-item Difficulty-item score A 0 0 1 1 0 0 0 0 0 0 2 B 1 0 1 1 0 0 0 0 0 0 3 C 1 1 1 1 1 1 1 0 0 0 7 D 1 1 1 1 1 0 1 1 0 1 9

# Consequences of Scales of measurement

- Why are we so interested in the type of scale that measures a dependent variable?
- The crux of the matter is the relationship between the variable's level of measurement and the statistics that can be meaningfully computed with that variable

- Example
- Favourite colour of 5 children

Colour Code Blue 1 Red 2 Yellow 3 Green 4 Purple 5 --------------------- Subject Colour Code 1 Blue 1 2 Red 2 3 Yellow 3 4 Green 4 5 Purple 1

...the average favorite colour, yellow (the colour with a code of 3) ?

# Quiz