https://training-course-material.com/index.php?action=history&feed=atom&title=Levels_of_MeasurementLevels of Measurement - Revision history2026-05-22T23:42:34ZRevision history for this page on the wikiMediaWiki 1.45.1https://training-course-material.com/index.php?title=Levels_of_Measurement&diff=17396&oldid=prevAhnboyoung: /* Quiz */2014-05-30T22:31:48Z<p><span class="autocomment">Quiz</span></p>
<p><b>New page</b></p><div>[[Category:Introduction to Statistics| 09]]<br />
* We measure our dependent variables<br />
* Different types are measured differently<br />
<br />
=Types of Scales of Measurement=<br />
4 Fundamental Scales of Measurement:<br />
# Nominal Scales<br />
# Ordinal Scales<br />
# Interval Scales<br />
# Ratio Scales<br />
<br />
<br />
==Nominal Scales==<br />
* Names or Categorizes<br />
* Lowest level of measurement<br />
<br />
<br />
;Examples:<br />
* Gender<br />
* Handedness<br />
* Favorite color<br />
* Religion<br />
<br />
<br />
==Ordinal Scales==<br />
Names or Categorizes and the order is meaningful<br />
<br />
;Examples:<br />
* Consumer satisfaction ratings<br />
* Military rank<br />
* Class ranking<br />
<br />
;Ordinal Scales are limited:<br />
* can't assume the differences between adjacent scale values are equal<br />
* can't make this assumption even if the labels are numbers, not words<br />
<br />
<br />
==Interval Scales==<br />
Names or Categorizes and the order is meaningful, and intervals have the same interpretation<br />
<br />
;Examples:<br />
* Fahrenheit temperature scale - zero doesn't mean that the temperature doesn't exist<br />
<br />
===No True Zero Point===<br />
;Ratios Do not make sense<br />
Since an interval scale has no true zero point, it does not make sense to compute ratios of temperatures. <br />
<br />
;Example:<br />
* 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; <br />
* no interesting physical property is preserved across the two ratios. <br />
* 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! <br />
* For this reason, it does not make sense to say that 80 degrees is "twice as hot" as 40 degrees.<br />
<br />
==Ratio Scales==<br />
* highest and most informative scale<br />
* contains the qualities of nominal, ordinal, and interval scales with the addition of an absolute zero point<br />
<br />
;Examples:<br />
*amount of money - zero money indicates the absence of money<br />
<br />
=Psychological Variables:=<br />
* Frequently use rating scales<br />
* Rating scales are ordinal<br />
<br />
<br />
;Example: Memory experiment<br />
What scale of measurement is number of item recalled? (ratio, interval or ordinal?)<br />
Subject Easy-item Difficulty-item score<br />
A 0 0 1 1 0 0 0 0 0 0 2<br />
B 1 0 1 1 0 0 0 0 0 0 3<br />
C 1 1 1 1 1 1 1 0 0 0 7<br />
D 1 1 1 1 1 0 1 1 0 1 9<br />
<br />
=Consequences of Scales of measurement=<br />
* Why are we so interested in the type of scale that measures a dependent variable? <br />
* 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<br />
<br />
;Example: Favourite colour of 5 children<br />
Colour Code <br />
Blue 1<br />
Red 2<br />
Yellow 3<br />
Green 4<br />
Purple 5<br />
---------------------<br />
Subject Colour Code<br />
1 Blue 1<br />
2 Red 2<br />
3 Yellow 3<br />
4 Green 4<br />
5 Purple 1<br />
<br />
...the average favorite colour, yellow (the colour with a code of 3) ?<br />
<br />
<br />
=Quiz=<br />
<quiz display=simple ><br />
<br />
{Identify the scale of measurement for the following: military title -- Lieutenant, Captain, Major. <br />
<br />
|type="()"}<br />
-nominal<br />
+ordinal<br />
-interval<br />
-ratio <br />
<br />
{<br />
{{Show Answer|<br />
ordinal<br />
<br />
The scale is ordinal. There is an inherent ordering in that a Major is higher than a Captain, which is higher than a Lieutenant. <br />
}}<br />
}<br />
<br />
{ Identify the scale of measurement for the following categorization of clothing: hat, shirt, shoes, pants <br />
<br />
|type="()"}<br />
+nominal<br />
-ordinal<br />
-interval<br />
-ratio <br />
<br />
{<br />
{{Show Answer|<br />
nominal<br />
<br />
Since clothes are categorized and have no inherent order, the scale is nominal. <br />
}}<br />
}<br />
<br />
{Identify the scale of measurement for the following: heat measured in degrees centigrade. <br />
<br />
|type="()"}<br />
-nominal<br />
-ordinal<br />
+interval<br />
-ratio <br />
<br />
{<br />
{{Show Answer|<br />
interval<br />
<br />
The scale is interval because there are equal intervals between temperatures but no true zero point. <br />
}}<br />
}<br />
<br />
{ A score on a 5-point quiz measuring knowledge of algebra is an example of a(n) <br />
<br />
|type="()"}<br />
-nominal<br />
+ordinal<br />
-interval<br />
-ratio <br />
<br />
{<br />
{{Show Answer|<br />
ordinal<br />
<br />
It is ordinal because higher scores are better than lower scores. However, there is no guarantee that the difference between, say, a 2 and a 3 represents the same difference in knowledge as the difference between a 4 and a 5.<br />
}}<br />
}<br />
<br />
{City of birth is an example of a(n) <br />
<br />
|type="()"}<br />
+nominal<br />
-ordinal<br />
-interval<br />
-ratio <br />
<br />
{<br />
{{Show Answer|<br />
nominal<br />
<br />
The city that someone was born in has no inherent order, thus can only be a nominal scale. <br />
}}<br />
}<br />
<br />
{ There is debate about the value of computing means for <br />
<br />
|type="()"}<br />
-nominal<br />
+ordinal<br />
-interval<br />
-ratio <br />
<br />
{<br />
{{Show Answer|<br />
ordinal<br />
<br />
Most statisticians agree that it is valid to compute means of ordinal data, although some vehemently disagree.<br />
}}<br />
}<br />
</quiz></div>Ahnboyoung