Levels of Measurement

From: Subject: Levels of Measurement Date: Thu, 8 Jan 2004 14:07:57 -0800 MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_000_0000_01C3D5F0.D15FF520"; type="text/html" X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2600.0000 This is a multi-part message in MIME format. ------=_NextPart_000_0000_01C3D5F0.D15FF520 Content-Type: text/html; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable Content-Location: http://trochim.human.cornell.edu/kb/measlevl.htm Levels of Measurement

3D"Levels
[ Home ]=20 [ Construct = Validity ]=20 [ Reliability= ]=20 [ Levels of Measurement ] = [ Survey Resea= rch ]=20 [ Scaling = ;]=20 [ Qualitative Me= asures ]=20 [ Unobtrusive&nbs= p;Measures ]=20

The level of measurement refers to the relationship among the = values=20 that are assigned to the attributes for a variable. What does that = mean?=20 Begin with the idea of the variable, in this example "party = affiliation."=20 That variable has a number of = attributes. Let's=20 assume that in this particular election context the only relevant=20 attributes are "republican", "democrat", and "independent". For = purposes=20 of analyzing the results of this variable, we arbitrarily assign = the=20 values 1, 2 and 3 to the three attributes. The level of=20 measurement describes the relationship among these three = values.=20 In this case, we simply are using the numbers as shorter = placeholders for=20 the lengthier text terms. We don't assume that higher values mean = "more"=20 of something and lower numbers signify "less". We don't assume the = the=20 value of 2 means that democrats are twice something that = republicans are.=20 We don't assume that republicans are in first place or have the = highest=20 priority just because they have the value of 1. In this case, we = only use=20 the values as a shorter name for the attribute. Here, we would = describe=20 the level of measurement as "nominal".

Why is Level of = Measurement=20 Important?

First, knowing the level of measurement helps you decide how to = interpret the data from that variable. When you know that a = measure is=20 nominal (like the one just described), then you know that the = numerical=20 values are just short codes for the longer names. Second, knowing = the=20 level of measurement helps you decide what statistical analysis is = appropriate on the values that were assigned. If a measure is = nominal,=20 then you know that you would never average the data values or do a = t-test=20 on the data.

There are typically four levels of measurement that are = defined:

	Nominal =
	Ordinal =
	Interval =
	Ratio =

In nominal measurement the numerical values just "name" = the=20 attribute uniquely. No ordering of the cases is implied. For = example,=20 jersey numbers in basketball are measures at the nominal level. A = player=20 with number 30 is not more of anything than a player with number = 15, and=20 is certainly not twice whatever number 15 is.

In ordinal measurement the attributes can be = rank-ordered. Here,=20 distances between attributes do not have any meaning. For example, = on a=20 survey you might code Educational Attainment as 0=3Dless than = H.S.; 1=3Dsome=20 H.S.; 2=3DH.S. degree; 3=3Dsome college; 4=3Dcollege degree; = 5=3Dpost college. In=20 this measure, higher numbers mean more education. But is = distance=20 from 0 to 1 same as 3 to 4? Of course not. The interval between = values is=20 not interpretable in an ordinal measure.

In interval measurement the = distance between=20 attributes does have meaning. For example, when we measure=20 temperature (in Fahrenheit), the distance from 30-40 is same as = distance=20 from 70-80. The interval between values is interpretable. Because = of this,=20 it makes sense to compute an average of an interval variable, = where it=20 doesn't make sense to do so for ordinal scales. But note that in = interval=20 measurement ratios don't make any sense - 80 degrees is not twice = as hot=20 as 40 degrees (although the attribute value is twice as = large).

Finally, in ratio measurement there is always an = absolute zero=20 that is meaningful. This means that you can construct a meaningful = fraction (or ratio) with a ratio variable. Weight is a ratio = variable. In=20 applied social research most "count" variables are ratio, for = example, the=20 number of clients in past six months. Why? Because you can have = zero=20 clients and because it is meaningful to say that "...we had twice = as many=20 clients in the past six months as we did in the previous six = months."

It's important to recognize that there is a hierarchy implied = in the=20 level of measurement idea. At lower levels of measurement, = assumptions=20 tend to be less restrictive and data analyses tend to be less = sensitive.=20 At each level up the hierarchy, the current level includes all of = the=20 qualities of the one below it and adds something new. In general, = it is=20 desirable to have a higher level of measurement (e.g., interval or = ratio)=20 rather than a lower one (nominal or ordinal).=20 =

Copyright =A92002, William M.K. = Trochim, All=20 Rights Reserved
Purchase a = printed=20 copy of the Research Methods Knowledge Base
Last Revised: = 06/29/2000

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