Data or scores we collect fit into one of the four scales of measurement.
?What are they?
     -Nominal
     -Ordinal
     -Ratio
     -Interval

NOMINAL (name) = numbers which are NOT rank ordered AND are NOT compared to one another with regard to value. (They may provide some sort of "order", but are not ranked from "best" to "worst") They merely identify.

?Examples?
     -phone numbers
     -room number
     -number on restaurant receipt
     -lottery ticket

?When are nominal numbers found in assessment?
     -page numbers on IEP documents, reports, etc.
     -question numbering on tests
     -numbers given to students to protect their identities
     -the number of the school attended (PS 4)
 

 ORDINAL (ordered) = numbers are rank ordered from "best" to "worst" (or vice- versa) on a continuum.

?Examples?
     -place in race/contest
     -

?When are ordinal numbers found in assessment?
     -test scores for a class
     -percentile ranks
 

Take a peek at the numbers below.  They are possible test scores on a test.  Is the difference between the 1st and 2nd ranked scores the same as the difference/magnitude between the 2nd and 3rd scores? (yes)

100 99 98 97 96 95 94 93 92 91 90 89 88....
 
 

RATIO = the size of the difference between two adjacent possible points/scores is always the same.

?Examples?
      -height and weight (the difference between 6'1" and 6'0" is the same as the difference between 5'3" and 5'4")

The ratio scale also has a zero point that means "nothing" or "none".
     -0 lbs means that something is weightless
     -0 feet of altitude means you are on the ocean surface (calm, no tide)
     -rulers (measuring sticks, not leaders of countries)

?When do we see the ratio scale in assessment?
     -number of correctly answered questions on a test (raw score)
  (22 correct out of 25 questions is one better than 21 out of 25)
     -% correct on a test (derived score)
   (the difference between 12% & 16% = the difference between 94% & 98%
 
 

 INTERVAL = a ratio scale without a logical zero point (a score of zero may not mean "none")
?Examples?
     -0 degrees on a thermometer does not mean "no temperature"
   (also, because of no logical zero point, we can't say that 100 degrees is twice as hot as 50 degrees
     -Latitude and longitude
 

?When do we see the interval scale in assessment? (Not very often)
  -Some tests like the SAT...even if you make no marks on your test, you get a score of 14.
 
 
 
 

Which Scale of Measurement? (a quiz)
 

The lines across the pages of your grade book are numbered from 1-25  (one student's name on each line).
 

There are 3 funded slots for Associate Professor of  Education at Hunter College.  The names of Professors up for  advancement are placed on a list with the most deserving at the  top (#1) and the least deserving at the bottom (#5).
 

The quarterly issue of your professional journal "Reclaiming Children and Youth at Risk" arrives in the mail.  It is "Volume 10, Issue 4".
 

You ask your student to read the multiple lists of ten words on the QRI.  Depending on which is the last successful listing read, a particular grade level passage is selected for the student to orally read.
 
 

Some drunken guys are being abusive and "rating" women who pass by on a 1-10 scale (commenting on their physical looks).

One highly rated gal is pinched by a "judge" as she walks by.
 

She's calls them all "jerks" and reports the incident to the manager of the bar/restaurant.  This results in her rating being reduced to a "zero".

Sorry for the bad example...it was a real life one witnessed recently.
 
 
 
 
 
 

Range of Scores = (highest score - lowest score) +1

100,  99,  98,  97,  96,  95,  94,  93,  92,  91
 

Range = (100-91) + 1

  9  + 1 = 10

Tom McIntyre at www.BehaviorAdvisor.com