Assessment: Norms, Percentiles, Stanines, Grade Equivalents etc

Norms

  • The results obtained by a supposedly representative sample of students on this particular test
  • Once the test is published, students who write the test have their results compared to these norms
  • This produces individual scores such as Grade Equivalent, Percentile, Stanine, etc.

Grade Equivalent           

  • A test score is related to the school grade ‘equivalent’
  • i.e. a grade equivalent of 6.2 indicates student performance is comparable to a student in the 2nd month of grade 6

Percentiles

  • A percentile rank is a type of converted score that expresses a student’s score relative to their group in percentile points.

–      Imagine lining up participants in a race in order of winning – they would line up as First place, Second Place, Third place, Fourth place…etc.

–      BUT, imagine doing this for 100 people!  Your First place winner would be standing in front of 99 other people.  Thus, they would be in the 99th percental (having performed better than 99% of the group)

– This indicates the percentage of students tested who made scores equal to or lower than the specified score.

– I.e. A student ranking at the 57th percentile performs better than 57 percent of students of the same age who wrote this test (norm group)

Important to know: Percentiles are a ranking system based on a line-up of performers

Percentile Chart

  • Percentile Chart – ranks the scores from low to high and assigns a percentile ranking to a particular score.  So if someone scored 3 % on a test and they were the only one out of 100 people to score this low, they would be at the 1st percentile.  (they ranked the lowest out of 100)
  • Ex. Your height is at the 2nd percentile.  This means that 98 percent of the population of people your age are taller than you are.

Bell Curve

  • The bell curve rises up over the 40-60th percentiles because most people score within this range.  (i.e. most people are medium-sized if we use height as an example)
  • This is callled a ‘normal curve’ because it reflects the ‘normal’ (statistical term) distribution of discret traits within a population – ie. height, weight, test scores.  This only applys to things you can quantify (measure).  It would be hard to develop a scale to determine how much ‘kindness’ a person has, never mind score it and plot ‘kindness’ within a population.
  • Percentiles and Stanines are often used together – ie. 40th percentile, stanine 4

Average: What is it?

  • NOT ‘normal’ (at least in the every day language sense)!
  • A statistical term analogous to Mean (sum of scores divided by the number of scores)
  • On standardized tests, the Average or Mean is the 50th percentile
  • Therefore scores above the 50th percentile are ‘above average’ and scores below the 50th percentile are ‘below average’
  • Average’ is usually reported as a range (i.e. 40th – 60th percentile)

 

AVERAGE means the middle range of scores
Someone scoreing in the average range would have more than some, but less than others.

Average is a range of scores in the middle of everyone else’s scores.  So people in the middle (40-60th percentile) scored more than the people who scored less than the 40th percentile (the left hand side of the curve).  However, the people in the middle scored less than the people on the right hand side of the curve.

  • Ex. Think of clothing sizes – average is medium.  A medium-sized person wears bigger clothes than a small-sized person (compared to the small-sized people the medium-sized people use more fabric) but they wear smaller clothes than an larger sized person (compared to the large-sized people the medium-sized people use less fabric)

Stanine Chart
The distribution of scores is divided into 9 intervals.

Stanines

  • “Standard NINE” (an army term)
  • A reporting scheme or way of ranking student performance on a test based on an equal interval scale of 1 to 9.  (5 is average, 6 is slightly above, 4 is slightly below average)
  • Usually used with percentiles

See it all in action together:

Here, the chart is flipped sideways with descriptive qualifiers.

(image from http://www.nzcersupport.org.nz/marking/?p=75)

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