**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 2
^{nd}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 99^{th} 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 57^{th} 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 1^{st}percentile. (they ranked the lowest out of 100)- Ex. Your height is at the 2
^{nd}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 40-60
^{th}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. 40**^{th}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 50
^{th}percentile - Therefore scores above the 50
^{th}percentile are ‘above average’ and scores below the 50^{th}percentile are ‘below average’ - ‘
**Average’ is usually reported as a range (i.e. 40**^{th}– 60^{th}percentile)

**Average** is a range of scores in the middle of everyone else’s scores. So people in the middle (40-60^{th} percentile) scored **more than** the people who scored less than the 40^{th} 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)

**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)