[senco-forum] Urgent question re statistics please

The size of a standard deviation varies according to the type of curve, as I
understand it.  The Bell Curve shown on the British Picture Vocabulary Test
has a standard deviation of 15.  Any difference of 15 points is
statistically significant.

Percentiles measure position against the group but not absolute size of the
improvement. Percentiles tell you where in the group the kid stands on the
day that they took the tests.  So you could say that they did test "A" and
were at percentile 10, for example, and on test "B" they were on percentile
60.  To state the absolutely obvious, the kid is doing better on test B than
A.  Suppose, the kid then resits a different form of the same tests some
time interval later and they are now at percentile 20 in test "A" and still
at 60 in test "B".  So you can say there has been an improvement in test A
in comparison to their peers, and not B.  It is the size of the improvement
over time that you cannot measure with percentiles.  

Look at the Bell Curve on the British Picture Vocabulary Score sheet at how
percentiles bunch around the mean and standard scores have equal intervals.
You’ll see that the gap between two points on one part of the line on your
percentile line is not the same as the gap on another part, cos percentiles
are not at equal intervals and therefore plot as a curve, whereas standard
scores are at equal intervals and plot as a linear graph.

So it is not the plotting and comparison of percentiles per se that is
invalid but the statement that Fred has made the same progress by moving
from reading age of 5 to 6 as he has when he moved from reading age 9 to 10
as he grew up cos one gap is smaller than the other in actual terms even
though when expressed in ordinal numbers they appear to be the same.

So comparing percentile is valid to see where the kid stands in relation to
the group.  But not to see if their progress between points A and B is the
same as between points C and D.

The above was helpfully explained to me years ago by Martin Turner and it
has been very useful when talking to parents, explaining dyslexia screening
results.  The BPVS diagram is also very useful to show to teachers and
parents so they can relate to the figures.

If you receive reports that only quote percentiles these can quickly be
converted to standard scores - again the BPVS has a chart.

Philippa

-----Original Message-----
From: senco-forum-bounces at lists.becta.org.uk
[mailto:senco-forum-bounces at lists.becta.org.uk] On Behalf Of Mary Kelly
Sent: 12 October 2006 23:35
To: senco-forum at lists.becta.org.uk
Subject: [senco-forum] Urgent question re statistics please

Could someone out there who is more statistics-literate than I am please
answer these two questions:
1.	Am I right in thinking that a difference of 15 points in
standard scores is a standard deviation and is statistically
significant?
2.	Am I right in thinking that it is NOT right to plot percentiles
as a graph because it would exaggerate any differences and make them
look more significant than they really are. That is, graphs should show
standard scores rather than percentiles?
I’d be really grateful for an answer tonight if at all possible please?
Many thanks,
Mary

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