Comparing two different results You can do this with your tests How well did you go Tim wants to know if is hard study has paid off He recently completed two math tests This is what I told him ID: 508670
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Slide1
Standard Scores
Comparing two different results
You can do this with your testsSlide2
How well did you go?
Tim wants to know if
is hard study has paid
off.
He recently completed two math tests.Slide3
This is what I told him
Test One
Mark of:
27
30
Test Two
Mark of:Slide4
This is what I told him
Test One
Mark of:
27
30
Test Two
Mark of:
Out of:
5
0
Out of:
40Slide5
So
I told him the average
Test One
Mark of:
27
30
Test Two
Mark of:
Out of:
5
0
Out of:
40
23
Mean :
25
Mean:Slide6
Then I told him the standard deviation
Test One
Mark of:
27
30
Test Two
Mark of:
Out of:
5
0
Out of:
40
23
Mean :
25
Mean:
5
Standard Deviation
10
Standard DeviationSlide7
Conclusion
Why is it so hard to tell?
Did Tim improve from
Test 1 to Test 2?Slide8
Conclusion
It is hard to
tell because the
tests a
re out of
different things.Slide9
Conclusion
How he compared to
e
verybody else mightgive a better indication of his possible improvement.Slide10
Standardising Scores
One way to compare scores that are
coming from different scales is to rescale them or standardise them.
The process will be demonstratedSlide11
Standardising Scores
Consider this set of test scores out
of ten
average =
1, 2, 3, 4, 5, 5, 5, 6, 6, 7, 8, 9
standard
deviation =
5
1.732Slide12
Standardising Scores
Compare each score to the average
-3, -2, -1, -1,
0
,
0
, 0, 1
, 1, 2, 3
Subtract
the average away from eachscore
2, 3, 4, 4, 5, 5, 5, 6, 6, 7, 8Slide13
Standardising Scores
Compare each new score to the standard deviation
-3, -2, -1, -1,
0
,
0
, 0, 1
, 1, 2, 3
Do this by dividing each score by the
standard deviation of 1.732
-1.73, -1.15, -0.57, -0.57, 0, 0, 0, 0.57, 0.57, 1.15, 1.73Slide14
What did we just do?
Take a raw score such as 7
Subtracted away the average giving 2
Then compared this descaled score to the variation of the group(Standard deviation)
Slide15
Look at TIM
Test One
Mark of:
27
Out of:
40
23
Mean :
5
Standard Deviation
Slide16
Interpreting the Results
The standardised score above 1 is starting to be very good
The larger the number the higher the score was in relation to the groupSlide17
TIM’S TEST TWo
30
Test Two
Mark of:
5
0
Out of:
25
Mean:
10
Standard Deviation
Slide18
Exercise 13ASlide19
Exercise 13ASlide20
Exercise 13ASlide21
Exercise 13ASlide22