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SchoolDigger.com Ranking Methodology
Summary:
SchoolDigger ranks schools by each school's Average Standard Score. The school with the highest Average Standard Score is ranked #1 in the state.
Why Standard Scores?
Comparing test scores from different grades and tests is problematic. As an example: from the table below, can you tell which school is perfoming best in math?
School 
Grade 
Math % Proficient 
Lincoln Elementary 
5th 
90.3 
Smith Elementary 
4th 
81.5 
Jefferson Elementary 
6th 
75.0 
The truth is, we can't tell from this data. The 4th grade test may be much more difficult than the 5th grade test, and therefore a lower score might actually be the "better" one.
So for a better method in comparing proficiency scores across different grades and tests, we map these raw scores onto a
Standard Normal Distribution.
This statistical method maps these numbers onto the same shaped bellcurve so that
we
can compare scores from different grades and tests.
For a terrific explanation of the process and why it is useful, see
Standard Normal Distribution at mathisfun.com.
How we calculate a school's Average Standard Score.
We will now walk through the mathmatical steps to calculate a school's Average Standard Score.
Let's use data from a fictional school: Smith Elementary in Topeka, Kansas.
In 4th grade math, Smith Elementary's students performed at an 81.5 percent proficiency level.
Test 
Grade 
% Proficient 
Math 
4th 
81.5% 
We first calculate a
ZScore for Smith Elementary's 4th grade math score. A ZScore is the multiple of standard deviations that Smith's 4th grade math score is from the 4th Kansas state mean (average) score. A positive ZScore means
the school score is above the Kansas state mean score, and a negative ZScore means the score is below the Kansas state mean score.
The ZScore calucation is:
Where χ is the 4th grade math proficiency score, μ is the mean score of all Kansas 4th grade math scores, and σ is the standard deviation of the Kansas 4th grade math scores.
In our case, the mean score for Kansas 4th grade math statewide (μ) is 59.960, and the standard deviation (σ) is 18.018.
So, the calculated ZScore for Smith Elementary is 1.195:
Test 
Grade 
% Proficient 
State Mean Score 
State Standard
Deviation 
ZScore 
Math 
4th 
81.5% 
59.96 
18.02 
1.195 
This ZScore is then mapped using the
standard normal distribution, which gives us our Standard Score:
Test 
Grade 
% Proficient 
State Mean Score 
State Standard
Deviation 
ZScore 
Standard Score 
Math 
4th 
81.5% 
59.96 
18.02 
1.195 
87.12% 
We do this for all the tests from Smith Elementary and calculate an Average Standard Score:
Test 
Grade 
% proficient 
State Average 
State Standard
Deviation 
ZScore 
Standard Score 
Math 
3rd 
85.90 
64.38 
17.09 
1.26 
89.60 
Math 
4th 
81.50 
61.06 
18.06 
1.13 
87.12 
Math 
5th 
68.90 
61.83 
17.08 
0.41 
66.07 
Math 
6th 
73.20 
59.85 
17.28 
0.77 
78.00 
Reading 
3rd 
87.20 
72.78 
14.47 
1.00 
84.05 
Reading 
4th 
87.30 
71.78 
14.45 
1.07 
85.86 
Reading 
5th 
83.60 
72.14 
14.70 
0.78 
78.23 
Reading 
6th 
77.50 
71.15 
14.21 
0.45 
67.26 
Science 
5th 
78.70 
65.72 
18.04 
0.72 
76.42 
Writing 
4th 
77.80 
60.85 
17.65 
0.96 
83.16 

Average: 
79.58 
So the final Average Standard Score for Smith Elementary is
79.58%. Our final ranking is based on this score, which is used in the rankings list:
Rank 
School 
Average Standard Score 
1 
Lincoln Elementary 
82.83 
2 
Smith Elementary 
79.58 
3 
Jefferson Elementary 
62.14 
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