Most common answers on the SAT

fignewton
Sun, 06 Oct 2013 20:18:31 +0000

^That kind of accidental question would be caught in the pre-testing, I imagine.

Anyway, here are the stats for all the math questions I have:

Total 5-choice questions:   968
Expected number per letter: 193.6
Expected range per letter: 181.2 - 206.0 (one std deviation)

Results:

observed expec one-var z chi-sq
    --------     -----  ---------  ------
A  187  (19.3%)  193.6  z = -0.53  0.225
B  201  (20.8%)  193.6  z =  0.59  0.283
C  200  (20.7%)  193.6  z =  0.51  0.212
D  201  (20.8%)  193.6  z =  0.59  0.283
E  179  (18.5%)  193.6  z = -1.17  1.101


For one variable z, we need |z| > 1.96 for
95% confidence of a non-uniform distribution.

Total chi-squared = 2.10 (4 degrees of freedom).

Here are the stats for the level 4 and level 5 questions only:

Total 5-choice questions:   245
Expected number per letter: 49.0
Expected range per letter: 42.7 - 55.3 (one std deviation)

Results:

observed expec one-var z chi-sq
    --------     -----  ---------  ------
A   53  (21.6%)   49.0  z =  0.64  0.327
B   47  (19.2%)   49.0  z = -0.32  0.082
C   45  (18.4%)   49.0  z = -0.64  0.327
D   43  (17.6%)   49.0  z = -0.96  0.735
E   57  (23.3%)   49.0  z =  1.28  1.306


Total chi-squared = 2.78 (4 degrees of freedom).



Looks like the harder questions are consistent with a uniform distribution as well.