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Friday, December 03, 2010

Do (our) students avoid mondays and fridays?

The registration data for the undergraduate classes in our college were released earlier this week. I dragged the data into Stata and calculated the number of empty seats in each class. I then estimated a silly model which tested for differences-in-means between classes that meet once a week, twice a week, and three days a week:


Source | SS df MS Number of obs = 117
-------------+------------------------------ F( 7, 109) = 3.54
Model | 9755.77055 7 1393.68151 Prob > F = 0.0018
Residual | 42913.785 109 393.70445 R-squared = 0.1852
-------------+------------------------------ Adj R-squared = 0.1329
Total | 52669.5556 116 454.047893 Root MSE = 19.842

------------------------------------------------------------------------------
empty | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mw | -26.35268 13.96763 -1.89 0.062 -54.03606 1.330705
tr | -28.25621 13.83294 -2.04 0.043 -55.67264 -.8397799
mwf | -.0714286 9.185055 -0.01 0.994 -18.27591 18.13305
monly | -5.083333 12.80795 -0.40 0.692 -30.46827 20.3016
tonly | -.3214286 15.76099 -0.02 0.984 -31.5592 30.91634
wonly | -16.17857 12.43662 -1.30 0.196 -40.82755 8.470412
ronly | -11.82143 19.48444 -0.61 0.545 -50.43896 26.79611
_cons | 33.82143 13.52004 2.50 0.014 7.025158 60.6177


The omitted category is Friday-only classes. Those classes that meet once a week tend to have more empty seats than those that meet twice a week but no more or less seats than classes that meet three times a week. However, there is on statistically meaningful difference between the number of empty seats (on average) for MW vs. TR classes.

However, those classes that meet once a week might be held in bigger classrooms. Thus, I ran the same model with available seats being the dependent variable:


Source | SS df MS Number of obs = 117
-------------+------------------------------ F( 7, 109) = 0.65
Model | 11449.1888 7 1635.59839 Prob > F = 0.7114
Residual | 273157.598 109 2506.03301 R-squared = 0.0402
-------------+------------------------------ Adj R-squared = -0.0214
Total | 284606.786 116 2453.50678 Root MSE = 50.06

------------------------------------------------------------------------------
avl | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mw | -49.45536 35.23959 -1.40 0.163 -119.2991 20.38837
tr | -43.18634 34.89978 -1.24 0.219 -112.3566 25.98388
mwf | -27.64286 23.17341 -1.19 0.236 -73.57181 18.28609
monly | .3333333 32.31378 0.01 0.992 -63.71153 64.3782
tonly | -29.97619 39.76415 -0.75 0.453 -108.7874 48.83506
wonly | -20.57143 31.37695 -0.66 0.513 -82.75952 41.61667
ronly | -50.64286 49.15823 -1.03 0.305 -148.0729 46.78716
_cons | 120.6429 34.11034 3.54 0.001 53.03727 188.2484

Interestingly, there does not seem to be a clear pattern in class size and when a class meets. If anything, classes that meet twice a week might be held in smaller classrooms.

I thus converted the original dependent variable of empty seats into the percent of seats unsubscribed:

Source | SS df MS Number of obs = 117
-------------+------------------------------ F( 7, 109) = 4.09
Model | .986905122 7 .140986446 Prob > F = 0.0005
Residual | 3.75886104 109 .034484964 R-squared = 0.2080
-------------+------------------------------ Adj R-squared = 0.1571
Total | 4.74576617 116 .040911777 Root MSE = .1857

------------------------------------------------------------------------------
pctempty | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mw | -.2804511 .1307231 -2.15 0.034 -.53954 -.0213621
tr | -.3286963 .1294625 -2.54 0.013 -.5852868 -.0721057
mwf | -.0323198 .085963 -0.38 0.708 -.2026956 .138056
monly | -.1040963 .1198697 -0.87 0.387 -.3416741 .1334814
tonly | -.0269122 .1475072 -0.18 0.856 -.3192666 .2654423
wonly | -.2180844 .1163944 -1.87 0.064 -.4487744 .0126056
ronly | -.0283804 .182355 -0.16 0.877 -.3898021 .3330413
_cons | .3950471 .1265341 3.12 0.002 .1442606 .6458335

So, Friday only classes have a 40% of seats unregistered. Twice a week classes have a substantially lower percentage of empty seats. I would have thought students would seek to avoid MW classes by loading up on TR or once a week classes in the middle of the week. Instead, Wednesday only classes are the only once-a-week classes that have statistically lower rates of empty seats than the other once-a-week classes.

It would be ideal to have registration data over time so that one could test whether TR classes fill first, then come MW (or W) classes, and then the other classes fill later. If students have preferences for specific classes why are they not charged a premium to enroll for them?

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