Re: Significance of Decline in Student Enrollment
- From: dave@xxxxxxxxxxx
- Date: 2 Sep 2006 19:29:43 -0700
Richard Ulrich wrote:
On 2 Sep 2006 05:33:52 -0700, dave@xxxxxxxxxxx wrote:
statamerica@xxxxxxxxx wrote:
To Whom It May Concern:
A study is being conducted in order to assess student attrition. For a
cohort of students, I have their enrollment data for a period of 5
terms. For example, for the fall 2001 students their data may appear
as follows.
01/FA 02/WI 02/FA 03/WI 03/FA
100% 73% 65% 59% 12%
980 720 640 575 115
Would you recommend a statistical test that would allow me to determine
if there is a significant decline in enrollment from one semester to
the next?
Appreciatively
Jon
Jon,
It appears that you have 5 consecutive readings of
980,720,640,575,115 and you wish to test the hypothesis of "significant
decline" . One could identify the appropriate model for these 5 values,
Dave,
It was named "student attrition" in the first sentence, though the
OP says "decline" several times. Thinking of attrition of an
original sample, I would look at the proportions that dropped
out at each interval, instead of the additively-linear decline.
be it a simple trend model or an ARIMA process or some combination
called a TRANSFER FUNCTION where the 5 data points ( or more if you
have them ) would be used to identify the model form and the best
parameters. Furthermore one could conduct INTERVENTION DETECTION to
detect anomalies or level shifts or local time trends which then might
be useful in testing possible hypotheses.
Using some powerful time series software like AUTOBOX's freeware
version FREEFORE you can get the following (
http://www.autobox.com/freef.exe )
With as few as 5 data points one might be well advised to suggest a
starting model , say a simple ols trend model. This yields the
following fitted points
time observed fit
1 980 981
2 720 793
3 640 606
4 575 418
5 115 231
woth no statistically significant outliers ( one time anomalies ) .
Furthermore no change in trend can be proven with this approach , which
doesn't mean that it doesn't exist ...just that it can't (yet !) be
proven.
I suppose that the proportional decline can be modeled by
using the logarithm of each Observed number....
Does that show a break?
This seems like an unusual application for ARIMA time-series
models.
ARIMA models can be useful in representing the general term e.g.
8,7,6,5,,,,,1 is a process that can be characterized as y(t)=y(t-1)-1
it can also be represented as y(t)=9-1*t where t-1,8
additionally if you have
20,19,18,17,16,15,13,11,9,...1 you can repesent this as a two trend
equation
y(t)=21-1*x1-1*x2
x1=i for i=1,13
x2=0,0,0,0,0,0,1,2,3,4,5,6,7
thus the detection of the break point in trend at time period 7 enables
one to suggest that
there has been a significant change in trend and one needs to find out
what may have been the "cause"
similarly
20,19,18,17,16,15.14.13.12,11,10,9,8,7,6,5,4,3,1
suggests an anomaly at time period 19 as the basic equation
y(t)=21-1*i for i=1,19 is violated at time period 19 suggesting
y(t)=21-1*i-2*x1 where x1 =0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1
ARIMA models are expressions of recursive relationships ..incorporating
x's into the equation generalizes the model to a transfer function.
Since only 5 values were available apurely empirical approach was not
very useful thus I suggested a simple everyday trend model and then
used Intervention Detection schemes to examine for anomalies using a
threshold or alpha=.05
Regards
Dave R
I note that when the Ns get smaller, the variances
will increase. Is there a way to explicitly handle that?
As you get more data points , it might be possible to actaully detect
break points in trend or level shifts suggesting structural break
points.
Hope this little exercise has been of help. For more discussion of time
series series analysis please enroll at AFS UNIVERSITY at
http://www.autobox.com and take some courses ....all free of charge !
--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.
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