Method for Adjusting critical Z values for very large sample sizes ?

[Hal 9000]

Dear List,

I am working on a report that involves analyzing average gpa by course
by instructor, where each class an instructor taught constitutes a
sample.I am using Z tests, because I possess all data that constitutes
the population, and therefore the pop mean and sd are known. Since the
data spans many years, it is frequently the case that a particular
course, say English 100, has been taught multiple times by a single
teacher. The average gpa and sd for English 100 for a particular
instructor, then, might be calculated upon 1000 individual grades (20
sections of English 100 with 50 students per class).

However, when I plug in these values into the Z-test formula (sample
mean - pop mean/ (sigma / sqrt(sample n)) I wind up getting some
Z-scores way up in the 15's and 20's. When I plot a histogram of all
Z-Scores and superimpose my p=.20 critical values, it looks like I'm
only getting small sliver of center of the distribution rather than
the 80% I was expecting to see. The mean of the Z-Score distribution
is .03, SD = 2.47, N = 5,906. I found that if I multiply my critical
value (1.29) by the actual standard deviation of the plotted Z-Scores
(2.47), the resulting critical value falls pretty much where I was
expecting it to, so that approximately 80% of the observations fall
between the critical values.

My question - is this an appropriate way to adjust the critical
values, should I use another method, or should I just let them be?

Thank you,
-Gary

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[Hal 9000]

I see that my question was a proof in disguise of how the std error of
the mean replaces the pop sd for z-tests. Getting answers from
knowledgeable people is good - answer your own question is better!

-Gary







On Tue, Aug 5, 2008 at 10:37 PM, Granaas, Michael
<[hidden email]> wrote:

>
> For z-scores your SD should be very close to 1.0  Since you are getting 2.47 there is some flaw in the way you are computing your z-scores.  That is the problem you need to correct.
>
> As I understand your problem you are taking all students and computing the mean and SD for their GPA.  You are then using this population mean as a standard of comparison for individual faculty in specific courses.
>
> I suspect that there is a problem in translating from student grades in a single class (3 credit hours) and overall student GPAs (~128 credit hours).  I would fully expect that individual class grades would be considerably more variable than career GPAs.
>
> If you have not already done this try finding the mean GPA and SD for all individual course grades.  If you have already done this, then I'm not sure where the problem is, only that there is a problem.
>
> Michael
> ****************************************************
> Michael Granaas             [hidden email]
> Assoc. Prof.                Phone: [phone]
> Dept. of Psychology         FAX:  [phone]
> University of South Dakota
> 414 E. Clark St.
> Vermillion, SD 57069
> *****************************************************
>
>
>
>
> -----Original Message-----
> From: SPSSX(r) Discussion on behalf of Hal 9000
> Sent: Tue 8/5/08 11:09 AM
> To: [hidden email]
> Subject: Method for Adjusting critical Z values for very large sample sizes ?
>
> Dear List,
>
> I am working on a report that involves analyzing average gpa by course
> by instructor, where each class an instructor taught constitutes a
> sample.I am using Z tests, because I possess all data that constitutes
> the population, and therefore the pop mean and sd are known. Since the
> data spans many years, it is frequently the case that a particular
> course, say English 100, has been taught multiple times by a single
> teacher. The average gpa and sd for English 100 for a particular
> instructor, then, might be calculated upon 1000 individual grades (20
> sections of English 100 with 50 students per class).
>
> However, when I plug in these values into the Z-test formula (sample
> mean - pop mean/ (sigma / sqrt(sample n)) I wind up getting some
> Z-scores way up in the 15's and 20's. When I plot a histogram of all
> Z-Scores and superimpose my p=.20 critical values, it looks like I'm
> only getting small sliver of center of the distribution rather than
> the 80% I was expecting to see. The mean of the Z-Score distribution
> is .03, SD = 2.47, N = 5,906. I found that if I multiply my critical
> value (1.29) by the actual standard deviation of the plotted Z-Scores
> (2.47), the resulting critical value falls pretty much where I was
> expecting it to, so that approximately 80% of the observations fall
> between the critical values.
>
> My question - is this an appropriate way to adjust the critical
> values, should I use another method, or should I just let them be?
>
> Thank you,
> -Gary
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD
>
>

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