[R-sig-teaching] [dmonterde at me.com: About the standard gaussian distribution]

[User Hayden]

Your English is better than that of many of my born-in-USA students;-)

I work regularly with high school teachers of AP Statistics -- a
program that allows high school students to get college credit for
college courses taken in high school -- in this case, an introductory
statistics course.  If I understand you then this is a question that
comes up regularly in AP Stats. (where the students use graphing
calculators with many statistical functions).

Should we work with the given units and technology that has normal
tables for any mu and sigma OR should we standardize everything?  When
we have the option, using the given units seems more natural.  OTOH,
standardizing provides review and practice of an important idea.  In
addition, if we introduce the t distrtibutin later, we will have to do
a kind of standardization there, so doing things different ways in
different chapters hides the essential difference behind a surface
difference. If we standardize in both cases students see that the
difference is whether we know sigma, not whether we standarize or
not. 


----- Forwarded message from David Monterde <dmonterde at me.com> -----

Date: Thu, 20 Apr 2017 17:07:45 +0200
From: David Monterde <dmonterde at me.com>
To: r-sig-teaching at r-project.org
Subject: [R-sig-teaching] About the standard gaussian distribution
X-Mailer: iPhone Mail (14E304)

First of all I have to apologize because my english is horrible. 

I am working in a basic and practical statistic course. 

I will speak about confidence intervals, of course. 

But when I was preparing this chapter I had a doubt: I wonder if it has sence today to explain the confidence intervals for a mean in terms of the standard normal distribution. 

If we show that the mean follows a normal distribution with variance/n then it is easy to explain (and to understand) that the confidence interval is due to two percentiles, the percentile alpha/2 and the percentile 1-alpha/2 from a normal distribution with the sample mean and the sample variance/n. 

I think that the standard gaussian distribution was usefull when we had to calculate CI in the past. 
That is, it was a simple way to have all possibilities in a single table (in paper). 

But now, we have R functions that let us to obtain the exact values for any normal distribution. 

I think that is not necessary to explain how to work with transformations if we can explain that a CI is simply to identify percentiles. 

What do you think?

Thanks

PD I know that the normal distribution for CI need some hipothesis. But I have focused the question

_________________________

David Monterde

Lo dif??cil se hace. 
Lo imposible se intenta. 
_________________________
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