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. _________________________
About the standard gaussian distribution
3 messages · David Monterde, R. Michael Weylandt, Richard M. Heiberger
I agree that, for an intro class, working with the z-score + standard normal is probably unnecessary. If your students go further, it's a useful example of the idea of a pivot, but you can probably explain that when they get there.
On Thu, Apr 20, 2017 at 10:07 AM, David Monterde <dmonterde at me.com> wrote:
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.
_________________________
[[alternative HTML version deleted]]
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Let me suggest the interactive graphic NTplot in the HH package.
## install.packages("HH") ## if you don't have it yet.
library(HH)
NTplot(shiny=TRUE)
[to exit a shiny app, use C-c C-c in the R window in Macintosh, and
<esc> in the R window in Windows]
This single display covers about 60% of the introductory course.
See ?NTplot for additional examples.
Be sure to read the Details section and the examples.
On Thu, Apr 20, 2017 at 11:07 AM, David Monterde <dmonterde at me.com> wrote:
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.
_________________________
[[alternative HTML version deleted]]
_______________________________________________
R-sig-teaching at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-teaching