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# Re: st: Why do -intreg- and -truncreg- not give me the same SD as -summarize- ?

 From Richard Williams To statalist@hsphsun2.harvard.edu Subject Re: st: Why do -intreg- and -truncreg- not give me the same SD as -summarize- ? Date Tue, 08 Nov 2011 11:11:22 -0500

```At 10:02 AM 11/8/2011, Seed, Paul wrote:
```
```Dear all,

Here is a puzzle that has been bothering me.

Interval regression is designed for the circumstances
where an outcome is sometimes observed only to be
in a particular range.  However it also copes with
some (or all) observed values being known exactly.
Like -summarize-, -intreg- and -truncreg-

But look at this:

* Begin program *
sysuse auto, clear
su price
truncreg  price ,
gen price2 = price
intreg price price2
* end program *

Putting the results together I get:
Method   |       Mean        Std. Dev/sigma
-------------+---------------------------------
summarize   |       6165.257    2949.496
intreg      |       6165.257    2929.499
truncreg    |       6165.257    2929.499

All 3 methods agree on the mean; but we have
two different estimates for the standard deviation.
The manual does not seem to discuss this.
Does anyone know what is going on, and is there any way
to correct the SD values from -intreg- & -truncreg-?
```
```
```
I think it has to do with the d.f. and how they are being adjusted for. If you do
```
reg price

```
you again get the 2949.496, which is the square root of the MST (8699525.97). MST is SST/73 = 635065396/73. If you instead use 74 in the calculations, you get
```
. di (635065396/74) ^ .5
2929.4991

```
which is what you are getting with intreg and truncreg. In other words, these routines seem to be using N rather than N-1 in their calculations.
```
```
I am not sure which SD you consider "correct" but it should just take a little algebra to convert from one to the other. The help files or manuals probably say something about how the SD is calculated, and why.
```

-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
HOME:   (574)289-5227
EMAIL:  Richard.A.Williams.5@ND.Edu
WWW:    http://www.nd.edu/~rwilliam

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