Re: st: significance of mean and median

 From Ronan Conroy To "statalist@hsphsun2.harvard.edu" Subject Re: st: significance of mean and median Date Tue, 25 Nov 2008 10:22:24 +0000

```On 24 Nov 2008, at 11:55, Bastian Steingros wrote:

```
After creating the descriptive statistics of my sample I want to show that the mean of a certain variable is statistically significant. For example the mean of var1 is 0,45. Now I want to show that the positive sign is significant.
```
```
A regression without any predictor variable is a constant-only model, and the test for significance of the constant is a test that the constant is zero.
```
. sysuse auto
(1978 Automobile Data)

. regress mpg

```
Source | SS df MS Number of obs = 74 -------------+------------------------------ F( 0, 73) = 0.00 Model | 0 0 . Prob > F = . Residual | 2443.45946 73 33.4720474 R-squared = 0.0000 -------------+------------------------------ Adj R-squared = 0.0000 Total | 2443.45946 73 33.4720474 Root MSE = 5.7855
```
------------------------------------------------------------------------------
```
mpg | Coef. Std. Err. t P>|t| [95% Conf. Interval] ------------- +---------------------------------------------------------------- _cons | 21.2973 .6725511 31.67 0.000 19.9569 22.63769
```------------------------------------------------------------------------------

```
The coefficient for the constant is the mean of the data (since the mean is the statistic that minimises prediction error, when we define prediction error as the squared difference between observed and expected).
```
Similarly, quantile regression will test that the median is zero

. qreg mpg
Iteration  1:  WLS sum of weighted deviations =  330.13202

Iteration  1: sum of abs. weighted deviations =        330
Iteration  2: sum of abs. weighted deviations =        328

```
Median regression Number of obs = 74
```  Raw sum of deviations      328 (about 20)
```
Min sum of deviations 328 Pseudo R2 = 0.0000
```
------------------------------------------------------------------------------
```
mpg | Coef. Std. Err. t P>|t| [95% Conf. Interval] ------------- +---------------------------------------------------------------- _cons | 20 .7799751 25.64 0.000 18.44551 21.55449
```------------------------------------------------------------------------------

```
the median being the statistic which minimises error, when we define error as the absolute difference between the observed and expected.
```

Ronan Conroy
=================================

rconroy@rcsi.ie
Royal College of Surgeons in Ireland
Epidemiology Department,
Beaux Lane House, Dublin 2, Ireland
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