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From |
"Nick Cox" <[email protected]> |

To |
<[email protected]> |

Subject |
st: RE: sktest interpretation |

Date |
Wed, 7 Dec 2005 11:34:59 -0000 |

This is a fairly common question on Statalist. Missings are irrelevant to -sktest-, and are just ignored, so that is no problem. However, the fact that you got missings may or may not indicate some much deeper problem, but that's for you to consider. -sktest- is here rejecting a null hypothesis of normality. With your sample sizes, this is totally unsurprising. You are being told that your sample is large enough to distinguish between "genuine" non-normality and "apparent" non-normality that is just the sampling fluctuation that would occur if the underlying distribution really were normal. However, with your sample sizes, the kind of non-normality at which -sktest- squawks would not necessarily trouble any data analyst with experience. It is salutary to cycle through the numeric variables in Stata's auto data and look at -sktest- results. Here n is much smaller than yours at n = 74 but -sktest- often reports rejection on what graphical analysis will reveal as an unproblematic distribution. For example, -sktest- may reject if a variable is shorter-tailed than normal. It may reject if a variable is somewhat irregular in distribution, but otherwise not problematic. In a word, it is typically over-sensitive for the practical problem. Any test in this area still leaves the question of measuring, or more generally assessing, the kind of non-normality you have and of deciding whether non-normality is really a problem for what you are doing. A direct calculation of moments (or alternative measures such as L-moments) is sometimes helpful here. The issue of -sktest- versus a Jarque-Bera test is also secondary. Jarque-Bera typically seems to mean using asymptotic sampling distributions for skewness and kurtosis for a problem in which they are often a poor approximation. (Also, Jarque and Bera just reinvented a very old test. Why they got credit for that is mysterious, except on the hypothesis that people have no time for proper reading.) -sktest- is, more or less, Jarque-Bera done better with adjustments for sample size. My guess would be that it would make no difference in your case. Graphical examination of your residuals with -qnorm- will teach you far more about their (non-)normality than a -sktest-. The only practical reason for using -sktest- is whenever that you are obliged to use it by instruction from someone in power over you, namely an advisor, boss, reviewer or journal editor. Another detail is that -sktest- does not know that your variable is a residual and makes no adjustment for that fact. A wild guess is that this is just a purist issue in your case. Nick [email protected] M. Haider Hussain > Sorry for such a novice-level question. > > I ran an ols regression with 15 estimators and 14831 observations. In > this process, 437 missing values were generated. Then I tested > normality of the residual using sktest and it returned following > output. > > Variable | Pr(Skewness) Pr(Kurtosis) adj chi2(2) Prob>chi2 > -------------------------------------------------------------- > ------------------------------- > ewhe | 0.000 0.000 . > . > > whereas, sktest with noadjust option returned the following output > > Variable | Pr(Skewness) Pr(Kurtosis) adj chi2(2) Prob>chi2 > -------------------------------------------------------------- > ------------------------------- > ewhe | 0.000 0.000 3693.33 > 0.0000 > > > Where're the statistics of chi2 in the first instance? Does it mean > that sktest (without no adjust) is sensitive to the missing values? > Can I use jb test with 14000+ observations? If not than what other > "quantitative" tests are available? > (Or am I misinterpreting something?) * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: RE: sktest interpretation***From:*"M. Haider Hussain" <[email protected]>

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