So sánh phép kiểm sktest swilk test

In Stata, you can test normality by either graphical or numerical methods. The former include drawing a stem-and-leaf plot, scatterplot, box-plot, histogram, probability-probability (P-P) plot, and quantile-quantile (Q-Q) plot. The latter involve computing the Shapiro-Wilk, Shapiro-Francia, and Skewness/Kurtosis tests.

The examples below are for the variable score:

Graphical methods Command Plot drawn`. stem score`stem-and-leaf`. dotplot score`scatterplot`. graph box score`box-plot`. histogram score`histogram`. pnorm score`P-P plot`. qnorm score`Q-Q plot

Numerical methods Command Test conducted`. swilk score`Shapiro-Wilk`. sfrancia score`Shapiro-Francia `. sktest score`Skewness/Kurtosis

The Shapiro–Wilk test is a test of normality. It was published in 1965 by Samuel Sanford Shapiro and Martin Wilk.

Theory[edit]

The Shapiro–Wilk test tests the null hypothesis that a sample x1, ..., xn came from a normally distributed population. The test statistic is

where

The coefficients are given by:

where C is a vector norm:

and the vector m,

is made of the expected values of the order statistics of independent and identically distributed random variables sampled from the standard normal distribution; finally, is the covariance matrix of those normal order statistics.

There is no name for the distribution of . The cutoff values for the statistics are calculated through Monte Carlo simulations.

Interpretation[edit]

The null-hypothesis of this test is that the population is normally distributed. Thus, if the p value is less than the chosen alpha level, then the null hypothesis is rejected and there is evidence that the data tested are not normally distributed. On the other hand, if the p value is greater than the chosen alpha level, then the null hypothesis (that the data came from a normally distributed population) can not be rejected (e.g., for an alpha level of .05, a data set with a p value of less than .05 rejects the null hypothesis that the data are from a normally distributed population – consequently, a data set with a p value more than the .05 alpha value fails to reject the null hypothesis that the data is from a normally distributed population).

Like most statistical significance tests, if the sample size is sufficiently large this test may detect even trivial departures from the null hypothesis (i.e., although there may be some , it may be too small to be of any practical significance); thus, additional investigation of the effect size is typically advisable, e.g., a Q–Q plot in this case.

Power analysis[edit]

Monte Carlo simulation has found that Shapiro–Wilk has the best power for a given significance, followed closely by Anderson–Darling when comparing the Shapiro–Wilk, Kolmogorov–Smirnov, and Lilliefors.

Approximation[edit]

Royston proposed an alternative method of calculating the coefficients vector by providing an algorithm for calculating values that extended the sample size from 50 to 2,000. This technique is used in several software packages including GraphPad Prism, Stata, SPSS and SAS. Rahman and Govidarajulu extended the sample size further up to 5,000.

I agree with all previous discussants (except that, contrary to Andrew, the phrase "academic purposes" is not necessarily pejorative!) .

I find normal quantile plots (sometimes called normal probability plots) enormously more helpful here than histograms with normal density functions superimposed. The latter tend to draw attention to apparent discrepancies in the middle of the distribution, which are often of no consequence, and do not make easy any analysis of discrepancies in the tails, which sometimes can be important and informative. Histograms are also sensitive to changes in bin start and bin width and Stata's default isn't optimized on your behalf.

Formal tests of residuals for normality here divide statistical people into two camps with no doubt some people wandering around confused in between. One camp people (no names, no fields for the sake of discretion) teaches that everything has to pass a significance test before you can possibly make a decision or an inference regarding it as established. The other camp. including myself FWIW, tend to sit loose and regard tests as providing some guidance but much less guidance than graphs provide. The biggest deal here, which isn't desperately controversial, is that if your sample size is large enough unimportant deviations from normality will be declared as significant at conventional levels, while with small samples failure to reject the null may just arise because you don't have enough data. These two cases don''t exhaust the logical possibilities, but they make significance tests problematic unless other evidence is also considered.

Here you have a hint from the normal quantile plot that two observations have slightly high positive residuals and it would always be worth going back to the data to examine which they are. They might turn out to be two really big countries or companies or two years that you know are unusual. As you don't name your variables or give example data, these are just indications.

If you have one predictor, then the main thing is to show us is a plot of the data with regression line superimposed. If you have several predictors, then show us added variable plots. A plot of residuals versus fitted is also often helpful.