How to assess 'close to normal' distribution using skew, kurtosis and -sktest-?

[Emily Mann]

Hi Stata list,

I am running 3x logistic regressions, each with an interaction.
For example,

logistic fightpart i.visittoptwohotspot i.clubbingfreq i.drinkconsumed c.restrictivetotal i.drinkconsumed#c.restrictivetotal

I looked at the distribution of each of the three predictors - restrictivetotal inhibitedtotal exageratedtotal. To me, the historgrams for restrictivetotal and inhibitedtotal do not look like a 'close to normal' distribution, though my judgment and experience in data analysis are limited. I think the skew and kurtosis numbers look OK. But the -sktest- command shows that they are not normal.

Do the skew and kurtosis figures represent a close to normal distribution? Is it worth paying attention to the results of the -sktest-?

cheers
Emily

. sum restrictivetotal inhibitedtotal exageratedtotal, detail

                      restrictivetotal
-------------------------------------------------------------
      Percentiles      Smallest
 1%            5              5
 5%            6              5
10%            8              5       Obs                 663
25%           11              5       Sum of Wgt.         663

50%           14                      Mean           14.37557
                        Largest       Std. Dev.      5.093015
75%           18             25
90%           21             25       Variance        25.9388
95%           23             25       Skewness       .1411719
99%           25             25       Kurtosis       2.379279

                       inhibitedtotal
-------------------------------------------------------------
      Percentiles      Smallest
 1%            5              5
 5%            5              5
10%            5              5       Obs                 663
25%            8              5       Sum of Wgt.         663

50%           11                      Mean           12.00905
                        Largest       Std. Dev.      5.233223
75%           15             25
90%           20             25       Variance       27.38662
95%           22             25       Skewness       .5554661
99%           25             25       Kurtosis       2.515539

                       exageratedtotal
-------------------------------------------------------------
      Percentiles      Smallest
 1%            8              5
 5%           10              6
10%           12              6       Obs                 663
25%           14              6       Sum of Wgt.         663

50%           17                      Mean           16.63499
                        Largest       Std. Dev.      3.794906
75%           19             25
90%           22             25       Variance       14.40131
95%           23             25       Skewness      -.0951031
99%           25             25       Kurtosis        2.88996


. sktest restrictivetotal inhibitedtotal exageratedtotal

                    Skewness/Kurtosis tests for Normality
                                                          ------ joint ------
    Variable |        Obs  Pr(Skewness)  Pr(Kurtosis) adj chi2(2)   Prob>chi2
-------------+---------------------------------------------------------------
restrictiv~l |        663     0.1354        0.0000       21.00         0.0000
inhibitedt~l |        663     0.0000        0.0010       33.98         0.0000
exagerated~l |        663     0.3132        0.6303        1.25         0.5345