Result interpretation of normality test "xtsktest"

[Waqar Ali Khan]

kindly help me to interpret the attached results. the results are produced after xtsktest normality test. kindly can any one tell me how can i interpret and what does highlighted (tick marked) values mean. thanks in advance

[Waqar Ali Khan]

sorry forgot to mention xtsktest test is used for checking the normality i.e. skewness and kurtosis of the panel data

[Nick Cox]

Kurtosis for your e terms is about 6. That's the most striking result. A reference is that is what you expect with a t distribution with 6 df. (That doesn't mean that they **have** that distribution and indeed your distribution is slightly right skewed, not symmetric; it just means that the kurtosis is the same.)

[Waqar Ali Khan]

Kurtosis for your e terms is about 6. That's the most striking result. A reference is that is what you expect with a t distribution with 6 df. (That doesn't mean that they **have** that distribution and indeed your distribution is slightly right skewed, not symmetric; it just means that the kurtosis is the same.)

so the data is not normally distributed. can i run panel regression on non-normally distributed data? or should i normalize the data first.

[Waqar Ali Khan]

and what is the difference between e terms and u terms.

[Nick Cox]

Do please read the help:

In the one-way error-components model, y_it = x_it*b + u_i + e_it,

If there is an issue it is not the data are normally distributed, it's terms within the model.

[carlton durrant]

Hi Nick
Can you help me interpret the normality results of the two models below using the xtsktest . Are they nonnormal distribution?

Model 1
Tests for skewness and kurtosis Number of obs = 370
Replications = 50

(Replications based on 37 clusters in CUID)
------------------------------------------------------------------------------
| Observed Bootstrap Normal-based
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Skewness_e | -4.08e-07 3.50e-07 -1.17 0.244 -1.09e-06 2.78e-07
Kurtosis_e | 6.13e-08 1.49e-08 4.12 0.000 3.21e-08 9.05e-08
Skewness_u | 1.40e-08 1.87e-07 0.07 0.941 -3.53e-07 3.81e-07
Kurtosis_u | -4.18e-09 3.58e-09 -1.17 0.244 -1.12e-08 2.85e-09
------------------------------------------------------------------------------
Joint test for Normality on e: chi2(2) = 18.29 Prob > chi2 = 0.0001
Joint test for Normality on u: chi2(2) = 1.36 Prob > chi2 = 0.5055


model 2

Tests for skewness and kurtosis Number of obs = 370
Replications = 50

(Replications based on 37 clusters in CUID)

Observed Bootstrap Normal-based
Coef. Std. Err. z P>z [95% Conf. Interval]

Skewness_e -9.40e-09 2.53e-07 -0.04 0.970 -5.06e-07 4.87e-07
Kurtosis_e 2.84e-08 6.54e-09 4.33 0.000 1.55e-08 4.12e-08
Skewness_u -2.46e-07 1.47e-07 -1.68 0.093 -5.34e-07 4.14e-08
Kurtosis_u 3.74e-09 2.11e-09 1.77 0.076 -3.94e-10 7.88e-09

Joint test for Normality on e: chi2(2) = 18.79 Prob > chi2 = 0.0001
Joint test for Normality on u: chi2(2) = 5.96 Prob > chi2 = 0.0508

the summary table is below.

Skewness/ Kurtosis test for panel data
	Model 1	Model 2	Model 3	Model 4
Test of Normality(P values)
Joint test for Normality on e	0.0001	0.0001	0.0001	0.0035
Joint test for Normality on u:	0.5055	0.0508	0.061	0.0361