# Lilliefors test for paired series + Bonferroni correction

#### memoreyx

##### New Member
Hi all,

I got two series where I want to find out if they differ. The two series are paired meaning they are values for the same subjects.

N = 21

After:
0.87348565, 0.88276705, 0.89083918, 0.89520159, 0.89519151, 0.90286579, 0.90586482, 0.90750014, 0.90978787, 0.91008748, 0.91230162, 0.91239919, 0.91351324, 0.91252678, 0.9143977 , 0.91455409, 0.91543535, 0.91477876, 0.91474258, 0.91621539

vs.

Before:
0.87237036, 0.88131683, 0.88707848, 0.89019844, 0.89377109, 0.89800741, 0.89815093, 0.900106 , 0.90219807, 0.9036949 , 0.90731192, 0.90601837, 0.9077442 , 0.90806874, 0.90857466, 0.90886431, 0.91059263, 0.91194405, 0.91107657, 0.91180172

Now I want to find out if I can apply paired t-test on these. For that I assume I can do the lilliefors test first to find if I can apply paired t-test.

1.) But do I apply lilliefors on both or on differences? Therefore e.g. on differences:

0.00111529, 0.00145023, 0.0037607 , 0.00500315, 0.00142042, 0.00485838, 0.00771389, 0.00739414, 0.00758981, 0.00639259, 0.0049897 , 0.00638082, 0.00576904, 0.00445804, 0.00582304, 0.00568977, 0.00484272, 0.00283471, 0.00366601, 0.00441366

2.) And what do I do If I have a second measure or third measure again on same subjects therefore paired e.g.

Before (2nd measure)
0.83426767, 0.85143792, 0.86502183, 0.86890158, 0.86880438, 0.87811419, 0.88113642, 0.88550411, 0.88583958, 0.88720482, 0.88974418, 0.88957568, 0.89189286, 0.89221044, 0.89314301, 0.893826 , 0.89443584, 0.89436046, 0.89435159, 0.89541199
vs.

After (2nd measure)
0.83671624, 0.84266659, 0.8558027 , 0.8652697 , 0.86899957, 0.87205584, 0.87333222, 0.87763563, 0.88049981, 0.88221946, 0.88485865, 0.88542038, 0.88760014, 0.88886179, 0.8887682 , 0.88867261, 0.89062065, 0.89223041, 0.89223299, 0.89283359

Can/Should I apply Bonferroni correction to adjust the limit for the p-value of the lilliefors test?