ANOVA Bonferroni Barlet

[Natalia Gonzalez]

Good afternoon,

I was wondering if somebody could help me with this question.
I am doing a test-retest study. I am classifying the values by tertiles and I am trying to identify if there is a significant difference between the three tertiles (a difference in the variability across tertiles)

I calculated the difference between test1 and test2, and then, I used oneway anova (mean difference) by tertile.
I was wondering if this is the proper way to do it. I also was wondering if I should do Bonferroni correction.
In addition to that, if Barlett's test is significant, what should I do?

(Picture attached)

Thank you so much for your help.

Natalia

[Carlo Lazzaro]

Natalia:
I'm wondering whether you can't go -regress-, as in the following toy-example:

use "http://www.stata-press.com/data/r15/auto.dta"
g price2=price*runiform()
g diff=price-price2
xtile tert = diff, nq(3)
reg diff i.tert
      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(2, 71)        =     79.25
       Model |   280718191         2   140359096   Prob > F        =    0.0000
    Residual |   125750375        71  1771132.04   R-squared       =    0.6906
-------------+----------------------------------   Adj R-squared   =    0.6819
       Total |   406468566        73  5568062.55   Root MSE        =    1330.8

------------------------------------------------------------------------------
        diff |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        tert |
          2  |   1782.053   376.4181     4.73   0.000     1031.497    2532.609
          3  |   4746.284   380.3189    12.48   0.000      3987.95    5504.618
             |
       _cons |   762.8876   266.1678     2.87   0.005     232.1641    1293.611
------------------------------------------------------------------------------

[Natalia Gonzalez]

Dear Carlo,

Thank you so much! It is really helpful.
At the time of reporting the p-values, doing the regression, I should report the p-value of each pair right? I was hoping to report just one p-value.
I am not sure if that is fine as in case of significance I am not specifying which groups are different. That is why I thought that Bonferroni would give me the p-value between each group , example tertile 1 vs tertile 2, tertile 1 vs tertile 3...
What are your thoughts on this?

Thank you so much!
Natalia

[Carlo Lazzaro]

Natalia:
you may want to try something along the following lines, that will give you back an oneway ANOVA-like results:

test(1.tert 2.tert 3.tert), mtest(bonferroni)

Otherwise you can -test- each couple of coefficients separately and impose 0.05/3 p-value as a yardstick to test whether there's a <0.05 statistical significance (please see below an example concerning the first and the second tertile):

. test 1b.tert=2.tert

 ( 1)  1b.tert - 2.tert = 0

       F(  1,    72) =   83.09
            Prob > F =    0.0000

[Marcos Almeida]

As a side note to Carlo's insightful replies, if you wish to stick with the "ANOVA frame of mind", maybe you should take a look at the user-written program - wtest - which performs Welch's ANOVA.

If you type - help wtest -, you'll get this information:

package wtest from https://stats.idre.ucla.edu/stat/stata/ado/analysis
-------------------------------------------------------------------------------

TITLE
      W test for test of equal means

DESCRIPTION/AUTHOR(S)
      Allows you to use perform tests similar to
      standard ANOVA F tests, but often with better
      control of Type I error rates when
      heterogeneity of variance is present.
      See also simanova and fstar.
      Statistical Consulting Group
      Institute for Digital Research and Education, UCLA
      [email protected]
      
      STATA ado and hlp files in the package
      distribution-date: 20150326

Hopefully that helps.

[Natalia Gonzalez]

Dear Carlo and Marcos,

Thank you so much! Both suggestions are perfect for my analyses. Thank you so much! Without your help, I wouldn't have figured this out...

If you find it appropriate, I may ask for more help... I was also wondering if you could help me with another side of this analyses. I place another comment as it is a different test than ANOVA.
https://www.statalist.org/forums/for...ge-test-retest

Thank you so much!

[Marcos Almeida]

Thank you for your kind feedback, Natalia.