0

I have one sample with values of sugar intake pre and post intervention. I transformed the values for t test as the change from pre to post was negatively skewed but now I dont know how to report the results from t test? Can I just square back the mean and CI?

kjetil b halvorsen
  • 63,378
  • 26
  • 142
  • 467
Masa
  • 11
  • 2
    If a t test on the original (untransformed) data is still significant, I'd suggest reporting everything in terms of the original data. (Perhaps mention skewness in a one-sentence footnote, quoting the P-value from the t test on transformed differences.) // Advocates of transforming data seldom discuss how to report results in a way that is meaningful for a nonstatistical audience. – BruceET Aug 14 '18 at 23:30
  • 3
    This may be a bit of an [X-Y problem](http://xyproblem.info/). Given that the means of the square roots differ, this doesn't automatically guarantee that the means of the original variables do. You may be better using a test more directly related to your actual hypothesis (and a suitable model for the data on that scale). What is your actual question of interest (i.e. why are you doing a test in the first place -- what are you specifically trying to find out?) – Glen_b Aug 15 '18 at 02:16
  • Thank you so much for answering! I am trying to see if the participants decreased sugar intake after 2 years from the baseline. When I do the t-test with non-transformed values the mean is bigger than the baseline value so I have 350 (median baseline), 88 (median 2 years) but then t-test gives the mean -380 (CI). When i use sqrt of baseline and 2 yrs i get 15.9 mean in t-test so not sure how to report this – Masa Aug 15 '18 at 08:40
  • 1
    p.s. yes tests are significant, both transformed and non-transformed @BruceET – Masa Aug 15 '18 at 08:41
  • 1
    Good. Then I guess I'd use the test that is easy to report and include a footnote to indicate you are paying attention to assumptions. (I'd want to see the data to be absolutely sure, but in practice t tests get used in many cases where assumptions aren't met exactly.) – BruceET Aug 15 '18 at 09:20
  • @BruceET Thank you! So you think it is fine if i just leave -15 and CI for the mean difference without squaring it back ? and then write a footnote saying that mean was obtained using sqrt transformation – Masa Aug 15 '18 at 09:39
  • t = -21.325, df = 141, p-value < 2.2e-16 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -16.95649 -14.07931 sample estimates: mean of the differences -15.5179 – Masa Aug 15 '18 at 09:39
  • or can i square it back to 15^2 ? – Masa Aug 15 '18 at 13:33
  • To clarify, my suggestion is this: In the main text of your report/paper, _ignore the transformation entirely,_ reporting the actual avg difference and p-value of t test. In a footnote mention skewness, that you did a t test on square roots, and show its p-value. // In view of large sample size and tiny p-value for untransformed data, I don't think the transformation was necessary, and that trying to defend the square root as _the_ transformation to use is an unnecessary distraction. A very brief footnote mentioning you noticed skewness seems fine. // If this causes a problem, please say why. – BruceET Aug 15 '18 at 20:54
  • @BruceET Thank you for getting back! Yes that sounds fine. It just looked weird reporting t-test for untransformed values as the mean change is greater than baseline value.( baseline median = 350, 2-year median = 80, mean change -385) but I'm guessing it is okay if i back it up with a footnote. (I used median for descriptive stats because mean and SD gives me again greater SD than the mean). – Masa Aug 15 '18 at 22:28
  • Something seems wrong: Did you take square roots before or after finding subject differences? Why are you mixing means and medians? Did you have any negative differences, and if so what did you do for square roots then? For original data, do you have $\bar X - \bar Y = \bar D?$ – BruceET Aug 15 '18 at 23:06
  • I don't have any negative values. I did the t test with untransformed values first and it showed mean change as -380. But I chose to express the baseline and 2yr values of sugar intake as median IQR since they are not normally distributed so i can't report mean and sd. Is that right? – Masa Aug 16 '18 at 00:01
  • when i do the test with sqrt baseline and 2yr values then it shows mean change -15 – Masa Aug 16 '18 at 00:02
  • @BruceET Or maybe i can just use non parametric test Wilcoxon because it also shows very small p value observed with sqrt transformation? also, this is additional analysis only attached in my appendix – Masa Aug 16 '18 at 08:35

0 Answers0