# How to analyze right skewed data with a continuous DV?

I got my data from a questionnaire: group 1 had 30 individuals and group 2 also 30 individuals. They answered the same 6 questions where the opinions of others were exposed and after they could provide a final decision on those questions. Thus I could calculate weights on opinions (my DV) that range from 0 to 1 (continuous data), namely

WOA = (final estimate $-$ initial estimate )/(advice $-$ initial estimate).

DV = 0 means that participants stick to their initial estimates; DV = 0.5 means that they compromise; DV = 1 means that they adopt fully the other's opinion.

At the end, I got 6 different WOAs (per question).

The IV group is a dummy variable where 0 is group 1 and 1 is group 2.

The data look like this:

The data area not normally distributed: most of the estimations are close to 0. For example, the WOAs for 2 different questions:

I have found from previous posts here that a generalised linear model with binomial family, logit link and robust standard errors would be the most appropriate for an analysis.

But since my DV is a continuous variable is then a fractional logit model the best? If yes, but I have multi-level data: individuals (30 - 30), group ( 2) and type of questions/treatments (6). Would it be then right to do a fractional logit if I do not control for the level (type) and plus my distribution is not normal?

According to O'Hara, R. B. & Kotze, D. J. 2010. Do not log‐transform count data it is better to use a GLM with negative binomial family.

I am quite confused. I appreciate any help you can provide!

Plus, a bit out of the regression topic, since the means do not tell me much about the data, would it be better to present in the analysis the medians of those WOAs as a descriptive analysis?

• How many zeros and ones does your data set have? – Stefan Feb 7 '18 at 21:55
• @Stefan so, if I take across all 6 questions, 45% of the data set is namely zeros (around 120 observations), while ones are 6% ( 15 observations). – K.Zv Feb 8 '18 at 12:22
• Generally, if you have continuous between zero and one, beta regression would be most appropriate. See the betareg package as an example for how to do that in R. However since you zeros and ones this won't work. Also, ideally you need a mixed effects model of some sort that accounts for the "repeated" aspect of your study (the "id" column). In R, you could also have a look at the zoib package to do zero/one inflated beta regression... – Stefan Feb 8 '18 at 16:30
• What is the original outcome/answer in your questions in the questionnaire? – Stefan Feb 8 '18 at 16:34
• @Stefan Thank you! So zoib might then account for a random effect, is it right? Dont you know by chance how to use it in Stata?:) I use Stata for my analysis. Regarding the original outcomes, I have initial estimates, advice estimates and final estimates that are also not normaly distributed. Depending on the questions, there are either answers in persentage or in millions. – K.Zv Feb 8 '18 at 17:20