Fractional ranking

[Helen Chang]

I have the variables in the data set that are the Pearson correlation coefficients. Do I need to convert them into fractional rankings first when use them in regressions? If so, how should I convert them into fractional rankings?

[Nick Cox]

Why would fractional ranks be better in any sense? What is the purpose of using correlations any way?

[Helen Chang]

It's the measure I am trying to replicate from prior literature. In previous papers, authors stated the following:

"The income-smoothing measure is the correlation between the change in discretionary accruals and the change in pre-discretionary income: Corr( DAP, PDI), using the current year’s and past four years’ observations. The use of five observations is a trade-off between a sufficiently long time-series for the income-smoothing measure and a large sample to test the model. We use annual data because there is much evidence that firms smooth fiscal year earnings and that fourth-quarter reporting is distinctively different from that of other quarters (Jacob and Jorgensen 2003; Das and Shroff 2002). To control for industry and time effects, we use a firm’s reversed fractional ranking of income smoothing (between 0 and 1) within its industry-year (two-digit SIC) and refer to it as IS. As a result, firms with a more negative correlation receive a higher income-smoothing ranking. (A fractional ranking is the raw rank divided by the number of observations. For example, the fractional rankings of 1 and 10 among the numbers 1 to 10 are 0.1 and 1, respectively.)"

I am a little bit lost on how to convert the correlation coefficients to fractional ranking in order to replicate this measure.

[Zien He]

I'm also replicating this paper. In particular, they said "reversed fractional ranking". Have you eventually figured out how to deal with this?

[Nick Cox]

#3 was a quick reply to #2. I couldn’t follow what it says.

[Muhammad Khurram Shabbir]

Hi, check this video, it also discusses fractional rankings; https://www.youtube.com/watch?v=twwT6FgwlAo

[Muhammad Khurram Shabbir]

You can also check this paper it has a good explanation, Templeton, G. F., & Burney, L. L. (2017). Using a Two-Step Transformation to Address Non-Normality from a Business Value of Information Technology Perspective. Journal of Information Systems, 31(2), 149–164. doi:10.2308/isys-51510