A quintile is a specific type of quantile - divided into 5ths. A quartile is is a quantile divided into 4ths.
A Quartile divides a population distribution into four quarters (25th, 50th and 75th percentile), whereas quintiles divides the population distribution into fifths. Therefore quintiles offer an improved analysis of the population distribution.
I would argue this differently. There is a substantial amount of literature that demonstrates that stratifying data into 5 quantiles can remove over 90% of the bias due to the covariates used in the modelling process (Cochran, 1968; Rosenbaum & Rubin, 1984). Cochran used one continuous variable for this purpose, whereas Rosenbaum and Rubin utilized the propensity score (which then serves as the scalar for the multiple covariates). In any case many researchers that focus on treatment effects have come to divide their continuous data into 5 quantiles due to these results. That said, there is no rule that says that 5 is the ultimate number. You should ensure there is adequate distribution of the sample in each quantile of the data and scale up or down accordingly.
See the attached link for a paper I wrote on stratification of the propensity score. Hopefully that may be useful to you.
Ariel
Cochran WG. The effectiveness of adjustment by subclassification in removing bias in observational studies. Biometrics 1968;24:205-213.
Rosenbaum PR, Rubin DB. Reducing bias in observational studies using subclassification on the propensity score. Journal of the American Statistical Association 1984;79:516-524.
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