FS4 (First Stage Stratification and Selection in Sampling)

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FS4 is an open source generalized software for first stage stratification and selection in sampling related to two or more stages, implemented completely in R language and with a GUI (Graphical User Interface).

It merges two data frames (whatever PSU – Primary Sampling Unit – population and allocation data frames) and then, computes stratification and selection of a fixed number of sample PSUs per stratum using the Sampford’s method (unequal probabilities, without replacement, fixed sample size), implemented by the UPsampford function of R package “sampling”.

As for stratification, the function carries out, for each estimation domain, the computation of a size threshold for a given size PSU. PSUs with measure of size exceeding a calculated threshold are identified as SR (Self Representative)  and each constitutes a stratum on its own. The remaining NSR (Non Self Representative) PSUs are ordered by measure of size and divided into strata having sizes approximately constant to the corrected threshold and with PSUs having sizes as homogeneous as possible. For each PSU, FS4  determines the size of  final sample units on the basis of the size planned in input.

The main features of FS4 are the following:

  • it is a flexible software allowing the user to:
    • choose the measure of size to define stratification and inclusion probability for PPS (Probability Proportional to Size);
    • insert as input a single or plural (variable between domains) planned size of final sample units to observe in each PSU;
    • launch the procedure in two separate steps, so to observe an initial output and on the basis of this modify the input parameters;
  • it is a open source package released under EUPL licence;
  • it has a user friendly GUI that also allows to non-expert R users to use it, implemented in Tcl/Tk by means the R “tcltk” package, although for expert R users the StratSel function from R command line can be used directly.


Status: validated
Author: Istat
Licence: EUPL-1.1
GSBPM code: 2.4 Design frame and sample
4.1 Create frame and select sample
Programming language: R
Language of the GUI: EN
Keywords: stratification, selection, sampling, PSU
Contact: name: Raffaella Cianchetta
email: cianchet@istat.it

Software and documentation


R (version ≥ 3.0.1)

R packages: tcltk2, svMisc, plyr and sampling


Copyright 2013 Istat

Licensed under the European Union Public Licence (EUPL), version 1.0 or subsequent. You may not use this work except in compliance with the Licence. You may obtain a copy of the Licence at: http://ec.europa.eu/idabc/eupl.html. Unless required by applicable law or agreed to in writing, software distributed under the Licence is distributed on an “AS IS” basis, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the Licence for the specific language governing permissions and limitations under the Licence.


Istat assumes no responsibility for the results arising from use of the instrument that is inconsistent with the methodological guidance contained in the documentation available.


Install the downloaded package from within R as follows:
> install.packages(path_to_file, repos = NULL)
where the character path_to_file is the path to the .zip or .tar.gz file you downloaded.


Reference manual – FS4 v. 2.0

User manual – FS4 v. 2.0

Last edit: 08 July 2020