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When we try to learn how to work with time series, it is very useful to have good data sets, and much better if they contain real data. It is difficult to obtain long series, or series presenting interesting and well located and identified patterns, with which we can perform practices. An excellent source of complex time series is our own organism, and everything we can learn by working with them can be extrapolated to any other context.

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The correspondence analysis is a statistical technique that allows us to study relationships between categorical data through optimal scaling and orthogonal projection in two or three dimensions of contingency tables. Its implementation is relatively simple, and in this article I will show an example using the csharp language. In addition, the sample program allows you to draw simple graphics with the resulting data.

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The PISA database contains, in addition to the scores of students, a lot of demographic, socioeconomic and cultural data about them, collected through a series of questionnaires, that allow contextualize the academic results and make studies with a great number of variables. Most of these data are categorical, making the correspondence analysis a particularly appropriate tool to work with them. In this article I will show you how to easily perform this analysis using the ca package of the R program.

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In this new article of the series dedicated to the graphic characterization of complex time series I will talk about two other graphical tools that can be useful, the power spectrum of the signal, which will be obtained through the Fourier transform, and the graph of the distribution of values of the series, a simple histogram with the frequency of the different values that also can provide us information about the series dynamics.

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Many of the data sets with which we usually work are in the form of time series. A time series can be seen as the evolution of a dynamic system, characterized by some variables and parameters. Depending on the type of dynamic of the system, the series may be stationary, periodic, quasiperiodic, chaotic or random. In this series of articles, I will focus on the characterization of chaotic dynamics, which is presented by complex systems, by using graphical methods.

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In this post you can download the R code samples to work with plausible values in the PISA database, to calculate averages, mean differences or linear regression of the scores of the students, using replicate weights to compute standard errors.

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In the previous article in this series we viewed how to computing standard errors with replicate weights in PISA database, in this article we will take an overview of one of the most controversial points of these studies, the complex system of scores implemented.

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In this post you can download the R code examples to compute the standard errors of the mean, standard deviation, proportions or mean differences, on the data of the PISA database, using the replicate weights method.

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In the previous article in this series we saw an introduction to PISA data analytics, with examples of functions in R code for sampling, and we talked about the sampling weights, which ponder each student so that it represents a group of individuals with the same characteristics rather than a single student, (remember that PISA aims to assess the effect of educational policies on the whole population of the country, not on individual students). In this article, we will see how to use these weights to calculate estimators from samples and we'll see also how to calculate standard errors of these estimators using replicated weights.

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In this post you will find examples of R code for data sampling in PISA database. In these examples the different weights of students, schools or parents are corrected depending on the number of records selected for the sample. Also there are examples of stratified sampling using the values in a particular column in the data set.

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Every three years, since 2000, the OECD (Organization for Economic Cooperation and Development) performs a series of tests in a number of countries at national level to 15-years-old students, in order to assess the degree of knowledge in three main groups of areas: science, reading and math. This is the PISA program, whose last edition took place in 2015.

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