Two-way ANOVA for repeated measures using Python

Previously I have shown how to analyze data collected using within-subjects designs using rpy2 (i.e., R from within Python) and Pyvttbl. In this post I will extend it into a factorial ANOVA using Python (i.e., Pyvttbl). In fact, we are going to carry out a Two-way ANOVA but the same method will enable you to analyze any factorial design. I start with importing the Python libraries that  are going to be use. Continue reading

Three ways to do a two-way ANOVA with Python

In an earlier post I showed four different techniques that enables one-way analysis of variance (ANOVA) using Python.  In this post we are going to learn how to do two-way ANOVA for independent measures using Python.

An important advantage of the two-way ANOVA is that it is more efficient compared to the one-way. There are two assignable sources of variation – supp and dose in our example – and this helps to reduce error variation thereby making this design more efficient. Two-way ANOVA (factorial) can be used to, for instance, compare the means of populations that are different in two ways. It can also be used to analyse the mean responses in an experiment with two factors. Unlike One-Way ANOVA, it enables us to test the effect of two factors at the same time. One can also test for independence of the factors provided there are more than one observation in each cell. The only restriction is that the number of observations in each cell has to be equal (there is no such restriction in case of one-way ANOVA).

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Four ways to conduct one-way ANOVAs with Python

The current post will focus on how to carry out between-subjects ANOVA using Python. As mentioned in an earlier post (Repeated measures ANOVA with Python) ANOVAs are commonly used in Psychology.


We start with some brief introduction on theory of ANOVA. If you are more interested in the four methods to carry out one-way ANOVA with Python click here. ANOVA is a means of comparing the ratio of systematic variance to unsystematic variance in an experimental study. Variance in the ANOVA is partitioned in to total variance, variance due to groups, and variance due to individual differences.

Python ANOVA - theory - partitioning of the sum of squares (i.e., the variance)
Partioning of Variance in the ANOVA. SS stands for Sum of Squares.

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Repeated measures ANOVA using Python

A common method in experimental psychology is within-subjects designs. One way to analysis the data collected using within-subjects designs are using repeated measures ANOVA. I recently wrote a post on how to conduct a repeated measures ANOVA using Python and rpy2. I wrote that post since the great Python package statsmodels do not include repeated measures ANOVA. However, the approach using rpy2 requires R statistical environment installed.  Recently, I found a python library called pyvttbl whith which you can do within-subjects ANOVAs.  Pyvttbl enables you to create multidimensional pivot tables, process data and carry out statistical tests. Using the method anova on pyvttbl’s DataFrame we can carry out repeated measures ANOVA using only Python. Continue reading

Descriptive statistics using Pandas, NumPy, and SciPy.

Descriptive Statistics using Python

Descriptive Statistics

After data collection, most Psychology researchers use different ways to summarise the data. In this tutorial we will learn how to do descriptive statistics in Python. Python, being a programming language, enables us  many ways to carry out descriptive statistics.
One useful library for data manipulation and summary statistics is Pandas.  Actually, Pandas offers an API similar to Rs. I think that the dataframe in R is very intuitive to use and Pandas offers a DataFrame method similar to Rs. Also, many Psychology researchers may have experience of R.

Thus, in this tutorial you will learn how to do descriptive statistics using  Pandas, but also using NumPy, and SciPy. We start with using Pandas for obtaining summary statistics and some variance measures. After that we continue with the central tenancy measures (e.g., mean and median) using Pandas and NumPy. The harmonic, geometric, and trimmed mean cannot be calculated using Pandas or NumPy. For these measures of central tendency we  will use SciPy. Towards the end we learn how get some measures of variability (e.g., variance using Pandas).

Simulate response time data

Many times in experimental psychology response time is the dependent variable. I to simulate an experiment in which the dependent variable is response time to some arbitrary targets. The simulated data will, further, have two independent variables (IV, “iv1” have 2 levels and “iv2” have 3 levels). The data are simulated as the same time as a dataframe is created and the first descriptive statistics is obtained using the method describe.

Descriptive statistics using Pandas

Pandas will output summary statistics by using this method. Output is a table, as you can see below.

Output table from Pandas DataFrame describe - descriptive statistics
Output table of data.describe()

Typically, a researcher is interested in the descriptive statistics of the IVs. Therefore, I group the data by these. Using describe on the grouped date aggregated data for each level in each IV.  As can be seen from the output it is somewhat hard to read. Note, the method unstack is used to get the mean, standard deviation (std), etc as columns and it becomes somewhat easier to read.

Output from describe on the grouped data
Descriptive statistics using Pandas Describe

Central tendency

Often we want to know something about the “average” or “middle” of our data. Using Pandas and NumPy the two most commonly used measures of central tenancy can be obtained; the mean and the median. The mode and trimmed mean  can also be obtained using Pandas but I will use methods from  SciPy.


There are at least two ways of doing this using our grouped data. First, Pandas have the method mean;

But the method aggregate in combination with NumPys mean can also be used;

Both methods will give the same output but the aggregate method have some advantages that I will explain later.

Output of aggregate using Numpy mean method
Output of mean and aggregate using NumPy – Mean

Here’s a YouTube Video on how to use Pandas describe() to do descriptive stats:

Geometric & Harmonic mean

Sometimes the geometric or harmonic mean  can be of interested. These two descriptive statistics can be obtained using the method apply with the methods gmean and hmean (from SciPy) as arguments. That is, there is no method in Pandas or NumPy that enables us to calculate geometric and harmonic means.



Trimmed mean

Trimmed means are, at times, used. Pandas or NumPy seems not to have methods for obtaining the trimmed mean. However, we can use the method trim_mean from SciPy . By using apply to our grouped data we can use the function (‘trim_mean’) with an argument that will make 10 % av the largest and smallest values to be removed.

Output from the mean values above (trimmed, harmonic, and geometric means):

Trimmed mean output from Pandas using SciPy
Trimmed Mean

Harmonic mean using Pandas DataFrame SciPy
Harmonic Mean

Descriptives - Geometric Mean
Geometric Mean


The median can also be obtained using two methods;

Output of aggregate using Numpy - Median.
Output of aggregate using Numpy – Median.


There is a method (i.e., pandas.DataFrame.mode()) for getting the mode for a DataFrame object. However, it cannot be used on the grouped data so I will use mode from SciPy:

Most of the time I probably would want to see all measures of central tendency at the same time. Luckily, aggregate enables us to use many NumPy and SciPy methods. In the example below the standard deviation (std), mean, harmonic mean,  geometric mean, and trimmed mean are all in the same output. Note that we will have to add the trimmed means afterwards.

Descriptive statistics using Pandas, NumPy, and SciPy.
Output of aggregate using some of the methods.

Measures of variability

Central tendency (e.g., the mean & median) is not the only type of summary statistic that we want to calculate. We will probably also want to have a look at a measure of the variability of the data.

Standard deviation

Inter quartile range

Note that here the use unstack()  also get the quantiles as columns and the output is easier to read.

Interquartile range (IQR) using Pandas quantile


Variance using pandas var method

That is all. Now you know how to obtain some of the most common descriptive statistics using Python. Pandas, NumPy, and SciPy really makes these calculation almost as easy as doing it in graphical statistical software such as SPSS. One great advantage of the methods apply and aggregate is that we can input other methods or functions to obtain other types of descriptives.

Update: Recently, I learned some methods to explore response times visualizing the distribution of different conditions: Exploring response time distributions using Python.

I am sorry that the images (i.e., the tables) are so ugly. If you happen to know a good way to output tables and figures from Python (something like Knitr & Rmarkdown) please let me know.

Six ways to reverse pandas dataframe

In this post we will learn how to reverse pandas dataframe. We start by changing the first column with the last column and continue with reversing the order completely. After we have learned how to do that we continue by reversing the order of the rows. That is, pandas data frame can be reversed such that the last column becomes the first or such that the last row becomes the first.

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Why Spyder is the Best Python IDE for Science

Spyder is the best Python IDE that I have tested so far for doing data analysis, but also for plain programming. In this post I will start to briefly describe the IDE. Following the description of this top IDE the text will continue with a discussion of my favorite features. You will also find out how to install Spyder on Ubuntu 14.04 and at the end of the post you will find a comparison of Rodeo (a newer IDE more RStudio like) and Spyder.

When I started programming in Python I used IDLE which is the IDE that you will get with your installation of Python (e.g., on Windows computers). I actually used IDLE IDE for some time. It was not until I started to learn R and found  RStudio IDE. I thought that RStudio was great (and it still is!). However, after learning R and RStudio I started to look for a better Python IDE.

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Every Psychologist Should Learn Programming

The aim of this post is to show you why you, as a psychology student or researcher (or any other kind researcher or student) should learn to program. The post is structured as follows. First I start with discussing why you should learn programming and then give some examples when programming skills are useful. I continue to suggest two programming languages that I think all Psychology students and researchers should learn.

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R resources for Psychologists

Good resources for learning R as a Psychologist are hard to find. By that I mean that there are so many great sites and blogs around the internet to learn R. Thus, it may be hard to find learning resources that targets Psychology researchers. Recently I wrote about 4 good R books targeted for Psychology students and researchers (i.e., R books for Psychologists). There are, however, of course other good resources for Psychological researchers to learn R programming. Therefore, this post will list some of the best blogs and sites to learn R.  The post will be divided into two categories; general and Psychology focused R sites and blogs. For those who are not familiar with R I will start with a brief introduction on what R is (if you know R already;click here to skip to the links).

What is R?

R is a free and open source programming language and environment. Data analysis in R is carried out by writing scripts and functions. R is a complete, interactive, object-oriented language.

R for Psychologists. R is interactive.
R is interactive

In R statistical environment you are able to carry out a variety of statistical and graphical techniques. For instance, linear and nonlinear modeling, classical statistical tests, time-series analysis, classification, and many more can be carried using both frequentist and bayesian paradigms.

You may want to start with R commander. It provides a menu which may make learning R a bit easier at the beginning. R can be downloaded here: The Comprehensive R Archive Network.


R resources

R has a broad and helpful community and, therefore, there are many good resources for learning the language. Continue reading

Rodeo - RStudio for Python - a good IDE for doing Data Science

Installing Rodeo IDE on Linux

I recently wrote a post on the RStudio like Python IDE Rodeo (RStudio-like Python IDEs – Rodeo and Spyder). In that post, I installed and tested Rodeo 0.44. However, Rodeo 1.0 was released in October. Rodeo 1.0 cannot be installed using Pip. Therefore, I wrote a bash script for downloading and unzipping Rodeo. Note, the script below will now install Rodeo 2 and is tested on my Ubuntu 16.04 machines.

What is Rodeo?

Rodeo is, as previously mentioned, a Python IDE very similar to RStudio. It is intended to use for Data Science. If you are coming from R and plan to add Python to your stack, Rodeo is probably going to be very familiar to you. Given that you have used RStudio, that is. I would still say that Spyder may be a better IDE for doing Data Science in Python. Why? Because, up to date, there are plenty of more features in Spyder compared Rodeo. Update: now you will get a .deb file when using wget (see below). Thus, we can use dpkg to install the Rodeo.

Installing Rodeo

The above code will download the Linux 64 binaries for Rodeo, unzip it into the ‘/usr/local/bin’ directory, and remove the downloaded file. Finally, a symbolic link to the executable is created. As Jo writes in the comments, it seems like Rodeo is released exclusively for 64 bit only – there is no 32 bit Rodeo.

Note, you can just cut & paste the code and paste it into a command window. If you, however, save it as a bash script (i.e., you need to make it executable; chmod +x To download and install Rodeo:

I have tested installing Rodeo IDE on Ubuntu 14.04 and 16.04 with the above script. If you don’t have Jupyter and Matplotlib installed it may need to install them also;

Installing Rodeo on Ubuntu/Debian

If you are using Ubuntu or Debian you can add Yhats repository (source Yhat Downloads):

Thats all, now you should know how to easily download and install Rodeo 1.0 on your Linux machine. Please let me know if you need to do more than I described in this post.