Eric’s Enlightenment for Friday, May 15, 2015

1. An infographic compares R and Python for statistics, data analysis, and data visualization – in a lot of detail!
2. Psychologist Brian Nosek tackles human biases in science – including motivated reasoning and confirmation bias – long but very worthwhile to read.
3. Scott Sumner’s wife documents her observations of Beijing during her current trip – very interesting comparisons of how normal life has changed rapidly over the past 10 years.
4. Is hot air or hot water more effective at melting a frozen pipe – a good answer based on heat capacity and heat resistivity ensues.

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Eric’s Enlightenment for Wednesday, April 29, 2015

1. Anscombe’s quartet is a collection of 4 data sets that have almost identical summary statistics but appear very differently when plotted.  They illustrate the importance of visualizing your data first before plugging them into a statistical model.
2. A potential geochemical explanation for the existence of Blood Falls, an outflow of saltwater tainted with iron (III) oxide at the snout of the Taylor Glacier in Antarctica.  Here is the original Nature paper by Jill Mikucki et al.
3. Jonathan Rothwell and Siddharth Kulkarni from the Brookings Institution use a value-added approach to rank 2-year and 4-year post-secondary institutions in the USA.  Some of the top-ranked universities by this measure are lesser known schools like Colgate University, Rose-Hulman Institute of Technology, and Carleton College.  I would love to see something similar for Canada!
4. Heather Krause from Datassist provides tips on how to avoid (accidentally) lying with your data.  Do read the linked sources of further information!

Eric’s Enlightenment for Monday, April 27, 2015

1. How much wealth do Canadians have?  What types of assets and debts do Canadians have?  Here is a very useful table to answer those questions from Statistics Canada.
2. Here is the Canadian Parliamentary Budget Officer’s assessment of the tax-free savings account (2015-02-24).
3. Tracey Weissberger et al. argue persuasively for fundamental changes to the visualization of continuous data in academic publications.  Instead of bar plots, use scatter plots, box plots, and histograms, which better allow readers to examine the distribution of the data.
4. Ram B. Gupta et al. have developed a new way to clean crude oil spills using soy.

Eric’s Enlightenment for Wednesday, April 22, 2015

1. Frances Woolley’s useful reading list on tax policy for Canadians with disabilities
2. Jeff Rosenthal asked a seemingly simple yet subtle question about uncorrelated normal random variables.
3. A great catalogue of colours with their names in R – very useful for data visualization!
4. Paul Crutzen’s proposed scheme to inject sulfur dioxide into the stratosphere – this would create sulfate aerosols for deflecting sunlight to counteract global warming, but he carefully weighed the serious pros and cons of this risky scheme.

Using PROC SGPLOT to Produce Box Plots with Contrasting Colours in SAS

I previously explained the statistics behind box plots and how to produce them in R in a very detailed tutorial.  I also illustrated how to produce side-by-side box plots with contrasting patterns in R.

Here is an example of how to make box plots in SAS using the VBOX statement in PROC SGPLOT.  I modified the built-in data set SASHELP.CLASS to generate one that suits my needs.

The PROC TEMPLATE statement specifies the contrasting colours to be used for different classes.  I also include code for exportingthe result into a PDF file using ODS PDF.  (I used varying shades of grey to allow the contrast to be shown when printed in black and white.)

Exploratory Data Analysis – All Blog Posts on The Chemical Statistician

This series of posts introduced various methods of exploratory data analysis, providing theoretical backgrounds and practical examples.  Fully commented and readily usable R scripts are available for all topics for you to copy and paste for your own analysis!  Most of these posts involve data visualization and plotting, and I include a lot of detail and comments on how to invoke specific plotting commands in R in these examples.

I will return to this blog post to add new links as I write more tutorials.

Useful R Functions for Exploring a Data Frame

The 5-Number Summary – Two Different Methods in R

Combining Histograms and Density Plots to Examine the Distribution of the Ozone Pollution Data from New York in R

Conceptual Foundations of Histograms – Illustrated with New York’s Ozone Pollution Data

Quantile-Quantile Plots for New York’s Ozone Pollution Data

Kernel Density Estimation and Rug Plots in R on Ozone Data in New York and Ozonopolis

2 Ways of Plotting Empirical Cumulative Distribution Functions in R

Conceptual Foundations of Empirical Cumulative Distribution Functions

Combining Box Plots and Kernel Density Plots into Violin Plots for Ozone Pollution Data

Kernel Density Estimation – Conceptual Foundations

Variations of Box Plots in R for Ozone Concentrations in New York City and Ozonopolis

Computing Descriptive Statistics in R for Data on Ozone Pollution in New York City

How to Get the Frequency Table of a Categorical Variable as a Data Frame in R

The advantages of using count() to get N-way frequency tables as data frames in R

Visual index of plots and corresponding R scripts

Dear Readers of The Chemical Statistician,

Joanna Zhao, an undergraduate researcher in the Department of Statistics at the University of British Columbia, produced a visual index of over 100 plots using ggplot2, the R package written by Hadley Wickham.

An example of a plot and its source R code on Joanna Zhao’s catalog.

Click on a thumbnail of any picture in this catalog – you will see the figure AND all of the necessary code to reproduce it.  These plots are from Naomi Robbins‘ book “Creating More Effective Graphs”.

If you

• want to produce an effective plot in R
• roughly know what the plot should look like
• but could really use an example to get started,

then this is a great resource for you!  A related GitHub repository has the code for ALL figures and the infrastructure for Joanna’s Shiny app.

I learned about this resource while working in my job at the British Columbia Cancer Agency; I am fortunate to attend a wonderful seminar series on statistics at the British Columbia Centre for Disease Control, and a colleague from this seminar told me about it.  By sharing this with you, I hope that it will immensely help you with your data visualization needs!

Side-by-Side Box Plots with Patterns From Data Sets Stacked by reshape2 and melt() in R

Introduction

A while ago, one of my co-workers asked me to group box plots by plotting them side-by-side within each group, and he wanted to use patterns rather than colours to distinguish between the box plots within a group; the publication that will display his plots prints in black-and-white only.  I gladly investigated how to do this in R, and I want to share my method and an example of what the final result looks like with you.

In generating a fictitious data set for this example, I will also demonstrate how to use the melt() function from the “reshape2” package in R to stack a data set while keeping categorical labels for the individual observations.  For now, here is a sneak peek at what we will produce at the end; the stripes are the harder pattern to produce.

Read the rest of this post to learn how to generate side-by-side box plots with patterns like the ones above!

Detecting Unfair Dice in Casinos with Bayes’ Theorem

Introduction

I saw an interesting problem that requires Bayes’ Theorem and some simple R programming while reading a bioinformatics textbook.  I will discuss the math behind solving this problem in detail, and I will illustrate some very useful plotting functions to generate a plot from R that visualizes the solution effectively.

The Problem

The following question is a slightly modified version of Exercise #1.2 on Page 8 in “Biological Sequence Analysis” by Durbin, Eddy, Krogh and Mitchison.

An occasionally dishonest casino uses 2 types of dice.  Of its dice, 97% are fair but 3% are unfair, and a “five” comes up 35% of the time for these unfair dice.  If you pick a die randomly and roll it, how many “fives”  in a row would you need to see before it was most likely that you had picked an unfair die?”

Read more to learn how to create the following plot and how it invokes Bayes’ Theorem to solve the above problem!

Exploratory Data Analysis: Combining Histograms and Density Plots to Examine the Distribution of the Ozone Pollution Data from New York in R

Introduction

This is a follow-up post to my recent introduction of histograms.  Previously, I presented the conceptual foundations of histograms and used a histogram to approximate the distribution of the “Ozone” data from the built-in data set “airquality” in R.  Today, I will examine this distribution in more detail by overlaying the histogram with parametric and non-parametric kernel density plots.  I will finally answer the question that I have asked (and hinted to answer) several times: Are the “Ozone” data normally distributed, or is another distribution more suitable?

Read the rest of this post to learn how to combine histograms with density curves like this above plot!

This is another post in my continuing series on exploratory data analysis (EDA).  Previous posts in this series on EDA include

• Descriptive statistics
• Box plots
• The conceptual foundations of kernel density estimation
• How to construct kernel density plots and rug plots in R
• Violin plots
• The conceptual foundations of empirical cumulative distribution functions (CDFs)
• 2 ways of plotting empirical CDFs in R
• The conceptual foundations of histograms

Exploratory Data Analysis: Conceptual Foundations of Histograms – Illustrated with New York’s Ozone Pollution Data

Introduction

Continuing my recent series on exploratory data analysis (EDA), today’s post focuses on histograms, which are very useful plots for visualizing the distribution of a data set.  I will discuss how histograms are constructed and use histograms to assess the distribution of the “Ozone” data from the built-in “airquality” data set in R.  In a later post, I will assess the distribution of the “Ozone” data in greater depth by combining histograms with various types of density plots.

Previous posts in this series on EDA include

• Descriptive statistics
• Box plots
• The conceptual foundations of kernel density estimation
• How to construct kernel density plots and rug plots in R
• Violin plots
• The conceptual foundations of empirical cumulative distribution functions (CDFs)
• 2 ways of plotting empirical CDFs in R

Read the rest of this post to learn how to construct a histogram and get the R code for producing the above plot!

How do Dew and Fog Form? Nature at Work with Temperature, Vapour Pressure, and Partial Pressure

In the early morning, especially here in Canada, I often see dew – water droplets formed by the condensation of water vapour on outside surfaces, like windows, car roofs, and leaves of trees.  I also sometimes see fog – water droplets or ice crystals that are suspended in air and often blocking visibility at great distances.  Have you ever wondered how they form?  It turns out that partial pressure, vapour pressure and temperature are the key phenomena at work.

Dew (by Staffan Enbom) and Fog (by Jon Zander)

Source: Wikimedia

Estimating the Decay Rate and the Half-Life of DDT in Trout – Applying Simple Linear Regression with Logarithmic Transformation

This blog post uses a function and a script written in R that were displayed in an earlier blog post.

Introduction

This is the second of a series of blog posts about simple linear regression; the first was written recently on some conceptual nuances and subtleties about this model.  In this blog post, I will use simple linear regression to analyze a data set with a logarithmic transformation and discuss how to make inferences on the regression coefficients and the means of the target on the original scale.  The data document the decay of dichlorodiphenyltrichloroethane (DDT) in trout in Lake Michigan; I found it on Page 49 in the book “Elements of Environmental Chemistry” by Ronald A. Hites.  Future posts will also be written on the chemical aspects of this topic, including the environmental chemistry of DDT and exponential decay in chemistry and, in particular, radiochemistry.

Dichlorodiphenyltrichloroethane (DDT)

Source: Wikimedia Commons

 

A serious student of statistics or a statistician re-learning the fundamentals like myself should always try to understand the math and the statistics behind a software’s built-in function rather than treating it like a black box.  This is especially worthwhile for a basic yet powerful tool like simple linear regression.  Thus, instead of simply using the lm() function in R, I will reproduce the calculations done by lm() with my own function and script (posted earlier on my blog) to obtain inferential statistics on the regression coefficients.  However, I will not write or explain the math behind the calculations; they are shown in my own function with very self-evident variable names, in case you are interested.  The calculations are arguably the most straightforward aspects of linear regression, and you can easily find the derivations and formulas on the web, in introductory or applied statistics textbooks, and in regression textbooks.

Discovering Argon with the 2-Sample t-Test

I learned about Lord Rayleigh’s discovery of argon in my 2nd-year analytical chemistry class while reading “Quantitative Chemical Analysis” by Daniel Harris.  (William Ramsay was also responsible for this discovery.)  This is one of my favourite stories in chemistry; it illustrates how diligence in measurement can lead to an elegant and surprising discovery.  I find no evidence that Rayleigh and Ramsay used statistics to confirm their findings; their paper was published 13 years before Gosset published about the t-test.  Thus, I will use a 2-sample t-test in R to confirm their result.

                                    

Photos of Lord Rayleigh and William Ramsay

Source: Wikimedia Commons

Adding Labels to Points in a Scatter Plot in R

What’s the Scatter?

A scatter plot displays the values of 2 variables for a set of data, and it is a very useful way to visualize data during exploratory data analysis, especially (though not exclusively) when you are interested in the relationship between a predictor variable and a target variable.  Sometimes, such data come with categorical labels that have important meanings, and the visualization of the relationship can be enhanced when these labels are attached to the data.

It is common practice to use a legend to label data that belong to a group, as I illustrated in a previous post on bar charts and pie charts.  However, what if every datum has a unique label, and there are many data in the scatter plot?  A legend would add unnecessary clutter in such situations.  Instead, it would be useful to write the label of each datum near its point in the scatter plot. I will show how to do this in R, illustrating the code with a built-in data set called LifeCycleSavings.

Displaying Isotopic Abundance Percentages with Bar Charts and Pie Charts

The Structure of an Atom

An atom consists of a nucleus at the centre and electrons moving around it.  The nucleus contains a mixture of protons and neutrons.  For most purposes in chemistry, the two most important properties about these 3 types of particles are their masses and charges.  In terms of charge, protons are positive, electrons are negative, and neutrons are neutral.  A proton’s mass is roughly the same as a neutron’s mass, but a proton is almost 2,000 times heavier than an electron.

This image shows a lithium atom, which has 3 electrons, 3 protons, and 4 neutrons.  

Source: Wikimedia Commons