This course is for anyone in the healthcare and life sciences interested in doing their own statistical analysis. You will learn an easy to use, powerful computer language and how to use it to do statistical analysis. The introduction shows you how to get a copy of Mathematica or how to use the free version in the cloud.
Although the course assumes some knowledge of statistical concepts, it does supply enough information on the basics of statistics, so that most learners will find it a useful resource enough resource to learn these concepts, over and above learning how to write code to do the actual analysis.
The course is made up of clearly defined sections, each with its own set of video lectures. The first video in each section is accompanied by notebook files and, where required, a spreadsheet data file. The notebook in each section marked Recording... is a copy of the notebook that I use in the video lectures. The other notebook file contains much more description of both the code and the statitics. You can use this as an additional study resource as you learn how to use Mathematica.
The course starts with a gentle introduction to using Mathematica by showing you how to perform simple calculations. From here it progresses through descriptive statistics, plotting and charting, the creation of simulated data and the importation of existing data.
Before too long you will be able to do advanced statistical tests such as parametric and nonparametric tests and even survival analysis. All with a few short lines of code.
Get ready to understand and do your own statistics.
In this video I tell you about how to get hold of a copy of Mathematica and how to use it free of charge, in the cloud.
In this video I show you around the user interface of the desktop version of Mathematica. The coding environment is the notebook. It allows for the entry of titles, subtitles, text, paragraphs, and computer code.
The cloud version of Mathematica is free to use. It offers the same notebook environment as the desktop version.
Introduction to this section.
In this first proper look at Mathematica we complete a few simple arithmetical calculations.
Now that we know how to do simple arithmetic, we take a look at calculating powers. We also consider the order of arithmetical operations and how to manually change the usual order. Finally, we calculate the mean or average of a set of numerical values.
Lists can contain other lists as elements. This video will show you how these are used to build up matrices.
Instead of typing in each element of a list, you can use a formula to create the elements of a list for you.
Once you have a list or lists, you might want to access only certain of the elements. Each element in a list has an address, which is what allows us to make this selection.
Lists come in various shapes and sizes. This video will show you how to calculate the number of elements in a list.
It is straight forward top add elements to a list that has already been created. This video also shows you how to extract all the elements of nested lists into one single list.
Measures of central tendency calculate a single value to represent a list of values. These include the mean or average, the median, and the mode.
Measures of dispersion give us an idea of the spread of the data. These include the standard deviation, the range, the interquartile range and various quartiles and percentiles.
It can be tedious to calculate each individual measure of central tendency and dispersion. This video will show you how to create a short Mathematica function. You can use it to calculate all of the descriptive statistics for a list of values in one go.
This video shows you how to create random integers and random real numbers.
Mathematica can also choose random categorical variables from a list.
In this video we take a closer look at the normal distribution.
Now that you know how to create random values, this video shows you how to select values at random that follow a specified distribution, i.e. the normal distribution, given a mean and a standard deviation.
In this video we import the HypothesisTesting package into Mathematica and use it to calculate the confidence interval around the mean of a list of values.
In this first video we create lists of values to use in our parametric tests.
In this vodeo we calculate a p-value for the comparison of a mean for the list of values to a given mean.
In this video we use the famous Student's t-test to calculate the p-value for the difference in means between two lists of values.
If the two lists of values are not independent, i.e. they come from the same individual such as before and after an intervention, we need a different version of the t-test.
One-way analysis of variance allows us to compare the means of three or more lists of values.
Instead of calculating the p-value for ANOVA manually, we can import and use the ANOVA package.
In this video we compare pairs of numerical values for two variables using simple linear regression or the strength of the correlation between two variables.
Until now we have created our own lists of values. More commonly, data is already stored in spreadsheets. In this video I show you the structure of a dataset in Mathematica by manually creating one.
In this video we take a look at specifying the directory or folder on your computer where the spreadsheet file resides so as to make it easier for Mathematica to import the file.
If you are using the cloud version, simply upload the spreadsheet file into the Home directory (where your notebook file should also be kept).
Just as we references elements of a list (collections), we can also access data point values in a data file.
At times we only want to select a subgroup of patients or subjects to use in our analysis. We can do this by creating a rule (or recipe) that will only select these cases.
We can calculate simple descriptive statistics on data in our dataset, similar to the way in which we calculated it for lists of values.
Instead of simply selecting a subset of subjects based on a rule, we can also group our dataset into subgroups for easier calculations.
For really complex calculations we can create standalone sub-datasets and even extract lists from a dataset. This is a very useful way of working with the data.
Plotting or charting is one of the most powerful ways of getting to know and understand your data. In this first video, we create some data that we will plot.
A list plot is used to plot pairs of values, i.e. one on the x-axis and one on the y-axis. A point is created where they meet. This first video looks at plotting the values in a list one-by-one.
The bubble chart adds a third dimension (another value to the pairs) that is plotted as the size of each point.
A histogram plot the frequency of occurrence of numerical values in interval ranges.
A smooth histogram creates a smooth curve from a kernel density estimate of the frequency distribution of a list of values. A 3D histogram plots the frequency of the combination of two numerical variables.
The box-and-whisker plot is one of the most common plots in healthcare analysis. It charts the middle two quartiles and median of a list of values, together with any outliers.
A bar chart shows the counts of categorical variables. A pie chart does the same, but represents the whole as a full circle, with proportional slices that make of the frequency of the categorical variable.
More than one independent variable can be used to compare three or more numerical variables. In this video we look at two-factor ANOVA.
In this video we look at three independent factor ANOVA.
We take a closer look at linear regression in this video.
We take a closer look at linear regression in this video.
The values that we compare need not only come in pairs, but also in triplets and even more.
I am a Senior Lecturer in Surgery and the Head of both Postgraduate Surgical Research and Surgical Education at the University of Cape Town, South Africa. My academic interests extend to online education and I am the recipient of the Open Education Consortium Educator of the Year Award in 2014. My course on Healthcare Statistics is also the first course from a University in Africa on the massive open online Coursera platform.