Mathematica for healthcare and life science statistics

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.

Introduction to this section.

In this video we take a look at creating a list of elements.

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.

Introduction to this section.

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.

Introduction to this section.

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.

Introduction to this section.

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.

Introduction to this section.

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.

Introduction to this section.

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.

While it is easy to use SemanticImport[] to work with a spreadsheet file in the desktop version of Mathematica, it is a bit more complicated to achieve this in the Cloud.  In this video lecture we look at how to upload a spreadsheet file and use it in an online notebook as a dataset.

Introduction to this section.

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.