Given a cloud of points in the plane, it can be useful to identify the convex hull of the points. The convex hull is the smallest convex set that contains the observations. For a finite set of points, it is a convex polygon that has some of the points as
I was recently asked how to create a frequency polygon in SAS. A frequency polygon is an alternative to a histogram that shows similar information about the distribution of univariate data. It is the piecewise linear curve formed by connecting the midpoints of the tops of the bins. The graph
Recall that the binomial distribution is the distribution of the number of successes in a set of independent Bernoulli trials, each having the same probability of success. Most introductory statistics textbooks discuss the approximation of the binomial distribution by the normal distribution. The graph to the right shows that the
A SAS programmer asked whether it is possible to add reference lines to the categorical axis of a bar chart. The answer is yes. You can use the VBAR statement, but I prefer to use the VBARBASIC (or VBARPARM) statement, which enables you to overlay a wide variety of graphs
A previous article discusses how to use SAS regression procedures to fit a two-parameter Weibull distribution in SAS. The article shows how to convert the regression output into the more familiar scale and shape parameters for the Weibull probability distribution, which are fit by using PROC UNIVARIATE. Although PROC UNIVARIATE
These days, many countries are moving away from coal, and towards natural gas, hydro, wind, and solar as ways to meet their electricity needs. I had heard that some countries still use a lot of coal (especially those countries with large coal deposits), and I was curious which countries use
Recently, the news has been all abuzz about William Shatner traveling into space. This was a cool event because he's the oldest person who has traveled into space (at 90 years old) ... and he was also the iconic Captain Kirk from the original Star Trek television series. This got
A reader asked whether it is possible to find a bootstrap sample that has some desirable properties. I am using the term "bootstrap sample" to refer to the result of randomly resampling with replacement from a data set. Specifically, he wanted to find a bootstrap sample that has a specific
Graphing data is almost always more informative than displaying a table of summary statistics. In a recent article about "dynamite plots," I briefly mentioned that graphs such as box plots and strip plots are better at showing data than graphs that merely show the mean and standard deviation. This article
The field of probability and statistics is full of asymptotic results. The Law of Large Numbers and the Central Limit Theorem are two famous examples. An asymptotic result can be both a blessing and a curse. For example, consider a result that says that the distribution of some statistic converges
Welcome back to my SAS Users blog series CAS Action! - a series on fundamentals. I've broken the series into logical, consumable parts. If you'd like to start by learning a little more about what CAS Actions are, please see CAS Actions and Action Sets - a brief intro. Or
A statistical programmer asked how to simulate event-trials data for groups. The subjects in each group have a different probability of experiencing the event. This article describes one way to simulate this scenario. The simulation is similar to simulating from a mixture distribution. This article also shows three different ways
A colleague spent a lot of time creating a panel of graphs to summarize some data. She did not use SAS software to create the graph, but I used SAS to create a simplified version of her graph, which is shown to the right. (The colors are from her graph.)
A colleague spent a lot of time creating a panel of graphs to summarize some data. She did not use SAS software to create the graph, but I used SAS to create a simplified version of her graph, which is shown to the right. (The colors are from her graph.)
You can use the bootstrap method to estimate confidence intervals. Unlike formulas, which assume that the data are drawn from a specified distribution (usually the normal distribution), the bootstrap method does not assume a distribution for the data. There are many articles about how to use SAS to bootstrap statistics
Many cities have Open Data pages. But once you download the data, what can you do with it? This is my fourth in a series of blog posts where I download public data about Cary, NC, and demonstrate how you might analyze that type of data (for Cary, or any
This article shows how to create a "sliced survival plot" for proportional-hazards models that are created by using PROC PHREG in SAS. Graphing the result of a statistical regression model is a valuable way to communicate the predictions of the model. Many SAS procedures use ODS graphics to produce graphs
In Part 1 of my series fetch CAS, fetch!, I executed the fetch CAS action to return rows from a CAS table. That was great, but what can you do with the results? Maybe you want to create a visualization that includes the top five cars by MSRP for all
A previous article discusses the geometry of weighted averages and shows how choosing different weights can lead to different rankings of the subjects. As an example, I showed how college programs might rank applicants by using a weighted average of factors such as test scores. "The best" applicant is determined
Many cities have Open Data pages. But once you download the data, what can you do with it? This is my second blog post where I download several datasets from Cary, NC's open data page, and and give you a few ideas to get you started on your own data
What happens if you need to edit graph output files from SAS in a different application (for example, Microsoft Word)? It is not recommended that you edit your SAS graph output outside of SAS, but, if you must do so, you need to create your graphics output as EMF (Enhanced Metafile Format) graph output.
In a previous article, I discussed a beautiful painting called "Phantom’s Shadow, 2018" by the Nigerian-born artist, Odili Donald Odita. I noted that if you overlay a 4 x 4 grid on the painting, then each cell contains a four-bladed pinwheel shape. The cells display rotations and reflections of the pinwheel. The
Art evokes an emotional response in the viewer, but sometimes art also evokes a cerebral response. When I see patterns and symmetries in art, I think about a related mathematical object or process. Recently, a Twitter user tweeted about a painting called "Phantom’s Shadow, 2018" by the Nigerian-born artist, Odili
Some claim that deaths in the US have been increasing, and some claim they have been decreasing. Which do you think is correct? Let's take a look at the data ... The Data Here in the US, the Centers for Disease Control and Prevention is a good/official source of data
How long do dogs live? ... That's a good/tough question. Some live longer than others, but what are the determining factors? Let's throw some data to this problem, and see if we can fetch some answers! But before we get started, how about a random picture to get you into
After my recent articles on simulating data by using copulas, many readers commented about the power of copulas. Yes, they are powerful, and the geometry of copulas is beautiful. However, it is important to be aware of the limitations of copulas. This article creates a bizarre example of bivariate data,
Who's to say that 'north' should always be at the top of a map? Perhaps in certain situations, you might want 'south' (or some other direction) to be at the top. Perhaps you're one of our crazy Australian customers who looks at the world a little differently. Well, whatever the
This article shows how to estimate and visualize a two-dimensional cumulative distribution function (CDF) in SAS. SAS has built-in support for this computation. Although the bivariate CDF is not used as much as the univariate CDF, the bivariate version is still a useful tool in understanding the probable values of
This article uses simulation to demonstrate the fact that any continuous distribution can be transformed into the uniform distribution on (0,1). The function that performs this transformation is a familiar one: it is the cumulative distribution function (CDF). A continuous CDF is defined as an integral, so the transformation is
Having earned the Eagle Scout rank in Boy Scouts, I am of course very conservation-minded, and against polluting. I'm also an avid boat paddler and fisherman, and therefore I'm especially concerned about pollution in our rivers, lakes, and oceans. I even volunteered for a week to help survey coral reefs
