Random numbers are very difficult to test since there are so many ways a series of numbers can exhibit non-random properties. Correlation between consecutive number in a random sequence and an uneven distribution of numbers across the entire sequence are just two important tests.
I was writing a simple random routine in C# and made the mistake of placing the declaration of the Random object inside the loop:
private ListRandNumbers()
{
var numbers = new List();
for (int i = 0; i < 100000; i++)
{
var rnd = new Random();
numbers.Add(rnd.Next(1, 1000));
}
return numbers;
}
In .NET this will produce a very poor series of random numbers since by default the Random object is automatically seeded with a DateTime and so if it is placed within a loop it will be created and seeded multiple times with identical values. Developers normally write tests to check an application’s data quality , but writing a battery of statistical tests to check a simple random number routine is working correctly is overkill.
A neat solution to this is to use a simple visual inspector with plots the values on a two dimensional surface. The below ASP.NET MVC controller would output the a bitmap of the above random number routine.
public ActionResult RandomNumberImage()
{
var path = @"c:usersyourfilepathfilename.bmp";
Bitmap bm = new Bitmap(1000, 1000);
var randNumbers = RandNumbers();
var randNumberCount = randNumbers.Count();
for (int i = 0; i {
bm.SetPixel(randNumbers[i], randNumbers[i+1], Color.Black);
}
bm.Save(path, System.Drawing.Imaging.ImageFormat.Bmp);
return File(path, "image/bmp");
}
This outputs the below visualisation:
Definitely not a random data set! Now we can correct the mistake and instantiate the Random object outside the loop:
private ListRandNumbers()
{
var numbers = new List();
var rnd = new Random();
for (int i = 0; i < 100000; i++)
{
numbers.Add(rnd.Next(1, 1000));
}
return numbers;
}
Now lets look at the output of the correctly implemented routine:
This appears much better. In addition to a broader scatter, note that there appears to be more data points, this is because in the previous routine numbers were often identical and hence plotted on top of eachother.
Visualisation can also help surface more subtle issues in random number generation. The below image is from a data set generated using the PHP random number generator on a Windows machine:
Source : random.org
The relationships between these numbers may be quite difficult to discern using statistical tests but for the above image there are clearly some relationships within the data set and hence it would not be random.
Note that this is not a robust statistical test, the inbuilt random number generation in .NET is generally considered to perform poorly (as is the case with Excel random numbers)