One sample runs test

One sample runs test is part of:

  • Pro Core statistical software

  • System configuration

    • Windows:
      • Versions: 9x/Me/NT/2000/XP/Vista/Win 7
      • Excel: 97 and later
      • Processor: 32 or 64 bits
      • Hard disk: 150 Mb
    • Mac OS X:
      • OS: OS X
      • Excel: X, 2004 and 2011
      • Hard disk: 150Mb.

Benefits

  • Easy and user-friendly
    Easy and user-friendly XLSTAT is flawlessly integrated with Microsoft Excel which is the most popular spreadsheet worldwide. This integration makes it one of the simplest available tools to work with as it utilizes the same philosophy as Microsoft Excel. The program is accessible in a dedicated XLSTAT tab. The analyses are grouped into functional menus. The dialog boxes are user-friendly and setting up an analysis is straightforward.
  • Data and results shared seamlessly
    Data and results shared seamlessly One of the greatest advantages of XLSTAT is the way you can share data and results seamlessly. As the results are stored in Microsoft Excel, anyone can access them. There is no need for the receiver to have an XLSTAT license or any additional viewer which makes your team-work easier and more affordable. In addition, results are easily integrable into other Microsoft Office software such as PowerPoint, so that you can create striking presentation in minutes.
  • Modular
    Modular XLSTAT is a modular product. XLSTAT-Pro is a core statistical module of XLSTAT which includes all the mainstream functionalities in statistics and multivariate analysis. More advanced features contained in add-on modules can be added for specific applications. This way you can adapt the software to your needs making the software more cost-efficient.
  • Didactic
    Didactic The results of XLSTAT are organized by analysis and are easy to navigate. Moreover useful information is provided along with the results to assist you in your interpretation.
  • Affordable
    Affordable XLSTAT is a complete and modular analytical solution that can suit any analytical business needs. It is very reasonably priced so that the return of your investment is almost immediate. Any XLSTAT license comes with top level support and assistance.
  • Accessible - Available in many languages
    Accessible - Available in many languages We have ensured XLSTAT is accessible to everyone by making the program available in many languages, including Chinese, English, French, German, Italian, Japanese, Polish, Portuguese and Spanish.
  • Automatable and customizable
    Automatable and customizable Most of the statistical functions available in XLSTAT can be called directly from the Visual Basic window of Microsoft Excel. They can be modified and integrated to more code to fit to the specificity of your domain. Adding tables and plots as well as modifying existing outputs becomes easy. Furthermore, XLSTAT includes some special tools on the dialog boxes to generate automatically the VBA code in order to reproduce your analysis using the VBA editor or to simply load pre-set settings. This effortless automation of routine analysis will be a huge time saver on your part.

One sample runs test definition

The one sample runs test is used to test whether a series of binary events can be considered as randomly distributed or not.

A run is a sequence of identical events, preceded and succeeded by different or no events. The runs test used here applies to binomial variables only. For example, in ABBABBB, we have 4 runs (A, BB, A, BBB).

The one sample runs test is used to test whether a series of binary events is randomly distributed or not.

One sample runs test hypothesis

In the case of the two-tailed (or two-sided) test, the null (H0) and alternative (Ha) hypotheses are:

In the one-tailed case, you need to distinguish the left-tailed (or lower-tailed or lower one-sided) test and the right-tailed (or upper-tailed or upper one-sided) test. In the left-tailed test, the following hypotheses are used:

In the right-tailed test, the following hypotheses are used:

Expectation and variance of the one sample runs test

The expectation of the number of runs R is given by:

E(R) = 2mn/N

where m is the number of events of type 1, and n the number of events of type 2, and N is the total sample size.

The variance of the number of runs R is given by:

V(R) = 2mn(2mn – N)/[N²(N-1)]

The minimum value of R is always 2. The maximum value is given by 2Min(m, n) - t, where t is 1 if m=n, and 0 if not.

If r is the number of runs measured on the sample, it was shown by Wald and Wolfowitz that asymptotically, when m or n tend to infinity,

(r - E(R)) / √V(R) --> N(0,1)

where N(0,1) is the standard normal distribution.

One sample runs test p-values

XLSTAT offers three ways to compute the p-values. You can compute the p-value based on:

One sample runs test in XLSTAT

XLSTAT accepts as input, continuous data or binary categorical data. For continuous data, a cut-point must be chosen by the user so that the data are transformed into a binary sample.

A sample will be considered as randomly distributed if no particular structure can be identified. Extreme cases are repulsion, where you have all observations of one kind on the left, and all the remaining observations on the right, and alternation where the elements of the two kinds are alternating as much as possible. With the previous case, repulsion would give "AABBBBB" or "BBBBBAA", and alternation "BABABBB" or "BABBABB" or "BBABABB" or "BBABBAB" or "BBBABAB".

Screenshots