Running a Cochran-Mantel-Haenszel test with XLSTAT

Dataset for Cochran-Mantel-Haenszel test XLS42.5 KB

Tutorial video
Cochran-Mantel-Haenszel test is part of: Download Trial version More details See users' feedback

  • 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.

Dataset to run a Cochran-Mantel-Haenszel test and goal of this tutorial

An Excel sheet with both the data and the results can be downloaded by clicking here.

The dataset has first been used in [Mantel N. (1963). Chi-Square Tests with One Degree of Freedom; Extensions of the Mantel- Haenszel Procedure. Journal of the American Statistical Association, 58, 303, 690-700], and corresponds to an experiment in which rabbits were injected with beta-hemolytic streptococci, and then immediately or after 90 minutes with a dose of penicillin varying from 1/8 to 4.

The aim of the experiment is to check first if there is a dependency between the survival or death of the rabbit and the delay in injection of penicillin.

Setting up a Cochran-Mantel-Haenszel test

After opening XLSTAT, click the Non parametric tests button in the ribbon and select Cochran-Mantel-Haenszel test (see below).

barcmh.gif

Once you've clicked the button, the dialog box appears. You can then select the data on the Excel sheet. Two formats are possible. For illustration the two data formats are presented in the datasheet. However for the tutorial, only the format Contingency Table is used.

You must select at first the 5 contingency tables (each corresponding to a level of penicillin). The option Column label is left enabled as the first line of the selection contains the names of two categories of the response variable (Cured or Died).

cmh1.gif

In the Options tab, the alternative hypothesis proposed is valid only when the selected tables are 2x2, which is the case here.

The Common odds ratio <> 1 option corresponds to the assumption of dependence. In the case of 2x2 tables it is possible to calculate an exact p-value.

cmh2.gif

Once you have clicked the OK button, the computation starts. The results are then displayed.

Interpreting the results of a Cochran-Mantel-Haenszel test

XLSTAT first provides a table that displays the Cramer's V, the chi-square statistics and the p-values (exact in the case of 2x2 tables) to evaluate for each sub-table if it corresponds to a case independence or not. These statistics are calculable only if the marginal sums are nonzero in each sub-tables. We see here that only the table corresponding to the dose 1 / 2 is close to dependence.

cmh3.gif

The Cramer's V has the advantage of being interpretable in terms of strength of link between variables. In the case of 2x2 tables, it is indeed close to 0 when there is no link, -1 if the cross categories (1 and 2, 2 and 1) are related, and close to 1 when categories with the same index (1 and 1, 2 and 2) are linked.

However, when taking the tables all together for a Cochran-Mantel-Haenszel test, we obtain a common odds ratio of 7, with a 95% confidence interval that does not included the value 1. The exact p-value of 0.04 (we would obtain 0.047 if the exact option was not selected) leads to the conclusion that there is generally a link between the delay and the fact that a rabbit will survive or not the injection of streptococci.

cmh4.gif

This result may seem surprising because none of the sub-tables for which one could calculate the statistics showed a dependency. By combining the tables we show there is a dependence. As the odds ratio is greater than 1, there is a positive effect of an immediate injection of penicillin on the survival.

The Cochran-Mantel-Haenszel should be used with caution. It is particularly not recommended when there is a level 3 interaction between the 3 variables. In our case, this would correspond to the situation where a higher dose of penicillin would increase the impact of delay on the survival. This situation can correspond to an evolution of Cramer's V from a value close to -1 to 1. And despite an obvious strong dependence, the Cochran-Mantel-Haenszel could conclude that there is independence. Hence the interest that the Cramer's V are almost homogeneous when one concludes there is independence.