The unpaired t test when all values in one group are identical.

Last modified July 16, 2010

 The unpaired t test is designed to compare the means of two groups, when all values are ratio or interval data.  GraphPad Prism can perform a t test either from raw data entered onto a Column data table or from the first row of a Grouped table formatted with data for each group entered asmean, SD (or SEM), and n

If all of the values in one group are identical (or you enter a SD or SEM of 0.0), Prism 5 will not compute the t test. 

There are several reasons why the SD of one of the groups equals zero. How to work around the limitation in Prism depends on the reason for why all values in one group are identical:

  • The identical values are not actually data, but rather are hypothetical values. Say you want to compare the mean of a column of values (expressed as percent of control) to the hypothetical value 100 (which would be the value for no effect). The unpaired t test is not the right way to do this analysis. Delete the t test analysis  page. Then go back to the data table, and delete that column of identical values. Now, click Analyze and choose Column Statistics from the list of Column analyses. On that dialog, choose to compare the mean of each column to a hypothetical value, and enter that value (100 for this example) into the dialog. Prism will compute a one-sample t test comparing the mean of every column of data to the hypothetical value you entered. Note that the one-sample t test is part of the Column Statistics analysis, not part of the t test analysis.
  • The data can be only a few possible values. Maybe the values represent the number of children someone has. The values must be integers. It certainly is possible that everyone in one of the samples (especially if the sample is small) has the same number of kids. One possibility is to use a nonparametric test. Another possibility is to enter the data on a contingency table. A third possibility is to add a tiny value onto one of the numbers (1.000001) so Prism will do the t test calculations for you. But note that the t test is designed to analyze data on a continuous scale. It is not really designed for data that can only be an integer.
  • The data are correct. The variable really is continuous (ratio or interval). Just by chance all of the values in one of the groups are identical, up to the number of digits recorded. In this case, change one of the values a tiny bit (change 3.00 to 3.0000001) and Prism will do the calculations for you.

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