When it comes to running statistics on one sample, an a priori hypothesis is a necessity for making proper inferences. Many survey instruments lack fundamental psychometric evidence to back up the constructs and/or items it is intended to measure.  When a Likert-scale type response set or an ordinal outcome is to be assessed statistically in one sample, the one-sample median test is used.

In order to run the test, researchers must specify where along the ordinal continuum that they hypothesize that the population mean exists.  The one-sample median test then compares the observed median to the hypothesized median and the p-value is interpreted.

Due to limited precision, accuracy, and variability in ordinal outcomes, it behooves researchers to use either 5-point, 7-point, or higher level Likert scales.  With more options, more unique variance can be accounted for the in the analysis and statistical power is increased.  One-sampled tests possess more statistical power than other between-subjects statistics because there is only one group being analyzed, no other independent groups are included.