Testing of mean interval for interval-valued data

A new parametric hypothesis test of mean interval for interval-valued data set, which can deal with massive information contained in nowadays massive data "Big data" sets, is proposed. An approach using an orthogonal transformation is introduced to obtain an equivalent hypothesis test of mean interval in terms of the mid-point and mid-range of the interval-valued variable. The new test is very efficient in small interval-valued sample scenarios. Some simulation studies are conducted for the investigation of the sample size and the power of test. The performance of the proposed test is illustrated with two real-life examples.