Two-Sample Hypothesis Test for Functional Data

Two Sample Hypothesis Testing for Functional Data

A nonparametric testing procedure is proposed for testing the hypothesis that two samples of curves observed at discrete grids and with noise have the same underlying distribution. Our method relies on representing the curves using a common orthogonal basis expansion. The approach reduces the dimension of the testing problem in a way that enables the application of traditional nonparametric uni...

Two-Sample Median Test for Vague Data

Classical statistical tests may be sensitive to violations of the fundamental model assumptions inherent in the derivation and construction of these tests. It is obvious that such violations are much more probable in the presence of vague data. Thus nonparametric tests seem to be promising statistical tools. A generalization of the median test for the two-sample problem with vague data is sugge...

One-Sample Hypothesis Test Examples

Test of hypothesis (two-tail)

We shall be testing hypotheses about the population mean (it is assumed we know the variance of the population). We shall fail to reject the hypotesis if the obseved sample mean (x-bar) is close to the hypothesized population mean (μ). We will shall reject the hypothesis if the observed sample mean (x-bar) is far from the hypothesized population mean (μ). Distance will be measured in standard d...

A multivariate two-sample mean test for small sample size and missing data.

We develop a new statistic for testing the equality of two multivariate mean vectors. A scaled chi-squared distribution is proposed as an approximating null distribution. Because the test statistic is based on componentwise statistics, it has the advantage over Hotelling's T2 test of being applicable to the case where the dimension of an observation exceeds the number of observations. An appeal...