A two-sample Kuiper test is a statistical test used to determine whether two samples of data come from the same underlying distribution. It is similar to a two-sample Kolmogorov-Smirnov test, but is more sensitive to differences in the tails of the distribution.
In R, the two-sample Kuiper test can be performed using the "kuiper.test" function from the "ks" package. This function takes in two vectors of data as input and returns the test statistic, p-value, and a plot of the cumulative distribution functions of the two samples.
The assumptions of a two-sample Kuiper test include: 1) the samples are independent, 2) the samples are drawn from continuous distributions, and 3) the samples have the same shape (e.g. both are normally distributed). Violations of these assumptions can lead to inaccurate results.
The test statistic of a two-sample Kuiper test ranges from 0 to 1, with higher values indicating more dissimilarity between the two samples. The p-value represents the probability of obtaining the observed test statistic if the two samples are drawn from the same distribution. A p-value < 0.05 is typically considered statistically significant, indicating that the two samples are likely from different distributions.
Yes, the two-sample Kuiper test can be used for non-parametric data as it makes no assumptions about the underlying distribution of the data. However, it may be less powerful in this scenario compared to alternative non-parametric tests such as the Wilcoxon rank-sum test.