Applied Nonparametric STATISTICS-LEC3

REF:

Https://onlinecourses.science.psu.edu/stat464/print/book/export/html/4

Advantages of using non-parametric methods:

1. There are few assumptions about the overall distribution, so the overall distribution is unknown;

2. easy to do;

3. Generally robust robust for outlier values;

4. Applicable to data containing ranks, ordinal or categorical.

In a skewed distribution, the population median,η, is a better typical value than the population meanμ.

Sign-test/binomial-test:

Here is an example:

This example, we use T-test first. The assumption is that the data is normally distributed, so using T-statistics, the mean value μ is tested.

Then, considering that the data is biased, we use the median median and then use the sign-test.

Solution: The probability of this calculation is P-value. So, we cannot reject the original hypothesis.

When the amount of data is large:

If NP ≥10 and n(1- P) ≥10, we can use the Normal distribution to approximate the B Inomial.

You can then use Z-score. Notice the variance and the mean value at this time. The following assumes that the part of the test is consistent with the content in LEC2.

To find the confidence interval:

The type I error is the false rejection of the original hypothesis; Type II error is a false acceptance of the original hypothesis.

The significance level of the test is α= P (Type I error)

Power = 1- P(Type II error)

If the alpha of the two test is equal, then the power of the big one is better.

In practice, use the R language package BSDA

Sign.test (x, MD = 0, alternative = "two.sided", conf.level = 0.95) # X-is The object where you store your data# md-the Hypothesized median (default is 0) # alternative-either ' two.sided ', ' greater ', or ' less than ' # Conf.level  

　

Applied Nonparametric STATISTICS-LEC3