Distingnish between parametric and nonparametric statistics. Why the parametric statistics are considered more powerful than the nonparametric statistics. Explain.?

Answer 1

Parametric statistical tests assume that the data belong to some type of probability distribution. The normal distribution is probably the most common. That is, when graphed, the data follow a "bell shaped curve".

On the other hand, non-parametric statistical tests are often called distribution free tests since don't make any assumptions about the distribution of data. They are often used in place of parametric tests when one feels that the assumptions of the have been violated such as skewed data.

For each parametric statistical test, there is one or more nonparametric tests. A one sample t-test allows us to test whether a sample mean (from a normally distributed interval variable) significantly differs from a hypothesized value. The nonparametric analog uses the One sample sign test In one sample sign test,

we can compare the sample values to the a hypothesized median (not a mean). In other words we are testing a population median against a hypothesized value k. We set up the hypothesis so that + and - signs are the values of random variables having equal size. A data value is given a plus if it is greater than the hypothesized mean, a negative if it is less, and a zero if it is equal.

he sign test for a population median can be left tailed, right tailed, or two tailed. The null and alternative hypothesis for each type of test will be one of the following:

Left tailed test: H0: median ≥ k and H1: median < k

Right tailed test: H0: median ≤ k and H1: median > k

Two tailed test: H0: median ≠ k and H1: median = k

To use the sign test, first compare each entry in the sample to the hypothesized median k.

If the entry is below the median, assign it a - sign.

If the entry is above the median, assign it a + sign.

If the entry is equal to the median, assign it a 0.

Then compare the number of + and - signs. The 0′s are ignored.

If there is a large difference in the number of + and - signs, then it is likely that the median is different from the hypothesized value and the null hypothesis should be rejected.

When using the sign test, the sample size n is the total number of + and - signs.

If the sample size > 25, we use the standard normal distribution to find the critical values and we find the test statistic by plugging n and x into a formula that can be found on the link.

When n ≤ 25, we find the test statistic x, by using the smaller number of + or - .

So if we had 10 +'s and 5 -'s, the test statistic x would be 5. The zeros are ignored.

I will provided a link to some nonparametric test that goes into more detail. The information about the Sign Test was just given as an example of one of the simplest nonparametric test so one can see how these tests work The Wilcoxon Rank Sum Test, The Mann-Whitney U test and the Kruskal-Wallis Test are a few more common nonparametric tests. Most statistics books will give you a list of the pros and cons of parametric vs noparametric tests.