## Stats on multiple samples when you have non-parametric data.

### Advantages of nonparametric procedures

The second disadvantage is that nonparametric procedures throw awayinformation! The sign test, for example, uses only the signs of theobservations. Ranks preserve information about the order of the data butdiscard the actual values. Because information is discarded,nonparametric procedures can never be as powerful (able to detectexisting differences) as their parametric counterparts when parametrictests can be used.

### Disadvantages of nonparametric procedures

The nonparametric procedures that we describe here follow the same general procedure. The outcome variable (ordinal, interval or continuous) is ranked from lowest to highest and the analysis focuses on the ranks as opposed to the measured or raw values. For example, suppose we measure self-reported pain using a visual analog scale with anchors at 0 (no pain) and 10 (agonizing pain) and record the following in a sample of n=6 participants:

The major disadvantage of nonparametric techniques is contained inits name. Because the procedures are , there are noparameters to describe and it becomes more difficult to make quantitativestatements about the actual difference between populations. (For example,when the sign test says two treatments are different, there's noconfidence interval and the test doesn't say by how much the treatmentsdiffer.) However, it is sometimes possible with the right software tocompute estimates (and even confidence intervals!) for medians,differences between medians. However, the calculations are often tootedious for pencil-and-paper. A computer is required. As statisticalsoftware goes though its various iterations, such confidence intervalsmay become readily available, but I'm still waiting!^{7}

## we might reasonably call such a hypothesis non-parametric.

Of course, randomization tests cannot be appliedblindly any more than normality can automatically beassumed when performing a t test. (Perhaps, in thelead levels example, one building's workers tend tolive in urban settings while the other building'sworkers live in rural settings. Then therandomization model would be inappropriate.)Nevertheless, there will be many situations where theless stringent requirements of the randomization testwill make it the test of choice. In the context ofrandomization models, randomization tests are the ONLYlegitimate tests; standard parametric test are validonly as approximations to randomization tests.^{[6]}

## Difference Between Parametric and Nonparametric Test …

Interpret the test Selecting Tests using the Choice Criteria Recommended Statistical Techniques by Measurement Level and Testing Situation Measurement

Scale Parametric Test

+ places emphasis on the importance of assumptions

+ date are derived from interval and ratio measurements

+ observations are independent

+ sample data have a normal distribution The T-Test used to determine the special significance between a simple distribution mean and a parameter sample mean specified value to be tested sample standard deviation size of the sample NULL HYPOTHESIS ALTERNATIVE HYPOTHESIS First, compute the sample mean and standard deviation Second, compute the t-value A professor wants to know if her introductory statistics class has a good grasp of basic math.

## Parametric and Nonparametric Methods in Statistics

also called conventional statistical procedures

use to test hypothesis with nominal and ordinal value

a sample statistic is obtained to estimate the population parameter

estimation process involves a sample , a sampling distribution, and a population "One finds the truth by making a hypothesis." David Douglas

Physicist at the University of Rochester 6-step hypothesis testing procedure 1.

## Compare and contrast parametric and nonparametric ..

Mallows and Tukey (1982) argued against the Winsor's principle. Intheir view, since this approach pays toomuch attention to the very center of the distribution, it is highlymisleading. Instead, he recommended to develop a way to describe theumbrae and penumbrae around the data. In addition, Keselman and Zumo(1997) found that the nonparametric approach has more power than thetrimmed-mean approach does. Nevertheless, Wilcox (2001) asserted thatthe trimmed-mean approach is still desirable if 20 percent of the dataare trimmed under non-normal distributions.