Parametric statistics are statistical techniques based on assumptions about the population from which the sample data are selected. For example, if a t statistic is being used to conduct a hypothesis test about a population mean, the assumption is that the data being analyzed are randomly selected from a normally distributed population. The name parametric statistics refers to the fact that an assumption (here, normally distributed data) is being made about the data used to test or estimate the parameter (in this case, the population mean). In addition, the use of parametric statistics requires quantitative measurements that yield interval or ratio level data.
For data that do not meet the assumptions made about the population, or when the level of data being measured is qualitative, statistical techniques called nonparametric, or distribution-free, techniques are used. Nonparametric statistics are based on fewer assumptions about the population and the parameters than are parametric statistics. Sometimes they are referred to as distribution-free statistics because many of them can be used regardless of the shape of the population distribution. A variety of nonparametric statistics are available for use with nominal or ordinal data. Some require at least ordinal-level data, but others can be specifically targeted for use with nominal-level data. Nonparametric techniques have the following advantages.
1.Sometimes there is no parametric alternative to the use of nonparametric statistics. 2.Certain nonparametric tests can be used to analyze nominal data. 3.Certain nonparametric tests can be used to analyze ordinal data. 4.The computations on nonparametric statistics are usually less complicated than those for parametric statistics, particularly for small samples. 5.Probability statements obtained from most nonparametric tests are exact probabilities.
Using nonparametric statistics also has some disadvantages. 1.Nonparametric tests can be wasteful of data if parametric tests are available for use with the data. 2.Nonparametric tests are usually not as widely available and well known as parametric tests. 3.For large samples, the calculations for many nonparametric statistics can be tedious.
The one-sample runs test is a nonparametric test of randomness. The runs test is used to determine whether the order or sequence of observations in a sample is random. The runs test examines the number of “runs” of each of two possible characteristics that sample items may have. A run is a succession of observations that have a particular one of the characteristics. For example, if a sample of people contains both men and women, one run could be a continuous succession of women.
In tossing coins, the outcome of three heads in a row would constitute a run, as would a succession of seven tails. In a random sample, the number of runs is likely to be somewhere between these extremes. What number of runs is reasonable? The one-sample runs test takes into consideration the size of the sample, n, the number observations in the sample having each characteristic, n1, n2 (man, woman, etc.), and the number of runs in the sample, R, to reach conclusions about hypotheses of randomness.