Disadvantages Of Nonparametric Statistics

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.

15.2.1 Advantages and Disadvantages of Nonparametric

(i) As a test of goodness of fit :

The chi-square goodness-of-fit test compares the expected, or theoretical, frequencies of categories from a population distribution to the observed, or actual, frequencies from a distribution to determine whether there is a difference between what was expected and what was observed.

For example, railway officials might theorize that the ages of airline ticket purchasers are distributed in a particular way. To validate or reject this expected distribution, an actual sample of ticket purchaser ages can be gathered randomly, and the observed results can be compared to the expected results with the chi-square goodness-of-fit test. This test also can be used to determine whether the observed arrivals at teller windows at a commercial bank are Poisson distributed, as might be expected.

The formula below is used to compute a chi-square goodness-of-fit

However, the goodness-of-fit test cannot be used to analyze two variables simultaneously. A different chi-square test, the chi-square test of independence, can be used to analyze the frequencies of two variables with multiple categories to determine whether the two variables are independent. Many times this type of analysis is desirable. For example, a market researcher might want to determine whether the type of soft drink preferred by a consumer is independent of the consumer’s age. Financial investors might want to determine whether type of preferred stock investment is independent of the region where the investor