In general, statistics is meant as the way of getting information from data. In more specific, meaning of statistic can be classified into three:
- statistics is the reporting of data, such as statistics of football, statistics of population, etc.
- statistics is a quantity counted from data, such as proportion, mean, etc.
- statistics is also meant as a science and art in making inference from specific unit for general condition.
Data are something that considered can be pictured about the situation or problem. Data are assumed as something that may be not true. However, assumption is often used as a guidance of decision making, for example government assumes that stock of rice is enough because paddy production shows increasing, so it is decided that importing of rice do not need to do yet. An assumption may not be true so if it is used as a guidance of decision making, this decision may also be mistaken or wrong. Because of that in statistical view the assumption, as a hypothesis, must be tested previously.
Talk about statistics is meant that we talk about samples. Sample is a part of population member that made as a research objects. Population is a group of the whole objects that want to be learned their characteristics. The activity for measuring the whole objects (population) is called a census, for example: population census, agriculture census, etc. The activity for measuring part of population objects is called a survey. Descriptive measurement from a population is parameter, while the descriptive measurement from a sample is statistics. So population has parameters, and sample has statistics. Data got from a census can be analyzed by descriptive way. Data got from a survey can be analyzed by descriptive and inference way. Inference is a decision making which are included statements, explanations, comparisons, estimations, forecasting, etc.
Statistical methods can be classified into two groups, that are parametric statistics and nonparametric statistics. Parametric testing is a hypothesis testing that needs several assumptions:
- sample observations must be chosen from the population assumed has normal distribution.
- In case of comparative testing of two or more parameters, populations are not only assuming have normal distribution but also have equal variances (homoscedasticity assumption).
The validities of those assumptions are determined the deeply signification of the parametric testing result. However, nonparametric methods are never using assumption of population from where samples are chosen. Statistical methods used in nonparametric statistics use qualitative data or data in ranking form or quantitative data that do not follow normal distribution. Because of that, nonparametric statistics is often called free distribution statistics. In nonparametric statistics, we will test population characteristics without using specific parameter. So, in nonparametric statistics we will test whether location of populations are different rather than to test the difference of population mean.
We need to realized that nonparametric statistics be properly not used if parametric testing can be applied, because the accuracy level of nonparametric testing is lower than parametric testing. However as the decision maker or researcher do not have misinterpretation about the usage degree of nonparametric statistics that is lower than parametric statistics method. Of course not really like that, every methods are made with specific usage related to the type of data that be used. Increasing the accuracy level of nonparametric statistics can be done by adding the number of samples. However, as we know that adding the number of samples will also could impact to the increasing of cost, time, and other measurements survey.
The explanation about what and how to use parametric and nonparametric statistics methods in application can be explained in other writing session. Have enjoying statistics.
*) Writer is a lecturer in Institute of Statistics, Jakarta, Indonesia.
Bachelor of Statistics from Institute of Statistics, Jakarta, Indonesia.
Master of Science in Experimental Statistics from NMSU, USA.