The practice or science of collecting and analyzing numerical data in large quantities, especially for the purpose of inferring proportions in a whole from those in a representative sample
Type of Statistic
Descriptive statistics give information that describes the data in some manner. For example, suppose a pet shop sells cats, dogs, birds and fish. If 100 pets are sold, and 40 out of the 100 were dogs, then one description of the data on the pets sold would be that 40% were dogs.
This same pet shop may conduct a study on the number of fish sold each day for one month and determine that an average of 10 fish were sold each day. The average is an example of descriptive statistics.
Some other measurements in descriptive statistics answer questions such as ‘How widely dispersed is this data?’, ‘Are there a lot of different values?’ or ‘Are many of the values the same?’, ‘What value is in the middle of this data?’, ‘Where does a particular data value stand with respect with the other values in the data set?’
A graphical representation of data is another method of descriptive statistics. Examples of this visual representation are histograms, bar graphs and pie graphs, to name a few. Using these methods, the data is described by compiling it into a graph, table or other visual representation.
This provides a quick method to make comparisons between different data sets and to spot the smallest and largest values and trends or changes over a period of time. If the pet shop owner wanted to know what type of pet was purchased most in the summer, a graph might be a good medium to compare the number of each type of pet sold and the months of the year
Definition of Inferential Statistics
Inferential Statistics is all about generalizing from the sample to the population, i.e. the results of analysis of the sample can be deduced to the larger population, from which the sample is taken. It is a convenient way to draw conclusions about the population when it is not possible to query each and every member of the universe. The sample chosen is a representative of the entire population; therefore, it should contain important features of the population.
Inferential Statistics is used to determine the probability of properties of the population on the basis of the properties of the sample, by employing probability theory. The major inferential statistics are based on the statistical models such as Analysis of Variance, chi-square test, student’s t distribution, regression analysis, etc. Methods of inferential statistics:
Estimation of parameters
Testing of hypothesis
Parametric tests: assume underlying statistical distributions in the data. Therefore, several conditions of validity must be met so that the result of a parametric test is reliable. For example, Student’s t-test for two independent samples is reliable only if each sample follows a normal distribution and if sample variances are homogeneous.
he parametric test is the hypothesis test which provides generalisations for making statements about the mean of the parent population. A t-test based on Student’s t-statistic, which is often used in this regard.
The t-statistic rests on the underlying assumption that there is the normal distribution of variable and the mean in known or assumed to be known. The population variance is calculated for the sample. It is assumed that the variables of interest, in the population are measured on an interval scale.
Nonparametric tests: do not rely on any distribution. They can thus be applied even if parametric conditions of validity are not met.
The nonparametric test is defined as the hypothesis test which is not based on underlying assumptions, i.e. it does not require population’s distribution to be denoted by specific parameters.
The test is mainly based on differences in medians. Hence, it is alternately known as the distribution-free test. The test assumes that the variables are measured on a nominal or ordinal level. It is used when the independent variables are non-metric.
Parametric tests often have nonparametric equivalents. You will find different parametric tests with their equivalents when they exist in
Key Differences between Parametric and Nonparametric Tests:
The fundamental differences between parametric and nonparametric test are discussed in the following points:
A statistical test, in which specific assumptions are made about the population parameter is known as the parametric test. A statistical test used in the case of non-metric independent variables is called nonparametric test.
In the parametric test, the test statistic is based on distribution. On the other hand, the test statistic is arbitrary in the case of the nonparametric test.
In the parametric test, it is assumed that the measurement of variables of interest is done on interval or ratio level. As opposed to the nonparametric test, wherein the variable of interest are measured on nominal or ordinal scale.
In general, the measure of central tendency in the parametric test is mean, while in the case of the nonparametric test is median.
In the parametric test, there is complete information about the population. Conversely, in the nonparametric test, there is no information about the population.
The applicability of parametric test is for variables only, whereas nonparametric test applies to both variables and attributes.
For measuring the degree of association between two quantitative variables, Pearson’s coefficient of correlation is used in the parametric test, while spearman’s rank correlation is used in the nonparametric test.