A statistical study requires a population. Population is a group from where information is gathered. This information is called data.
Statistics is a major branch of mathematics and deals with the study, classification, analysis, and representation of data. The null hypothesis statement is an important statistical procedure that is used to define the relationship between two quantities. If the statement is rejected, a contradictory statement to the null hypothesis, called an alternative hypothesis, is taken into consideration.
Statistics encompasses many methodologies and procedures for data research and analysis. These procedures are used in scientific, mathematical, industrial, and even societal applications. In general, it comprises two major branches for data analysis: descriptive and inferential statistics.
- In descriptive statistics the data is described in a very accurate manner; complete information is provided about that particular data set.
- That said, the data can only be described; it may not be feasible for the same description or analysis to extend to a similar larger group.
- Graphical elements are used to describe this data set as well; visual representation helps us understand the data better.
- Consider a simple example of descriptive statistics. Assume that there are 70 students in a class, and their marks in 5 subjects have to be displayed.
- This data can be presented in a number of ways. The marks can be listed down from highest to lowest, for each subject, and the students can be categorized accordingly.
- Or, the subjects can be ranked as per importance, and the students' marks can be presented from highest to lowest.
- The average scores in every subject can be listed. Or, the overall average score among the students can be calculated and presented. Thus, the data set mentioned above can be described in a variety of ways: subject-wise, student-wise, score-wise - from highest to lowest.
- Inferential statistics involves studying a sample of data; the term implies that information has to be inferred from the presented data.
- A sample of the data is considered, studied, and analyzed.
- Unlike descriptive statistics, this data analysis can extend to a similar larger group and can be visually represented by means of graphic elements.
- Consider a country's population. For the sake of convenience, a smaller sample of the population is considered, results are drawn, and the analysis is extended to the larger data set.
- Assume that you want to find out if the citizens in a state like a particular author. In such a case, data is collected from every city, small samples are described graphically, and conclusions are drawn.
- If 45% of the population in 5 cities, out of 8, vote for that particular author, you can, to an extent, assume that 45% of the state population likes that author.
- You have to make use of certain other methods as well, to reach a slightly more reliable conclusion.
Descriptive Vs. Inferential Statistics
|Descriptive Statistics||Inferential Statistics|
|It helps you describe, organize, and summarize the data. It presents information in a manageable form.||It helps you observe and analyze a sample of the data. It is used to generalize and make judgments.|
|Graphical Methodologies Used|
Inferential statistics is used when we have to generalize information about the available data. It is used in salary, population, and many other similar statistics, where estimates are calculated using a sample. Descriptive statistics, by contrast, may be used to describe a sample or the whole population, but cannot be used in instances where conclusions have to be drawn and studied for future references.