Descriptive and Inferential Statistics

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Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation and organization of data. Statistics is a highly interdisciplinary field; research in statistics finds applicability in virtually all scientific fields. Statistical methods can broadly be divided into two categories.

  1. Descriptive Statistics: Descriptive Statistics is that branch of statistics which is concerned with describing the entire population under study. Charts, Graphs and Tables are common way to summarize the data while studying the entire population.
  2. Inferential Statistics: Inferential Statistics is a type of statistics that focuses on drawing conclusions about the population, on the basis of sample analysis and observation. In Inferential statistics, certain tests (Z, t, chi square etc.) are used to predict the properties of data. Generally, final results are shown on the basis of occurrence of data.

Types of Measurement Scales:

  1. Nominal: Nominal scales are used for labeling variables without any quantitative value. “Nominal” scales could simply be called “labels.”G. Gender could either be Male or Female.

 

  1. Ordinal: With ordinal scales, it is the order of the values is what’s important and significant, but the differences between each one is not really known. For example, the ranking of 1,000 small cap growth stocks by performance may be done by assigning the number 1 to the 100 best performing stocks, the number 2 to the next 1 00 best performing stocks, and so on, assigning the number 10 to the 100 worst performing stocks. Based on this type of measurement, it can be concluded that a stock ranked 3 is better than a stock ranked 4, but the scale reveals nothing about performance differences or whether the difference between 3 and 4 is the same as the difference between 4 and 5.
  1. Interval: Interval scales are numeric scales in which we know not only the order, but also the exact differences between the values.  The classic example of an interval scale is Celsius temperature because the difference between each value is the same.  For example, the difference between 60 and 50 degrees is a measurable 10 degrees, as is the difference between 80 and 70 degrees.  Time is another good example of an interval scale in which the increments are known, consistent, and measurable. The problem with interval scales: they don’t have a “true zero.”  For example, there is no such thing as “no temperature.”  Without a true zero, it is impossible to compute ratios.  With interval data, we can add and subtract, but cannot multiply or divide.
  2. Ratio: Ratio scales are the ultimate nirvana when it comes to measurement scales because they tell us about the order, they tell us the exact value between units, AND they also have an absolute zero–which allows for a wide range of both descriptive and inferential statistics to be applied.

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