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Applied Statistics

The origin of statistics was due to the administrative requirements of the state. Statistical methods are techniques or principles with the help of which numerical data is systematically treated, so as to present a comprehensible view of them. Statistics is a science of collection, presentation, analysis and interpretation of data.

Thus, statistics speaks about data. But, in addition, statistics is a field involving the in-depth knowledge of data. Statistical methods are used in all fields including business, economics, biology, physics, astronomy, meteorology, chemistry, medicine, sociology, psychology and so on. Probably, there are no fields where statistics has not been utilized.

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What is Applied Statistics ?

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Statistics is an aggregate of facts affected to a marked extent by multiplicity of causes numerically expressed, enumerated or estimated according to a reasonable standard of accuracy, collected in a systematic manner for a predetermined purpose and placed in relation to each other. Statistics is the science, which deals with the method of collecting, classifying and interpreting numerical data collected.

Statistics simplifies complexity. It presents raw facts in a definite and precise form. It helps in the condensation of data. It helps in the comparison and in the testing of data. It helps the government in formulating policies. So we can say that Statistics plays a vital role in every walk of life.

Levels of Measurement

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In statistics, there are four types of level of measurement or measurement scales used in applied statistics methods:

  • Nominal
  • Ordinal
  • Interval
  • Ratio
They have various degrees of usefulness in applied statistics methods.

1) Nominal Measurements

It contain no significant rank sequence amongst values.

2) Ordinal Measurements

It contain inaccurate differences between successive values, but have a significant order to those values.

3) Interval Measurements

It have significant distances between measurements described, but have no consequential zero value defined.

4) Ratio Measurements

It have together a zero value described and the distances between different measurements classified. The maximum flexibility in applied statistical methods that will be used for examining the data. Since variables conforming only to the nominal or ordinal measurements will not be logically measured.


Statistics Terms

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Some statistics terms are given below:

Null Hypothesis


Interpretation of applied statistical methods will frequently occupy the development of a null hypothesis. In that, the statement is that, whatever is future as a reason has no effect on the variable measured. The most excellent illustration for a trainee is the predicament meet by a jury trial. The reflection comes because of suspicion of the guilt.

Errors

Working from a null hypothesis, the following two basic forms of error is standard.

Type I Errors

This type of error occurs where the null hypothesis is incorrectly discarded giving a false positive.

Type II Errors

This type of error occurs where the null hypothesis fails to be discarded and a real difference between populations is missed.

Limitations of Statistics
  1. Statistics can be used to study numerical facts. It cannot be used for measuring qualitative data like intelligence or beauty.
  2. Statistics cannot study individual items. In Statistics we can consider only a group of values. It is not possible to say the average mark of a student in a particular subject.
  3. It is only a method of solving a problem.
  4. Only experts can understand statistics.
  5. It is true only to an average. It need not be accurate in all cases.

Applied Statistics in Business and Economics

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Applied Statistics has its applications in both business and economics.

In Business


Any modern business firm faces uncertainty concerning future operations such as production, investments, inventory and marketing of products. In order to be successful in decision making under the atmosphere of uncertainty, a business man has to use statistical methods to analyze and synthesize data relating to business. A businessman needs Statistics right from the time he plans to start a business. He has to collect the required details to generate financial plan for the business. For this, he has to get the aid of Statistical methods.

Before launching his product in the market, the businessman should know the probable demand of the commodity in the market. So, he must make careful study of the seasonal variations and habits and tastes of the people. He also should take into consideration the purchasing power of the people. When he studies demand, what he is doing is nothing but statistical investigation.

In Economics


Economics is concerned with the production and distribution of wealth as well as complex institutional setup connected with the consumption, saving and investment of income.

Statistical data and statistical methods provide valuable assistance for the study and solution of economic problems and also help in designing economic policies. The science of Economics is becoming statistical in its method. It is almost impossible to find a problem in Economics, which does not require an extensive use of statistical data. The use of statistical methods increases with the increase in the usage of economic theory. The laws in Economics like law of demand, law of supply etc are established with the help of statistical methods.

Therefore, statistical methods are inevitable to prove economic laws. It is said that statistics are the straw out of which I like every other economist to make bricks.

Applied Statistics for the Behavioral Sciences

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Statistics courses typically introduce parametric methods, which have more assumptions about the data than nonparametric methods. Statistics finds application in many other branches like banking, insurance, planning, administration, broking, research etc.

Nominal Measurement of Data

This type of measurement includes the qualitative characteristics of data. In this case we do not consider the magnitude of the data. Statistical operations cannot be applied on this type of data.

Example:


Categorization of people based on the hair color is an example of Nominal data. Here the hair color of the person selected is checked. The different categories will be black, brown, blonde, and red.

Ordinal Measurement of Data


The ordinal measurement of data is based on the ranks of data. In this case, we order the data based on some quantity. It is not necessary that the difference between the two ranks is the same. In this case also we cannot apply the statistical operations.

Example:

Students can be ranked based on marks. But the difference between the marks need not be the same. So the data can be considered ordinal data.

Interval Measurement of Data


The interval measurement of data is the measurement based on both the ranking and meaningful intervals between scale points. It not only orders the measurement, but also clearly defines the distance between the orders. The main disadvantage of the interval measurement of data is that it does not have zero as the point of reference.

Example:

The difference between the intervals 10-20 is same as the difference between 50-60. In both cases, the difference is 10 and also we know that 50-60 is higher than 20-30. So, in this case, we know both the order and also the distance between the intervals.

Ratio Measurement of Data


When we include a meaningful zero in the interval measurement of data, it becomes the ratio measurement of data. Hence the ratio measurement of data is very similar to the interval measurement. The ratio measurement of data is the best in all levels for the measurement of data. Zero is considered as the point of reference in this type of measurement of data. It is not compulsory that zero is the value of one of the items in this case. In the ratio level of measurement, the distance between the orders on the scale will be equal, and the ranks are assigned to the items, according to their size or magnitudes.
Example:

If we say a baby of one year is 1.5 times heavier than a newly born baby. Here the baby's weight is clearly a ratio data. We know that a baby cannot have zero weight. But the ratio is meaningful

Nominal Measurement - Based on attributes
Ordinal Measurement - Based on ranks
Interval Measurement - Based on order with no meaningful 0
Ratio Measurement - Based on order with a meaningful 0

Applied Nonparametric Statistics

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Nonparametric statistics has probably become the leading methodology for researchers performing data analysis. Applied Nonparametric Statistics in reliability is focused on the use of modern statistical methods for the estimation of dependability measures of reliability systems that operate under different conditions. There are various stages involved in a statistical investigation. They can be the collection of data, organization of data, presentation of the data, analysis and interpretation of data.
 
Every step is equally important and needs to be carefully observed. Statistics was considered as a branch of economics earlier. But now, it has developed itself into a full size independent status with all types of quantitative analysis relating to any department of enquiry being included in it. This is because statistics helps in drawing conclusions from the facts affected by the multiplicity of causes in any department of enquiry.

Modern Applied Statistics

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The field of statistics involves methods and theory as they are applied to numerical data or observations with the objective of making a rational decision in the face of uncertainty. Let’s now understand the applications of statistics in the sector of physical science and state.

Statistics and Physical Science:


Statistics plays a great role in the study of physical sciences especially astronomy, geology, physics, meteorology and chemistry. The use of statistical methods is not only very essential but to some extent is unavoidable. Conversion of heterogeneous data into homogenous, interpretation methods and drawing inferences are places where physical sciences depend to a great extent on the science of statistics.

Statistics and State or Country:


Earlier statistics was said to be science of king (However they didn’t term it as statistics). The kings relied heavily on statistics for knowing man power for military purposes. Statistics was used as a tool to study the functions for the welfare of the states to frame suitable policies and corrective actions. Statistics was used by the government in understanding the census, finances, and other recurrences. Even now the governments across the globe rely on statistical data for analyzing, understanding and taking important decisions towards development of the country
More topics in Applied Statistics
Confidence Interval Level of Measurement
Hypothesis Testing Sample Size
Normal Approximation to the Binomial Distribution Chi Square Test
Margin of Error Exterior Angle Property
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