Importance of Statistics in Various Disciplines

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Introduction to the Importance of Statistics

Statistics is used as a tool to make appropriate decisions in the face of uncertainty. We all apply statistical concepts in our daily life either we are educated or uneducated. Therefore the importance of Statistics cannot be ignored.

The information collected in the form of data (observation) from any field/discipline will almost always involve some sort of variability or uncertainty, so this subject has applications in almost all fields of research. The researchers use statistics in the analysis, interpretation, and communication of their research findings.

Some examples of the questions which statistics might help to answer with appropriate data are:

  1. How much better yield of wheat do we get if we use a new fertilizer as opposed to a commonly used fertilizer?
  2. Does the company’s sales are likely to increase in the next year as compared to the previous?
  3. What dose of insecticide is used successfully to monitor an insect population?
  4. What is the likely weather in the coming season?
Importance of Statistics
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Application of Statistics

Statistical techniques being powerful tools for analyzing numerical data are used in almost every branch of learning. Statistics plays a vital role in every field of human activity. Statistics has an important role in determining the existing position of per capita income, unemployment, population growth rate, housing, schooling medical facilities, etc in a country. Now statistics holds a central position in almost every field like Industry, Commerce, Biological and Physical sciences, Genetics, Agronomy, Anthropometry, Astronomy, Geology, Psychology, Sociology, etc are the main areas where statistical techniques have been developed and are being used increasingly.

Statistics has its application in almost every field where research is carried out and findings are reported. Application of statistics (by keeping in view the importance of statistics) in different fields as follows:

Social Sciences

In social sciences, one of the major objectives is to establish a relationship that exists between certain variables. This end is achieved through postulating hypothesis and their testing by using different statistical techniques. Most of the areas of our economy can be studied by econometric models because these help in forecasting and forecasts are important for future planning.

Plant Sciences

The most important aspect of statistics in plant sciences is its role in the efficient planning of experiments and drawing valid conclusions. A technique in statistics known as “Design of Experiments” helps introduce new varieties. Optimum plot sizes can be worked out for different crops like wheat, cotton, sugarcane, and others under different environmental conditions using statistical techniques.

Physical Sciences

The application of statistics in physical sciences is widely accepted. The researchers use these methods in the analysis, interpretation, and communication of their research findings, linear and nonlinear regression models are used to establish cause and effect relationships between different variables, and also these days computers have facilitated experimentation and it is possible to simulate the process rather than experimentation.

Medical Sciences

The interest may be in the effectiveness of new drugs, the effect of environmental factors, heritability, standardization of various records, and other related problems. Statistics come to the rescue. It helps to plan the next investigation to get trustworthy information from the limited resources. It also helps to analyze the current data and integrate the information with that previously existing.

How statistics is used by banks, insurance companies, Business and economic planning and administration, Accounting and controlling of events, Construction Companies, Politicians

Banks

Banks are a very important economic part of a country. They do their work on the guess that all the depositors do not take their money on the same day. Bankers use probability theory to approximate the deposits and claims to take out their money.

Insurance Companies

Insurance companies play an important role in increasing economic progress. These companies collect payment from the people. They approximate the death rate, accident rate, and average expected life of people from the life tables. The payment per month is decided on these rates.

Business

Business planning for the future is very important such as the price, quality, quantity, demand, etc of a particular product. Businessmen can make correct decisions about the location of the business, marketing of the products, financial resources, etc. Statistics helps a businessman to plan production according to the taste of the customers, the quality of the products can also be checked more efficiently by using statistical methods

The relationship between supply and demand is a very important topic of everyday life. The changes in prices and demands are studied by index numbers. The relation between supply and demand is determined by correlation and regression.

Economic Planning

Economic planning for the future is a very important problem for economists. For example (i) opening of new educational institutions such as schools, and colleges, revision of pay scales of employees, construction of new hospitals, and preparation of government budgets, etc. all these require estimates at some future time which is called forecasting which is done by regression analysis and the different sources of earning, planning of projects, forecasting of economic trends are administered by the use of various statistical techniques.

Accounting and Controlling of Events

All the events in the world are recorded, for example, births, deaths, imports, exports, and crops grown by the farmer etc. These are recorded as statistical data and analyzed to make better policies for the betterment of the nation.

Administrator

An administrator whether in the public or private sector leans on statistical data to provide a factual basis for appropriate decisions.

Politician

A politician uses statistical advantageously to lend support and credence to his argument while elucidating the problems he handles.

Construction Companies

All kinds of construction companies start and run their programs after making judgments about the total cost of the project (job, work). To guess the expenditure a very important statistical technique of estimation is used.

Biology

In biology correlation and regression are used for analysis of hereditary relations. To classify the organization into different classes according to their age, height, weight, hair color, eyebrow color, etc. the rules of classification are tabulation of statistics are used.

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Important MCQs Sampling Techniques Quiz with Answers 12

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The post is about Multiple Choice Questions Related to Sampling and Sampling Techniques Quiz. There are 20 MCQs about Sampling Techniques covering the topics related, to stratified sampling, cluster sampling, and simple random sampling. Let us start with the Sampling Techniques Quiz.

Online Multiple Choice Questions about Sampling and Sampling Techniques with Answers

1. In a stratified random sampling method

 
 
 
 

2. The cluster sampling method differs from the stratified sampling method in that

 
 
 
 

3. Problem of non-Response

 
 
 
 

4. Which of the following would usually require the smallest sample size because of efficiency?

 
 
 
 

5. If larger units have more probability of their inclusion in the sample, the sampling is known as

 
 
 
 

6. A group consists of 300 people and we are interviewing all members of a given group called

 
 
 
 

7. ————- is a set of elements taken from a larger population according to certain rules.

 
 
 
 

8. If the respondents do not provide the required information to the researcher, then it is known as

 
 
 
 

9. Suppose that all the units in the population are divided into ten mutually exclusive groups. The word “mutually exclusive” means that

 
 
 
 

10. Before completing a survey, an individual acknowledges reading information about how and why the data they provide will be used. What is this concept called?

 
 
 
 

11. The mean of clusters average is the biased estimator of a population mean when

 
 
 
 

12. Sample allocation plan that provides the most precision, given a fixed sample size is

 
 
 
 

13. When the procedure of selecting the elements from the population is not based on probability is known as

 
 
 
 

14. When the population is badly affected, which type of sampling is appropriate?

 
 
 
 

15. In stratified random sampling with strata weights 0.35, 0.55, and 0.10, and standard deviations 16, 23, and 19, and sample sizes 70, 110, and 20, the variance of the sample mean estimator is?

 
 
 
 

16. One similarity between the stratified sampling method and the cluster sampling method is that

 
 
 
 

17. Which of the following is not a characteristic of quota sampling?

 
 
 
 

18. A randomly selected sample of 1000 college students was asked whether they had ever used the drug Ecstasy. Sixteen percent (16% or 0.16) of the 1000 students surveyed said they had which one of the following statements about the number 0.16 is correct?

 
 
 
 

19. Which ONE of the following is the main problem with using non-probability sampling techniques?

 
 
 
 

20. In a cluster random sampling method

 
 
 
 

MCQs Sampling Techniques Quiz with Answers

  • Sample allocation plan that provides the most precision, given a fixed sample size is
  • In stratified random sampling with strata weights 0.35, 0.55, and 0.10, and standard deviations 16, 23, and 19, and sample sizes 70, 110, and 20, the variance of the sample mean estimator is?
  • A group consists of 300 people and we are interviewing all members of a given group called
  • When the procedure of selecting the elements from the population is not based on probability is known as
  • Problem of non-Response
  • If the respondents do not provide the required information to the researcher, then it is known as
  • If larger units have more probability of their inclusion in the sample, the sampling is known as
  • The cluster sampling method differs from the stratified sampling method in that
  • One similarity between the stratified sampling method and the cluster sampling method is that
  • In a cluster random sampling method
  • In a stratified random sampling method
  • Suppose that all the units in the population are divided into ten mutually exclusive groups. The word “mutually exclusive” means that
  • When the population is badly affected, which type of sampling is appropriate?
  • A randomly selected sample of 1000 college students was asked whether they had ever used the drug Ecstasy. Sixteen percent (16% or 0.16) of the 1000 students surveyed said they had which one of the following statements about the number 0.16 is correct?
  • Which ONE of the following is the main problem with using non-probability sampling techniques?
  • Which of the following is not a characteristic of quota sampling?
  • Before completing a survey, an individual acknowledges reading information about how and why the data they provide will be used. What is this concept called?
  • ————- is a set of elements taken from a larger population according to certain rules.
  • The mean of clusters average is the biased estimator of a population mean when
  • Which of the following would usually require the smallest sample size because of efficiency?
Sampling and Sampling Techniques Quiz

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Statistical Hypotheses: Made Easy

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Overview of Statistical Hypotheses

A statistical hypothesis is a claim about a population parameter. For example,

  • The mean height of males is less than 65 inches tall
  • The percentage of people favoring a bullet train is about 59%
  • The daily average expense for a college student is more than Rs. 250
  • At least 5% of Pakistan earn more than Rs 2,500,000 per year

A statistical method is used to determine if there is enough evidence in sample data to support a claim about a population.

The claimed hypotheses are written in certain statistical and concise forms. For example, the above statements about population can be written as

  • $H_0: \mu < 65$
  • $H_0: \pi = 0.59$
  • $H_0:\mu > 250$
  • $H_0: \pi \ge 0.05$

If someone is interested in knowing that above stated statistical hypotheses are either true or false, one needs to conduct a hypothesis test. To test a statistical hypothesis, one needs to follow the following basic procedure, to fulfill the requirements.

  1. Draw a random sample from the population of interest (for example, the height of males)
  2. Determine if the results from the sample data are consistent or not with the hypothesis under study.
  3. If the collected sample data is (significantly) different from the claimed hypothesis, then reject the hypothesis as being false. However, if the sampled data is not significantly different, one would not reject the hypothesis.

Statistical Hypotheses Example

Example: Suppose a battery manufacturer claims that the average life of their batteries is at least 300 minutes.

To test this hypothesis, we follow the procedure as

  1. Select a sample of say $n=100$ batteries. The sample of batteries is tested and the mean life of sampled batteries was found to be $\overline{x} = 294$ minutes with a sample standard deviation of $s=204 minutes.
  2. We need to test whether “is this data sufficiently different from the manufacturer’s claim to justify rejecting the claim as false”?
  3. Since the sample drawn is large enough, the Central Limit Theorem allows us to conclude that the distribution of sample means $\overline{x}$ is approximately normal.
  4. If the manufacturer’s claim is correct, then $\mu_{\overline{x}} = \mu \ge 300$ and we will assume that $\mu_{\overline{x}} = \mu = 300$.
  5. The Z-score will be $$Z = \frac{\overline{x} – \mu_{\overline{x}}}{\frac{s}{\sqrt{n}}}=\frac{294-300}{\frac{20}{\sqrt{100}}} = -3.0$$
  6. Search the Probability value from Standard Normal Table, as $P(\overline{x} \le 294)=0.0013$
Statistical Hypotheses

Decision about Hypothesis

Now one of the following must be true

  1. The assumption that $\mu = 300$ is incorrect
  2. The sample drawn has a so small mean that only 13 in 10,000 samples have a mean as low.

The probability of the second statement being true is quite small (0.0013). Thus there is strong evidence to believe that the first statement is true, and hence the manufacturer overstated the mean life of their batteries.

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Akaike Information Criteria: A Comprehensive Guide

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The Akaike Information Criteria/Criterion (AIC) is a method used in statistics and machine learning to compare the relative quality of different models for a given dataset. The AIC method helps in selecting the best model out of a bunch by penalizing models that are overly complex. Akaike Information Criterion provides a means for comparing among models i.e. a tool for model selection.

  • A too-simple model leads to a large approximation error.
  • A too-complex model leads to a large estimation error.

AIC is a measure of goodness of fit of a statistical model developed by Hirotsugo Akaike under the name of “an information Criteria (AIC) and published by him in 1974 first time. It is grounded in the concept of information entropy in between bias and variance in model construction or between accuracy and complexity of the model.

The Formula of Akaike Information Criteria

Given a data set, several candidate models can be ranked according to their AIC values. From AIC values one may infer that the top two models are roughly in a tie and the rest far worse.

$$AIC = 2k-ln(L)$$

where $k$ is the number of parameters in the model, and $L$ is the maximized value of the likelihood function for the estimated model.

Akaike Information Criteria/ Criterion (AIC)

For a set of candidate models for the data, the preferred model is the one that has a minimum AIC value. AIC estimates relative support for a model, which means that AIC scores by themselves are not very meaningful

Akaike Information Criteria focuses on:

  • Balances fit and complexity: A model that perfectly fits the data might not be the best because it might be memorizing the data instead of capturing the underlying trend. AIC considers both how well a model fits the data (goodness of fit) and how complex it is (number of variables).
  • A lower score is better: Models having lower AIC scores are preferred as they achieve a good balance between fitting the data and avoiding overfitting.
  • Comparison tool: AIC scores are most meaningful when comparing models for the same dataset. The model with the lowest AIC score is considered the best relative to the other models being evaluated.

Summary

The AIC score is a single number and is used as model selection criteria. One cannot interpret the AIC score in isolation. However, one can compare the AIC scores of different model fits to the same data. The model with the lowest AIC is generally considered the best choice.

The AIC is the most useful model selection criterion when there are multiple candidate models to choose from. It works well for larger datasets. However, for smaller datasets, the corrected AIC should be preferred. AIC is not perfect, and there can be situations where it fails to choose the optimal model.

There are many other model selection criteria. For more detail read the article: Model Selection Criteria

Akaike Information Criteria

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