Statistical Methods In Economics

[Pages:398]StatisticalMethodsInEconomics

DECO504

Edited by: Dr.Pavitar Parkash Singh

STATISTICAL METHODS IN ECONOMICS

Edited By

Dr. Pavitar Parkash Singh

Printed by USI PUBLICATIONS 2/31, Nehru Enclave, Kalkaji Ext.,

New Delhi-110019 for

Lovely Professional University

Phagwara

SYLLABUS Statistical Methods in Economics

Objectives: The course aims to equip the students with statistical tools and concepts that help in decision making. The emphasis is on their application in business.

Sr. No.

Content

1 Definition of Statistics: Importance and scope of statistics and its limitations, Types

of data collection: Primary and Secondary: Methods of collecting Primary data,

Classification and Tabulation of data: Frequency and cumulative frequency

distribution

2 Central Tendency: Mean, Median and Mode and their Properties, Application of

Mean, Median and Mode

3 Dispersion: Meaning and characteristics. Absolute and relative measures of

dispersion including Range, Quartile deviation, Percentile, Mean deviation,

Standard deviation, Skewness and Kurtosis: Karl Pearson, Bowley, Kelly's

methods

4 Correlation: Definition, types and its application for Economists, Correlation:

Scatter Diagram Method, Karl Pearson's coefficient of correlation, Rank

correlation method

5 Linear Regression Analysis: Introduction and lines of Regression, Coefficient of

regression method simple, Correlation analysis vs. Regression Analysis

6 Index number: Introduction and Use of index numbers and their types, Methods:

Simple (unweighted) Aggregate Method, Weighted aggregate method, Methods:

Simple (unweighted) Aggregate Method, Methods: Simple Average of Price

Relatives, Methods: Weighted Average of Price Relatives, Test of consistency:

Unit test, Time Reversal Test, Factor Reversal Test and Circular, Cost of Living

index and its uses. Limitation of Index Numbers

7 Time Series Analysis: Introduction and components of time series, Time Series

Methods: Graphic, method of semi-averages, Time Series Methods: Principle of

Least Square and its application, Methods of Moving Averages

8 Theory of Probability: Introduction and uses, Additive and Multiplicative law of

probability

9 Theory of Estimation: Point estimation, Unbiasedness, Consistency, Efficiency and

Sufficiency, Method of point estimation and interval estimation

10 Types of Hypothesis: Null and Alternative, types of errors in testing hypothesis,

Level of significance

CONTENTS

Unit 1: Definition of Statistics, Importance and Scope of Statistics and its Limitations

1

Dilfraz Singh, Lovely Professional University

Unit 2: Types of Data Collection: Primary and Secondary, Methods of Collecting Primary Data

8

Pavitar Parkash Singh, Lovely Professional University

Unit 3: Classification and Tabulation of Data: Frequency and Cumulative Frequency Distribution

17

Pavitar Parkash Singh, Lovely Professional University

Unit 4: Central Tendency: Mean, Median and Mode and their Properties

37

Hitesh Jhanji, Lovely Professional University

Unit 5: Application of Mean, Median and Mode

48

Dilfraz Singh, Lovely Professional University

Unit 6: Dispersion: Meaning and Characteristics, Absolute and Relative Measures of Dispersion

including Range, Quartile Deviation and Percentile

72

Pavitar Parkash Singh, Lovely Professional University

Unit 7: Mean Deviation and Standard Deviation

91

Dilfraz Singh, Lovely Professional University

Unit 8: Skewness and Kurtosis: Karl Pearson, Bowley, Kelly's Methods

116

Pavitar Parkash Singh, Lovely Professional University

Unit 9: Correlation: Definition, Types and its Application for Economists

128

Hitesh Jhanji, Lovely Professional University

Unit 10: Correlation: Scatter Diagram Method, Karl Pearson's Coefficient of Correlation

147

Pavitar Parkash Singh, Lovely Professional University

Unit 11: Rank Correlation Method

167

Dilfraz Singh, Lovely Professional University

Unit 12: Linear Regression Analysis: Introduction and Lines of Regression

176

Dilfraz Singh, Lovely Professional University

Unit 13: Coefficient of Simple Regression Method

187

Pavitar Parkash Singh, Lovely Professional University

Unit 14: Correlation Analysis Vs. Regression Analysis

201

Dilfraz Singh, Lovely Professional University

Unit 15: Index Number: Introduction and Use of Index Numbers and their Types

207

Pavitar Parkash Singh, Lovely Professional University

Unit 16: Methods--Simple (Unweighted) Aggregate Method and Weighted Aggregate Method

216

Dilfraz Singh, Lovely Professional University

Unit 17: Unit 18: Unit 19: Unit 20: Unit 21: Unit 22: Unit 23: Unit 24: Unit 25: Unit 26: Unit 27: Unit 28: Unit 29: Unit 30:

Methods: Simple (Unweighted) Aggregate Method Pavitar Parkash Singh, Lovely Professional University

Methods--Simple Average of Price Relatives Dilfraz Singh, Lovely Professional University

Methods--Weighted Average of Price Relatives Pavitar Parkash Singh, Lovely Professional University Test of Consistency: Unit Test, Time Reversal Test, Factor Reversal Test and Circular Test Dilfraz Singh, Lovely Professional University

Cost of Living Index and Its Uses and Limitation of Index Numbers Pavitar Parkash Singh, Lovely Professional University Time Series Analysis--Introduction and Components of Time Series Pavitar Parkash Singh, Lovely Professional University

Time Series Methods--Graphic, Method of Semi-averages Dilfraz Singh, Lovely Professional University Time Series Methods--Principle of Least Square and Its Application Pavitar Parkash Singh, Lovely Professional University Methods of Moving Averages Hitesh Jhanji, Lovely Professional University Theory of Probability: Introduction and Uses Dilfraz Singh, Lovely Professional University

Additive and Multiplicative Law of Probability Dilfraz Singh, Lovely Professional University Theory of Estimation: Point Estimation, Unbiasedness, Consistency, Efficiency and Sufficiency Hitesh Jhanji, Lovely Professional University

Methods of Point Estimation and Interval Estimation Dilfraz Singh, Lovely Professional University

Types of Hypothesis: Null and Alternative, Types of Errors in Testing Hypothesis and Level of Significance Dilfraz Singh, Lovely Professional University

229 234 241 249 258 274 295 305 317 325 340

352 363

379

Dilfraz Singh, LPU

Unit 1: Definition of Statistics, Importance and Scope of Statistics and Its Limitations

Unit 1: Definition of Statistics, Importance and Scope

Notes

of Statistics and Its Limitations

CONTENTS Objectives Introduction 1.1 Definition of Statistics 1.2 Importance and Scope of Statistics 1.3 Limitations of Statistics 1.4 Summary 1.5 Key-Words 1.6 Review Questions 1.7 Further Readings

Objectives

After reading this unit students will be able to: ? Know the Definition of Statistics. ? Discuss the Importance and Scope of Statistics. ? Explain the Limitations of Statistics

Introduction

In general sense the word Statistics means facts and figures of a particular phenomenon--Under reference in numerical numbers. In the traditional period the scope of Statistics was very much limited to the collection of facts and figures pertaining to the age-wise and sets-wise distribution of population, wealth etc. But now-a-days we can say that Statistics constitutes an integral part of every scientific and economic inquiry: Social and economic studies without Statistics are useless. Statistics thus play a vital role and as Tippet has rightly remarked, "It affects everybody and touches life at many points."

1.1 Definition of Statistics

It has been observed that the word `Statistics' comes from Latin word `Status' which means Political State. It has also been believed that the word Statistics comes from Italian word `Stato'. This word was used in the fifteenth century for the `State' in actual practice these words were used for Political State or Stateman's art. Now-a-days Statisticians use statistics both in singular and plural sense. In the singular sense the term Statistics is associated with "A body of methods for making decisions when there is uncertainty arising from incompleteness or the instability of the information available for making such decisions." In its plural sense Statistics refers to numerical Statements of facts such as per capita income, population etc. Thus, some authorities have defined Statistics as Statical data (Plural sense) whereas other as Statistical method (Singular sense). According to Oxford Concise Dictionary, "Statistics--(as treated as plural): numerical facts, systematically collected, as Statistics of population, crime etc. (treated as singular): Science of collecting, classifying and using Statistics."

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1

Statistical Methods in Economics

Notes

Definition

The definition of Statistics can be divided into the following two heads: (A) In Plural Sense, (B) In Singular Sense. (A) In Plural Sense: The following are the definitions of Statistics in Plural Sense:

According to H. Secrist--"By Statistics we mean aggregate of facts affected to a marked extent by multiplicity of causes, numerically expressed, enumerated or estimated according to a reasonable standards of accuracy, collected in a systematic manner for a predetermined purpose and placed in relation to each other." In the words of L. R. Connor--"Statistics are measurements, enumeration or estimater of natural or social phenomena systematically arranged so as to exhibit their interrelations." According to Yule & Kendall--"By Statistics we mean quantitative data affected to a marked extent by multiplicity of causes." In the opinion of A. L. Bowley--"Statistics are numerical statement of facts in any department of enquiry placed in relation to each other." According to Webster--"Classified facts, representing the condition of the people in a State, specially those facts which can be stated in numbers or in tables of numbers or in any tabular or classified arrangement." On the basis of the above definitions the following characteristics are there in Statistics: 1. Statistics are aggregate of facts: Single and unconnected figures are not Statistics.

A single age of 22 years or 37 years is not Statistics but a series relating to the ages of a group of people would be called Statistics. Likewise single figure relating to birth, death, sale, etc. cannot be called Statistics but aggregates of such figures would be Statistics because they can be studied in relation to each other and are capable of comparison. 2. Statistics are affected to a marked extent by multiplicity of causes: Usually facts and figures are affected, to a considerable extent, by a number of factors operating together. For example --Statistics of prices are affected by conditions of demand, supply, imports, exports, currency circulation, etc. and various other factors. 3. Statistics are numerically expressed: Qualitative expression like good, bad, young, old etc. do not form a part of statisical study unless numerical equivalent is assigned to such expression. If it is said that the production of rice per acre in 1997 was 30 quintals and in the year 2002 it was 50 quintals, we shall be making Statistical statements. 4. Statistics are enumerated according to reasonable standard of accuracy: Facts and figures relating to any subject can be derived in two way, example--by actual counting and measurement or by estimates. Estimates cannot be as accurate and precise as actual measurements. For example--If the heights of a group of people are being measured, it is right if the measurements are correct to a centimetre but if are measuring the distance from Agra to Gwalior, a difference of a few kilometres even, can be easily ignored. 5. Collected in a systematic manner: If Statistics are collected in a haphazard manner, it might fail to give the accurate result. It is, therefore, essential that statistics must be collected in a systematic manner so that they may Conform to reasonable standard of accuracy. 6. Collected for a pre-determined purpose: Statistical data are collected and processed for a definite and pre-determined purpose. In general, no data are collected without a predetermine purpose. 7. Placed in relation to each other: The Statistics should be comparable. If they are not comparable, they lose part of their value and thus the efforts in collecting them may not prove to be as useful as the requirements may be. It is necessary that the figures which are collected should be a homogeneous so as to make them comparable and more useful. On the basis of the above description it may be said that numerical data cannot be called Statistics hence "All Statistics are numerical statements of facts but all numerical statements of facts may not essentially be Statistics." (B) In Singular Sense: The following are the definitions of Statistics in Singular Sense. Lovitt defines the science as, "That which deals with the collection, classification and tabulation of numerical facts as the basis for explanation, description and comparison of phenomena."

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