Unit 6.1 - Introduction to Statistics

Introduction to Statistics

Statistics is the discipline (some consider branch of mathematics) that concerns the collection, organization, analysis, interpretation and presentation of data.

Data: Set of information (any fact, figure, sign, symbol, number) describes a given entity

Data Types: Qualitative data, Quantitative data

Data Analysis

1. Descriptive Statistics: Quantitatively describes or summarizes features of collected information using table, graphs and calculated using central tendency, dispersion, index number. Generalization of data is not possible, only provide worthy information regarding the nature of a specific group of individuals.
2. Inferential Statistics: Learn about the population through appropriate sample of data  using probability, estimation, different statistical test. It facilitates the generalization of data.

Definitions of Statistics

"Methods for making wise decisions on the face of uncertainty.” —Wallis and Roberts

 "The science of quantitative reasoning" — Stephen Senn

Singular Sense (Process)

In the singular sense, statistics refers to the "Methodology and principles of Statistical Analysis" or "Stages of Investigations".

For example: Investigation: Distribution of student's weights in DAV.

• First: Information collection (college records, or directly from student)
• Second: Presentation using table & graph (Arrangement of weights in various groups such as “50 Kg to 60 Kg”, “60 Kg to 70 Kg” )
• Third: Analysis (computing averages or some other measures)
• Fourth: Interpretation (either there is obesity or not)

All this involves a procedure and a method from the primary stage to the final stage of analysis and conclusions.

"Science of averages”, "Science of Counting", "Science of estimates and probability"

“Statistics may be defined as the collection, presentation, analysis, and interpretation of numerical data.” —Croxton and Cowden

Methodology of Statistical Analysis or Stages of Investigations

• 1^st: Collection of data from the field of inquiry using different methods like primary and secondary, census and sampling etc.
• 2^nd: Organization (classification) of data in a systematic manner according to date, time, place
• 3^rd: Presentation of data to make simple and attractive using table and graphs
• 3^rd: Analysis of data using various tools like average, co-relation, regression, dispersion, etc.
• 4^th: Interpretation of data to draw the conclusion, to make comparison, to forecast

Plural Sense (Feature)

In the plural sense, statistics refers to the "characteristics or features or quality" contained in it.

"All statistics are numerical statements of facts, but all facts numerically stated are not statistics".

“By statistics we mean aggregates of facts affected to a marked extent by multiplicity of causes, numerically expressed, enumerated or estimated according to reasonable standard of accuracy, collected in a systematic manner for a predetermined purpose, and placed in relation to each other.”—Horace Sacrist

Features of Statistics

1.     Aggregate of Facts: single and unconnected numerical figure has no meaning.

2.  Numerical Expression: Countable quantity only not the qualitative phenomena like honesty, goodness, ability, beauty etc. But if we assign numerical expression, it may be described as ‘statistics’.

3.  Systematic Collection: By applying suitable methods and procedure (rough and haphazard method is not desirable)

4.   Pre-determined purpose: Must have a well-defined purpose, specific aims, and objectives before we collect data

5.  Comparable: To make a valid comparison, the data should be homogeneous. For e. g., passed number of students of DAV and other College constitute statistics but weight of the students & their intelligence does not constitute statistics.

6.   Affected by Multiplicity of Causes: In social sciences, there may be combined effect of multiple causes. For example, deterioration of  academic achievement score of some students may not be only due to lack of interest in school subjects, but may also due to lack of motivation, effective teaching methods, attitude of the students on school subjects etc.

7.  Level of Accuracy: No any unique standard of accuracy, it differs from enquiry to enquiry or from purpose to purpose and availability of time and resources. For e. g. we can ignore ten deaths in a country but we cannot ignore even a single death in a family.

Scope or Importance of Statistics 

in Different Fields

In ancient times, statistics was regarded as the science of statecraft and was used to collect information related to military force, population, wealth, etc. But in modern times, the use of statistics is broad.

Statistics plays a vital role in every field of human activity and holds a central position in almost every field, including industry, commerce, trade, physics, chemistry, economics, mathematics, biology, botany, psychology, astronomy, etc., so the application of statistics is very wide. 

1. In Business: To take accurate managerial decision for businessman by analyzing risk & uncertainty, taste & preference of the consumer, quality of the product, location of business, marketing, financial resource management, production possibility, investment & output 
2. In Mathematics: The large number of statistical methods like probability, averages, dispersion, estimation etc. are used in mathematics. So, advancement in statistical techniques are the outcome of wide applications of mathematics. 
3. In Banking: Liquidity management, revenue forecasting, impact analysis of planning (IMPLAN), interest rate determination
4. In state management (Administration): Formulation of policy and plan or administrative decision of the government based on statistics. For e. g. in budget formulation (tax & subsidy), in fiscal policy formulation (economic policy, industrial policy, trade policy, wage policy)
5. In Accounting & Auditing: Accounting is not possible without exactness. But  for decision making process, so much precision is not essential. So, decision can be made on approximation using accounting results (balance sheet, CFS, P&L statement) as statistics. Auditing process may apply sampling techniques to draw conclusion.

Importance of Statistics in Economics

“Without an adequate understanding of the statistical methods, the investigators in the social sciences may be like the blind man groping in a dark room for a black cat that is not there."

Croxton & Cowden--

Statistical data and techniques of statistical analysis are immensely useful (irreplaceable tool) in economics. Economics uses statistical significance often to get necessary facts and figures.

Statistics and Economics are interrelated with each other. Almost every branch of Economics uses statistics i.e., consumption, production, distribution, exchange, public finance. All these Economic branches use statistics for comparison, presentation, interpretation, and so on.

1. Quantitative Expression of  Economic  Problems and activities: Poverty, unemployment, economic inequality, inflation, NIA, BOT (X&M), BOP, business cycle.

2. Comparisons: inter-sectoral comparison (agriculture, tourism, hydroelectricity), inter-temporal comparisons (over different plan periods of the rural and urban unemployment)

3.  Cause  and  Effect  Relationship: price & demand, GDP growth rate & poverty level, migration & imports

4.  Economic  Equilibrium: To  understand  the behavior  of  the producer  and  consumer  in  the  market by equilibrium condition.  For Producer – max. profit and for Consumer – max. satisfaction

5.  Developing  Economic  Theories: To understand, analyze and develop (Law of demand, law of supply, theory of production, theory of consumer behavior, quantity theory of money, theory of intl' trade)

6.  Forecasting: Statistical  data and tool like time series analysis, estimation and  probability  are  useful  to  forecast  the  changes  in economic variables. This information enables economists or government to formulate polices and suggestions to overcome the problem.

7.  Formulation of economic policies: Such as fiscal policies (budget), trade policy, industrial policy and monetary policies are determined by the help of statistics.

Functions of Statistics

1. Present Facts in Definite Form: Vague idea or data into definite and precise form with the help of statistical tools and techniques. For e. g. in Nepal, Population and poverty is increasing in faster rate (Idea) - 1.35% and 18.7 (Fact)

2. Condensation of Data: Simplifying complex data to simple to make them understandable with the help of graph, diagram or through an average etc. For e. g. general price level, PCI.

3. Comparisons: Data can be correlated as well as compared by using average, ratio, coefficients etc.

4. Formulation and Testing of Hypothesis and Develop New Theory: For e. g. (1) effect of imposing tax on the exports of tea on the consumption of tea in other countries, (2) whether hydroxychloroquine is effective in preventing COVID-19, (3) whether students have been benefited from the online classes during lock-down etc., can be tested by appropriate statistical tools.

5. Forecasting: To formulate suitable plan and policies for future, statistics provide tools to analyze trend, tendencies, pattern and nature of data. For e. g. demand forecasting, business expansion plan.

6. Draw Valid Inferences: With the measure of reliability about the population parameters from the sample data.

"The fundamental gospel of statistics is to push back the domain of ignorance, rule of thumb, arbitrary or premature decisions, traditions and dogmatism and to increase the domain in which decisions are made and principles are formulated on the basis of analyzed quantitative facts"

– Robert W. Burgess

Limitations of Statistics

"There are three kinds of lies: lies, damned lies, statistics" - Benjamin Disraeli 
"Statistics does not have any label for their quality". - Wilford I. King
Studying the boundaries of statistics helps to be aware of possible mistakes. 

(1) Ignores Qualitative Phenomenon: A qualitative phenomenon like empowerment, leadership, honesty, character, culture, love, care, friendship, emotional impact of racial discrimination, etc., can’t be expressed numerically or direct statistical analysis. However, that phenomenon can be expressed indirectly of numbers and analyzed in statistics. But translated poor qualitative data into quantitative form may not always valid and provide faulty results.

(2) Results are True Only on Average: “Statistics largely deals with averages and these averages may be made up of individual items radically different from each other.” —Wilford I. King
For e.g. (a) If the average grade of two sections of students is same, it doesn’t mean that all the students in section A got the same marks as all the students in section B.(b) If it is said that Nepalese are poor, then this statement points to a trend. This does not mean that there is no rich in Nepal.

(3) Liable to be Misused: “Statistics are like clay of which you can make a ‘God’ or a ‘Devil’ as you please.” - Wilford I. King (Chances of misuse)
“The science of statistics is a useful servant but only of great value to those who understand its proper use.” - Wilford I. King (Knowledge required)
Data may have been collected by inexperienced persons or they may have been dishonest or biased. The validity of certain statistical methods depends on the nature of data, the levels of measurement, the knowledge of the pertinent aspects of the situations and lastly, the assumptions made vis-a-vis the sample from which the data are secured. The researcher may be tempted to twist results to suit his fond conclusions or hypotheses by applying very sensitive tools. So, data must be used with a caution. Otherwise results may prove to be disastrous.

(4) To Many Methods to Study Problems: “It must not be assumed that statistics is the only method to use in research, neither should this method be considered the best attack for the problem.” – Frederick Croxten and Dudley Cowden

(5) Its Laws are Not Exact: Although the law of inertia of large numbers and law of statistical regularity are the fundamental laws of statistics, these laws do not give definite results like other scientific laws. Results from statistics may not be the final ‘truth’ because statistical analysis rely on approximation and probability but not in terms of certainty. For example, according to the law of statistics, if we roll a dice 60 times, we are likely to get the number 3 ten times, but this isn’t a guarantee.

Statistical Tools Used in Economic Analysis

"Statistics are the straw out of which I, like every other economist, have to make bricks." 

 Alfred Marshall, 1980–

1. Collection of data (Primary or secondary)

2. Editing

3. Classification and tabulation

4. Tools of presentation: Diagrams and Graphs (Of various types)

5. Measures of Central Tendency: Mean, Mode, Median, G.M, H.M to find average

6. Measures of Dispersion: Q.D, M.D., S.D. to find variability of an individual item from central value.

7. Skewness and Kurtosis – 

(a) Skewness: Skewness is asymmetry in statistical distribution, in which the curve appears distorted or skewed either to the left or to the right.

Skewed Distribution

Symmetrical Distribution: Mean = Median = Mode

Positive Skewed Distribution: Mean > Median > Mode

Negative Skewed Distribution: Mean <Median < Mode

(b) Kurtosis: Kurtosis is the degree of flatness or peaked-ness in the region of mode of a frequency curve. 

8. Correlation and regression:

(a) Correlation: Correlation (dependence) shows whether and how strongly pairs of variables are related (causal or not).

(b) Regression: Regression attempts to determine the strength and character of the relationship between one dependent variable and a series of other independent variables.

Simple linear regression: Y = a + bX + u

• Y = the variable that you are trying to predict (dependent variable).
• X = the variable that you are using to predict Y (independent variable).
• a = the intercept.
• b = the slope.
• u = the regression residual.

             Q^d_X = f (P_x)                        👉  Q^d_X = a - b P_X

9. Index numbers: An index number is the measure of change in a variable (or group of variables) over time. It is typically used in economics to measure trends in a wide variety of areas including: stock market prices, cost of living, industrial or agricultural production, and imports. Laspeyres, Paasche, Fishers' index number are popular methods to calculate index number.

10. Time Series Analysis: It deals with time series data or trend analysis. Time series data means that data is in a series of particular time periods or intervals.

11. Probability: In ordinary language the term probability refers to the chance of happening or not happening of an event. 'Chance' refers to uncertainty. In economics, it is used as risk analysis to predict the future value. 

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