Advance Research Methods Vishnu Parmar Assistant Professor, IBA University of Sindh, Jamshoro

WHAT IS STATISTICS? Definition Statistics is a group of methods used to collect, analyze, present, and interpret data and to make decisions.

What is statistics? a branch of mathematics that provides techniques to analyze whether or not your data is significant (meaningful) Statistical applications are based on probability statements Nothing is “proved” with statistics Statistics are reported Statistics report the probability that similar results would occur if you repeated the experiment 3

Why Statistics ?   "The objective of a national statistical system is to provide relevant, comprehensive, accurate and objective statistical information. Generally, statistics are valuable for monitoring the country’s economic and social conditions, the planning and evaluation of government and private sector programmes and investment, policy debates and advocacy, and the creation and maintenance of an informed public." CTO/CRSTDP Statistics Workshop 2005 – McHale Andrew

Why Statistics ? Cont’d Essential in: Official decision-making, policy formulation Policy Analysis & Research Academic, business, industrial & other research Business planning & CRM Citizens/residents being informed about performance of governments

Why Statistics ? Facilitate comparison across countries/regions Benchmarking ‘Best Practices’ Evaluation of performance However, good statistics must be collected in accordance with agreed international standards using appropriate methods for data collection, processing and dissemination.

TYPES OF STATISTICS Definition Descriptive Statistics consists of methods for organizing, displaying, and describing data by using tables, graphs, and summary measures.

TYPES OF STATISTICS Definition Inferential Statistics consists of methods that use sample results to help make decisions or predictions about a population.

POPULATION VERSUS SAMPLE Definition A population consists of all elements – individuals, items, or objects – whose characteristics are being studied. The population that is being studied is also called the target population.

POPULATION VERSUS SAMPLE cont. Definition A portion of the population selected for study is referred to as a sample.

Figure 1.1 Population and sample.

POPULATION VERSUS SAMPLE cont. Definition A survey that includes every number of the population is called a census. The technique of collecting information from a portion of the population is called a sample survey.

POPULATION VERSUS SAMPLE cont. Definition A sample that represents the characteristics of the population as closely as possible is called a representative sample.

POPULATION VERSUS SAMPLE cont. Definition A sample drawn in such a way that each element of the population has a chance of being selected is called a random sample. If the chance of being selected is the same for each element of the population, it is called a simple random sample.

TYPES OF VARIABLES Quantitative Variables Discrete Variables Continuous Variables Qualitative or Categorical Variables

Quantitative Variables Definition A variable that can be measured numerically is called a quantitative variable. The data collected on a quantitative variable are called quantitative data.

Quantitative Variables cont. Definition A variable whose values are countable is called a discrete variable. In other words, a discrete variable can assume only certain values with no intermediate values. (e.g, 100 students in section A, or 2 or 3 bedrooms in an apartment, there won’t be 2.5. in an home)

Quantitative Variables cont. Definition A variable that can assume any numerical value over a certain interval or intervals is called a continuous variable. (e.g, 1.5kg bag of rice, or flight is late for 2 hrs and 30 min.)

Qualitative or Categorical Variables Definition A variable that cannot assume a numerical value but can be classified into two or more nonnumeric categories is called a qualitative or categorical variable. The data collected on such a variable are called qualitative data.

Qualitative, attitude, or Categorical Variables, cont… Qualitative data is often summarized in bar graphs and charts E.g, % of minority population in an area What % of population has blue eyes? What % of women is highly educated?

Figure 1.2 Types of variables.

Levels of Measurement Measurement is the process of assigning numbers to quantities. The process is so familiar that perhaps we often overlook its fundamental characteristics.

Levels (or Scales) of Measurement Measurement is a process whereby values (scores) are assigned to properties of people, places, things, or events. You might rate preferences of perfumes or TV show. You may collect data about marital status or gender, or count the number of times people report feeling depressed. These different measures all have different properties, which in turn, lead to different sorts of appropriate Statistical tests. The level of measurement refers to the amount of information the measurement procedure can convey about the actual quantity of the variable present and about the differences individuals with different scores.

Properties of Numbers and Attributes Nominal (Same-Different). My income is the same as yours or different. Ordinal (Ordering). If our incomes are different, mine is greater or less than yours. Interval (Relative Differences). The difference between my income and yours might be, say, twice as great as the different between my income and the governor’s. Ratio (Ratios and Zero Point). My brother’s income is about 10 times what mine is.

Levels (or Scales) of Measurement 1. Nominal scale: based on categories or names, and tells us nothing about magnitude. 2. Ordinal scale: a rank-order scale that reflects differences in magnitude, but the intervals between values may not be equal and there is no absolute zero. 3. Interval scale: also measures magnitude and has equal intervals between values, but the scale has no absolute zero. 4. Ratio scale: Has equal intervals between all its values and an absolute zero point.

Nominal Scale The nominal scale is the most basic. It seeks to name things, to categorize or classify them. Nominal scales satisfy only the property of identity. Examples are gender, job title, religion, marital status, etc. Numbers can also be used to identify or categorize, such as the numbers of players on the football team. The numbers themselves do not indicate magnitude, and it would make no sense to try to add or multiply the numbers on football jerseys.

Properties of Nominal Data Data categories are mutually exclusive, so an object belongs to only category Data Category have logical order

Mutually Exclusive and Exhaustive Mutually Exclusive means an individual, object, or measurement is included in only category Exhaustive: Each individual object or measurement must appear in a category

Ordinal Scale The ordinal scale of measurement deals with order or ranking. Common examples are the grades of A, B, C, D, and F; the “top 20” ratings for sports teams; the “top 40” ratings for music. While an ordinal scale allows us to know which category is larger, higher, or better, it does not allow us to say anything about the interval between the rankings, or how much better one team or song is than another. The only mathematical operation allowed on ordinal data is ranking.

Properties of Ordinal Level Data The data categories are mutually exclusive and exhaustive Data categories are ranked or ordered according to the particular trait they possess

Interval Scale The interval scale of measurement tells us about the rank order and about the intervals between the numbers. On an interval scale, a difference of 1 point always means the same thing. Temperatures measured with either the Celsius or Fahrenheit scales provide scores on an interval scale. However, these thermometers do not have true zero points: a temperature of 0° does not mean the absence of heat. The mathematical operations allowed are addition and subtraction, but never multiplication or division. 80° is not twice as hot as 40°

Properties of Interval Level Data Data categories are mutually exclusive and exhaustive Data categories are scaled according to the amount of the characteristics they possess Equal difference in the characteristic are represented by the equal differences in the numbers assigned to the categories

Ratio Level It is highest level of measurement It has all characteristics of interval level but in addition the zero (o) point is meaningful, and the ratio between two numbers is meaningful E.g, wages, Units of Production, Weight, and Height

Properties of Ratio Level Data Data Categories are mutually exclusive and exhaustive Data Categories are scaled according to the amount of the characteristics they possess Equal difference in the characteristic are represented by equal differences in the numbers assigned to the categories The point 0 reflects the absence of the characteristic