Sampling

Introduction to Statistics Definition of Statistics: 1. Statistics can be defined as the collection presentation and interpretation of numerical data.- Croxton and Crowed. 2. Statistics are numerical statement of facts in any department of enquiry placed interrelation to each other.- Bouly. 3. Statistics are measurement, enumerations or estimates of natural or social phenomena systematically arrangement to exhibit their inner relation.- Conner. 4. By Statistics we mean quantitative data affected to a marked extend by a multiplicity of causes. – Yule and Kendal. 5. The science of Statistics is essentially a branch of applied mathematics and can be regarded as a mathematics applied to observation data.- R.A fisher. Statistics is concerned with scientific methods for collecting, organizing , summarizing, presenting and analyzing sample data as drawing valid conclusions about population characteristics and making reasonable decisions on the basis of such analysis. Types 1.Descriptive Statistics: The descriptive statistics gives a description about a sample.. Inferential Statistics: the inferential statistics predicts and infers about a much larger data or population. There are two major divisions of inferential statistics: a) Confidence Interval: The confidence interval is represented in the form of an interval that provides a range for the parameter of given population. b) Hypothesis Test: Hypothesis tests are also known as tests of significance which tests some claim for the population by analyzing sample

Scope and importance of Statistics: 1. Statistics and planning: Statistics in indispensable into planning in the modern age which is termed as “the age of planning”. Almost all over the world the govt. are re-storing to planning for economic development. 2. Statistics and economics: Statistical data and techniques of statistical analysis have to immensely useful involving economical problem. Such as wages, price, time series analysis, demand analysis. 3. Statistics and business: Statistics is an irresponsible tool of production control. Business executive are relying more and more on statistical techniques for studying the much and desire of the valued customers. 4. Statistics and industry: In industry statistics is widely used inequality control. In production engineering to find out whether the product is confirming to the specifications or not. Statistical tools, such as inspection plan, control chart etc.

5. Statistics and mathematics: Statistics are intimately related recent advancements in statistical technique are the outcome of wide applications of mathematics. 6. Statistics and modern science: In medical science the statistical tools for collection, presentation and analysis of observed facts relating to causes and incidence of dieses and the result of application various drugs and medicine are of great importance. 7. Statistics, psychology and education: In education and physiology statistics has found wide application such as, determining or to determine the reliability and validity to a test, factor analysis etc. 8. Statistics and war: In war the theory of decision function can be a great assistance to the military and personal to plan “maximum destruction with minimum effort.”

Statistics in business and management: 1. Marketing: Statistical analysis are frequently used in providing information for making decision in the field of marketing it is necessary first to find out what can be sold and the to evolve suitable strategy, so that the goods which to the ultimate consumer. A skill full analysis of data on production purchasing power, man power, habits of compotators, habits of consumer, transportation cost should be consider to take any attempt to establish a new market. 2. Production: In the field of production statistical data and method play a very important role. The decision about what to produce? How to produce? When to produce? For whom to produce is based largely on statistical analysis. 3. Finance: The financial organization discharging their finance function effectively depend very heavily on statistical analysis of peat and tigers. 3. Banking: Banking institute have found if increasingly to establish research department within their organization for the purpose of gathering and analysis information, not only regarding their own business but also regarding general economic situation and every segment of business in which they may have interest. 4. Investment: Statistics greatly assists investors in making clear and valued judgment in his investment decision in selecting securities which are safe and have the best prospects of yielding a good income. 5. Purchase: the purchase department in discharging their function makes use of statistical data to frame suitable purchase policies such as what to buy? What quantity to buy? What time to buy? Where to buy? Whom to buy? 6. Accounting: statistical data are also employer in accounting particularly in auditing function, the technique of sampling and destination is frequently used.

7. Control: the management control process combines statistical and accounting method in making the overall budget for the coming year including sales, materials, labor and other costs and net profits and capital requirement. Census. A census is a study that obtains data from every member of a population. In most studies, a census is not practical, because of the cost and/or time required. Sample survey. A sample survey is a study that obtains data from a subset of a population, in order to estimate population attributes. Experiment . An experiment is a controlled study in which the researcher attempts to understand causeand-effect relationships. The study is "controlled" in the sense that the researcher controls (1) how subjects are assigned to groups and (2) which treatments each group receives. In the analysis phase, the researcher compares group scores on some dependent variable. Based on the analysis, the researcher draws a conclusion about whether the treatment (independent variable) had a causal effect on the dependent variable. Observational study. Like experiments, observational studies attempt to understand cause-and-effect relationships. However, unlike experiments, the researcher is not able to control (1) how subjects are assigned to groups and/or (2) which treatments each group receives.

Sampling is a statistical procedure that is concerned with the selection of the individual observation; it helps us to make statistical inferences about the population

Suppose that we have a population of 86 college students and want to form a simple random sample of size eleven to survey about some issues on campus. We begin by assigning numbers to each of our students. Since there is a total of 86 students, and 86 is a two digit number, every individual in the population is assigned a two digit number beginning 01, 02, 03, .. . 83, 84, 85. A simple random sample (SRS) of size n consists of n individuals from the population chosen in such a way

that every set of n individuals has an equal chance to be the sample actually selected Here, population refers to the collection of people, animals, locations, etc. that the study is focusing on.

USE OF THE TABLE

We will use a table of random numbers to determine which of the 85 students should be chosen in our sample. We blindly start at any place in our table and write the random digits in groups of two. Beginning at the fifth digit of the first line we have: 23 44 92 72 75 19 82 88 29 39 81 82 88 The first eleven numbers that are in the range from 01 to 85 are selected from the list. The numbers below that are in bold print correspond to this: 23 44 92 72 75 19 82 88 29 39 81 82 88 At this point, there are a few things to note about this particular example of the process of selecting a simple random sample. The number 92 was omitted because this number is greater than the total number of students in our population. We omit the final two numbers in the list, 82 and 88. This is because we have already included these two numbers in our sample. We only have ten individuals

in our sample. To obtain another subject it is necessary to continue to the next row of the table. This line begins: 29 39 81 82 86 04 The numbers 29, 39, 81 and 82 have already been included in our sample. So we see that the first two-digit number that fits in our range and does not repeat a number that has already been selected for the sample is 86.

CONCLUSION OF THE PROBLEM The final step is to contact students who have been identified with the following numbers: 23, 44, 72, 75, 19, 82, 88, 29, 39, 81, 86 A well-constructed survey can be administered to this group of students and the results tabulated. Stratified sampling. With stratified sampling, the population is divided into groups, based on some characteristic. Then, within each group, a probability sample (often a simple random sample) is selected. In stratified sampling, the groups are called strata. As a example, suppose we conduct a national survey. We might divide the population into groups or strata, based on geography - north, east, south, and west. Then, within each stratum, we might randomly select survey respondents. Cluster sampling. With cluster sampling, every member of the population is assigned to one, and only one, group. Each group is called a cluster. A sample of clusters is chosen, using a probability method (often simple random sampling). Only individuals within sampled clusters are surveyed. Note the difference between cluster sampling and stratified sampling. With stratified sampling, the sample includes elements from each stratum. With cluster sampling, in contrast, the sample includes elements only from sampled clusters. Multistage sampling. With multistage sampling, we select a sample by using combinations of different sampling methods. For example, in Stage 1, we might use cluster sampling to choose clusters from a population. Then, in Stage 2, we might use simple random sampling to select a subset of elements from each chosen cluster for the final sample. Systematic random sampling. With systematic random sampling, we create a list of every member of the population. From the list, we randomly select the first sample element from the first k elements on the population list. Thereafter, we select every kth element on the list. This method is different from simple random sampling since every possible sample of nelements is not equally likely. Primary data used in research originally obtained through the direct efforts of

the researcher through surveys, interviews and direct observation. Primary data is more costly to obtain than secondary data Secondary data is the data that have been already collected by and readily available from other sources. Such data are cheaper and more quickly obtainable than the primary data and also may be available when primary data can not be obtained at all.

An estimate is a value that is inferred for a population based on data collected from a sample of units from that population. Estimation is a technique that systematically adjusts the sample data to determine an estimated value for the population. For example, if our sample data shows that 51% of the sample are female, then the population value will be estimated to be 51% (as estimation is based on the assumption that the sampleis representative of the population). An estimate is not a guess, it is a value based on sampled data which has been adjusted using statistical estimation procedures.

A variable is any characteristics, number, or quantity that can be measured or counted. A variable may also be called a data item. Age, sex, business income and expenses, country of birth, capital expenditure, class grades, eye color and vehicle type are examples of variables.

Quantitative Variables - Variables whose values result from counting or measuring something. Examples: height, weight, time in the 100 yard dash, number of items sold to a shopper Qualitative Variables - Variables that are not measurement variables. Their values do not result from measuring or counting. Examples: hair color, religion, political party, profession. Discrete Variable A discrete variable does not admit intermediate values between two specific numbers. It is represented by whole integer values. For example: The number of brothers of 5 friends: 2, 1, 0, 1, 3.

Examples Discrete Variable Number of printing mistakes in a book. Number of road accidents in Dhaka City. Number of siblings of an individual. Continuous Variable A continuous variable can take values between two numbers. For example: The height of 5 friends measured in meters : 1.73, 1.82, 1.77, 1.69, 1.75.

Continuous Variable Height of a person Age of a person Profit earned by the company.

Nominal Ordinal Interval Ratio: Examples 1. Nominal Nominal: nominal is from the Latin normal’s, which means “pertaining to names”. It’s another name for a category. Examples: Gender: Male, Female, Other. Hair Color: Brown, Black, Blonde, Red, Other. Type of living accommodation: House, Apartment, Trailer, Other. Genotype: Bb, bb, BB, bB. Religious preference: Buddhist, Mormon, Muslim, Jewish, Christian, Other. 2. Ordinal The ordinal scale classifies according to rank. Ordinal: means in order. Includes “First,” “second” and “ninety ninth.” Examples: High school class ranking: 1st, 9th, 87th… Socioeconomic status: poor, middle class, rich. The Liker Scale: strongly disagree, disagree, neutral, agree, strongly agree. Level of Agreement: yes, maybe, no. Time of Day: dawn, morning, noon, afternoon, evening, night. Political Orientation: left, center, right.

3. Interval Interval: has values of equal intervals that mean something. For example, a thermometer might have intervals of ten degrees.

Examples: Celsius Temperature. Fahrenheit Temperature. IQ (intelligence scale). SAT scores. Time on a clock with hands.

4. Ratio Weight is measured on the ratio scale. Ratio: exactly the same as the interval scale except that the zero on the scale means: does not exist. For example, a weight of zero doesn’t exist; an age of zero doesn’t exist. On the other hand, temperature is not a ratio scale, because zero exists (i.e. zero on the Celsius scale is just the freezing point; it doesn’t mean that water ceases to exist).

Examples: Age.* Weight. Height. Sales Figures. Ruler measurements. Income earned in a week. Years of education. Number of children A parameter is a characteristic of a population. For example, say we want to know the average income of the subscribers to a particular magazine—a parameter of a population.

A statistic is a characteristic of a sample. You draw a random sample of 100 subscribers and determine that their mean income is $27,500 (a statistic)

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Comparison Chart BASIS FOR STATISTICS COMPARISON

PARAMETER

Meaning

Statistic is a measure which describes a fraction of population.

Parameter refers to a measure which describes population.

Numerical value

Variable and Known

Fixed and Unknown

Statistical Notation

x̄ = Sample Mean

μ = Population Mean

s = Sample Standard Deviation

σ = Population Standard Deviation

p̂ = Sample Proportion

P = Population Proportion

x = Data Elements

X = Data Elements

n = Size of sample

N = Size of Population

r = Correlation coefficient

ρ = Correlation coefficient