Posted by emerjoytvale on August 13th, 2010

THE STUDY OF STATISTICS

WHY STATISTICS?

?         important in empirical studies

?         aids in decision making

?         helps to forecast or predict future outcomes

?         estimates unknown values

?         aids in making inferences, comparison or establishing relationship

?         summarizes data

DEFINITIONS

?         (plural sense) ? a set of numerical data or observations

Ex.

o   Vital statistics in a beauty pageant

o   Yearly income

o   Monthly expenses

?         (singular sense) ? a branch of science which deals with the collection, presentation, analysis and interpretation of data.

MAIN DIVISION OF STATISTICS

?         Descriptive Statistics ? pertains to the methods dealing with the collection, organization and analysis of a set of data without making conclusions, predictions or inferences about a larger set.

o   the main goal is simply to provide a description of a particular data set

o   the conclusions or the important characteristics apply only to the data on hand

?         Inferential Statistic ? pertains to the methods dealing with making inferences, estimation or prediction about a larger set of data using the information gathered from a subset of this larger set

o   the main goal is not merely to provide a description of a particular data set but also to make prediction and inferences based on the available information gathered

o   the conclusions or the important characteristics apply to a larger set from which the data on hand is only a subset

Collection of Data ? refers to the method of data gathering

Presentation of Data ? refers to the process of organizing data such as tabulation, presenting through the use of charts, graph or paragraphs

Analysis of Data ? refers to the methods of obtaining necessary, relevant and noteworthy information from the given data

Interpretation of Data ? refers to the tools of drawing of conclusions or inferences from the analyzed data

Examples:

Descriptive Statistics

?         A college dean wants to determine the average semestral enrolment in the past 5 school years.

?         An instructor wants to know the exact number of students who pass in his subject.

?         A school president wants to determine the number of student-dropouts for this current school year

Inferential Statistics

?         A college dean wants to forecast the average semestral enrolment based on the enrolment for the last 5 school years

?         An instructor would like to predict the number of students who will pass in his subject based on the number of failures last year

?         A school president would like to estimate the number of student dropouts next school year based on the current data.

DESCRIPTIVE STATISTICS

POPULATION AND SAMPLE

?         Population ? collection of all cases in which the researcher is interested in a statistical study

-          the entity that the researcher wished to understand

Examples:

?         All subjects of University of Bohol

?         All department heads in UB

?         Sample ? a portion or a subset of the population from which the information is gathered

-          a representation of the population

Examples:

?         All students of University of Bohol  coming from the rural areas

?         All department heads in UB who have finished Ph.D. Degree

?         Parameter ? a numerical characteristic of a population

-          denoted by small Greek letters

Examples:

?         ? - population mean

?         σ ? population standard deviation

?         Statistic ? a numerical characteristic of a sample

-          Denoted by lower case letters of the English alphabet

Examples:

?         X ? sample mean

?         SD ? sample standard deviation

TYPES OF DATA

?         Variable ? a characteristic or attribute of persons or objects which assumes different values or label

?         Measurement ? process of assigning the value or label of a particular variable for a particular experimental unit

?         Experimental unit ? the person or the object on which a variable is measured

?         Classification of Variables

?  Qualitative Variable ? yields categorical or qualitative responses

Examples:       Civil Status (Single, Married, Widow, etc.)

Religious Affiliation (Catholic, Protestant, etc.)

?  Quantitative Variable ? yields numerical responses representing an amount or quantity

Examples:       Height, Weight, no. of children

Types of Quantitative Variable

?  Discrete Variable ? assumes finite or countable infinite values such as 1,2,3,?

Example:         no. of children (0,1,2,3,?)

no. of student-dropouts

?  Continuous Variable ? cannot take on finite values but the values are related/associated with points on an interval of the real line

Examples:       Height (5?4?)

Weight (130.42 kilos)

Temperature (32.5?C)

Levels of Measurement

?  NOMINAL LEVEL

-          Crudest form of measurement

-          Numbers or symbols are used for the purpose of categorizing subjects into groups

-          The categories are mutually exclusive, that is being in one category automatically excludes inclusion in another

-          The categories are exhaustive, that is all possible categories of a variable should be included

Examples:       Sex:                             1 ? Male                      0 ? Female

Faculty Tenure:           1 ? Tenured                 0 ? Non-Tenured

?  ORDINAL LEVEL

-          Improvement of nominal level

-          Order/rank the data in a somewhat ?bottom to top? or ?low to high? manner

Examples:       Class Standing (Excellent, Good, Poor)

Teacher Evaluation     1 ? Poor

2 ? Fair

3 ? Good

4 ? Very Good

?  INTERVAL LEVEL

-          Possesses the properties of the nominal and ordinal levels

-          Distances between any two numbers on the scale are known

-          Does not have a stable starting point (an absolute zero)

Example: Consider the IQ scores of four students

70, 140, 75 and 145

Here, we can say that the difference between 70 and 140 is the same as the differences between 75 and 145 but we cannot claim that the second student is twice as intelligent as the first.

?  RATIO LEVEL

-          Possesses all the properties of the nominal, ordinal and interval levels and in addition, this has or absolute zero point

-          We can classify it, place it in proper order

-          We can also compare magnitudes

Examples:             Age, Income, Exam Scores

SUMMARY CHARACTERISTICS OF LEVELS

OF MEASUREMENT

Levels of Measurement           Classify           Order               Equal Limits    Absolute Zero

NOMINAL                             Yes                  No                   No                   No

ORDINAL                             Yes                  Yes                  No                   No

INTERVAL                            Yes                  Yes                  Yes                  No

RATIO                                    Yes                  Yes                  Yes                  Yes

?         Other Classification of Data

?  Raw Data                    - data in their original form and structure

?  Grouped Data             - data placed in tabular form

?  Primary Data              - measured and gathered by the researcher that published it

?  Secondary Data          - any republication of data by another researcher or agency

METHODS OF DATA COLLECTION

?         Observation Method

-          Data can be obtained by observing the behavior of persons or objects but only at a particular time of occurrence

-          The data obtained is called an observational data

?         Experimental Method

-          Especially useful when one wants to collect data for cause and effects studies

-          There is actual human interference with the conditions or situations that can affect the variable under study

-          Prevalent in scientific researches

?         Use of Existing Studies

-          CHED or DECS enrollment data

-          Census Data

?         Registration Method

-          Respondents provide the necessary information in observance and compliance with existing laws

-          Our registration, birth registration, student registration, voter?s registration

?         Survey Method

-          The desired information is obtained through asking questions

Common Forms of Survey Method

?  Personal Interview Method

-          There is a person-to-person contact between the interviewer and the interviewee

-          Considered as one of the most effective methods of data collection because accurate and precise information can be directly obtained and verified from the respondents

-          Higher response rate

-          Can be administered to the respondents one at a time

?  Questionnaire Method

-          Considered the easiest method of data collection

-          Utilizes an instrument which is the questionnaire as a tool

-          Lower response rate

-          Can be administered to a large number of respondents simultaneously

General Classification of Data Collection

?  Census or Complete Enumeration

-          Method of gathering data from every unit in the population

-          Not always possible because of money, time and effort

?  Survey Sampling

-          Method of gathering data from every unit in the selected sample

-          Reduces cost, greater speed, scope and accuracy

PROBABILITY AND NON-PROBABILITY SAMPLING

?         Probability Sampling ? sampling procedure in which every element in the population has known non-zero chance of being included in the sample

Common Methods of Probability Sampling

?         Simple Random Sampling (SRS)

-          Sampling procedure in which every element in the population has an equal chance of being included in the sample

-          Select n units out of N units in the population

-          The selection is through lottery or the use of the table of random numbers

?         Stratified Random Sampling

-          The