Basic Concepts in Statistics

statistics derived from the Latin word _____ meaning state

In _____ sense, statistics is defined as any set of numerical data (e.g. vital statistics, monthly sales)

In ______ sense, statistics is defined as a branch of science that deals with the collection, presentation, analysis, and interpretation of data

• Concerned with describing a set of data without drawing conclusions or inferences from it

• Includes collecting, presenting, and analyzing of data

• Utilizes sample data to make inferences and draw conclusions about a larger set of data

• Includes interpreting, making inferences, hypothesis testing, determining relationships, and making predictions

facts or figures from which conclusions may be drawn

collection of facts and figures or data

entities on which data are collected

a characteristic or attribute of elements which can assume different values or labels under statistical study

set of measurements collected for a particular element

outcomes of the variables expressed nonnumerically or categorically

• example: name, gender, eye color, religion, etc.

outcomes are expressed numerically that are meaningful or indicate some sort of amount

• example: age, allowance, number of students, height, etc.

a variable which can assume finite, or at most , countably infinite number of values

• usually measured by counting

• answers the question “how many”

• example: # of students, # of children

• a variable which can assume infinitely many values corresponding to a line interval

• example: weight, allowance, height

• gives rise to measurement

• answers the question “how much”

• classificatory scale

• weakest level of measurement where numbers or symbols are used simply for labeling or categorizing subjects into different groups

• example: sex (male/female) marital status (single/married) favorite color (red/blue/black)

• classificatory with ordering scale

• numbers assigned to categories of any variable may be ranked or ordered • example:

• educational attainment (elementary/HS/college/MS/PhD)

• size of shirt (XS/S/M/L/XL)

• level of satisfaction (excellent/good/bad)

has the properties of the nominal and ordinal levels

• in addition, the distances between any two numbers on the scale are of known sizes

• has arbitrary zero

• example: - temperature - IQ scores

• highest level of measurement

• has the properties of the nominal, ordinal, and interval levels

• anything that is countable or measurable

• has absolute zero or true zero

• example:

• height of plant

• number of students in a class

• length of time studying

• acquired directly from the original source of information

• data that are measured or gathered by the researcher themselves

• data taken from published or unpublished data which have been previously gathered by others

• means “from someone’s point of view”

• commonly about perceptions, beliefs, feelings, and opinions

• fact-based, measurable, countable, and observable

• there is a person-to-person contact or exchange of information between the interviewer and interviewee

• more appropriate for obtaining complex emotional-laden topics probing sentiments underlying an expressed opinion

• provides consistent and more precise information since the interviewee may give clarifications

• time consuming and has limited field of coverage

• data are collected by means of written responses based on a list of questions which are relevant to the problems of the study

• inexpensive and can cover a wide area in a shorter period of time

• high possibility of incomplete response or may not return the questionnaire, especially if it is mailed

• used when the objective is to determine the cause-and-effect relationship of certain phenomena under controlled conditions

• if properly designed and executed, experiments will reveal a good deal of accuracy

• the researcher observes the behavior of persons and their outcomes • potential bias caused by the interviewing process is reduced and eliminated in this method

• potential bias caused by the interviewing process is reduced and eliminated in this method

• this method of collecting data is enforced by certain laws such as registration of births, deaths, licenses, etc.

information are kept systematized and made available to all because of the requirement of the law

entire group of observations or elements where inferences and conclusions are made

a numerical characteristic of the population

subset of the entire group of observations or elements where data is collected

a numerical characteristic of the sample

process of gathering information from every unit or all the units of the population

process of obtaining a part or subset of the population

the elements in the population do not have equal chances of being selected as a sample

elements of the population are taken depending to a large extent on the personal feelings or purpose of the researcher and without regard for some chance mechanism for choosing an element

each unit in the population has a known, non-zero probability of selection, and have equal chances of being selected as a sample

uses some chance mechanism

a listing of all individual units in the population, is required in the execution of probability sampling methods

Method of selecting n units out of N units in the population where all elements in the population have an equal chance of being included in the sample

This sampling method is suitable when the population being studied is homogeneous or have the same characteristics

This is usually done by draw lots, use of table of random numbers, or random number generator in calculators or softwares

It is done if the population is heterogeneous and can be subdivided into non-overlapping homogeneous subpopulation called strata

A method of sampling where a sample of distinct groups, or clusters, of elements is randomly selected and then a census or all elements in the selected clusters is taken

Clusters are non-overlapping subpopulations which together comprise the entire population

• For example, a household is a cluster of individuals living together.

Clusters are preferably formed with heterogeneous, rather than homogeneous elements so that each cluster will be a typical population

are collected data which have not been arranged numerically

When collected data are arranged numerically according to magnitude, those data are termed as ____.

• Lowest to highest/ highest to lowest

• Data are put into an array to make data comprehensible.

In this method, data are incorporated to a paragraph of texts

It is the simplest and most appropriate approach when only a few numbers are to be presented

Only gives emphasis to significant figures and comparisons.

Tables are designed to summarize facts revealed by enquiry and to present them in such a way that all the important factors contained in the data under review are displayed.

This method takes the form of arranging statistical data in columns and rows

consists of table number, title, and headnote

contains the column heads which describe the data

the portion of the table comprising the first column on the left

main part of the table that contains the substance or figures of the data

A graph or chart is a device showing numerical values or relationships in pictorial form

In a graph, the main features and implications of a body of data can be grasped at a glance

It can simplify a concept that would otherwise have been expressed in so many words.

consists of a series of rectangular bars where the length of the bar represents the quantity or frequency for each category

the height of the bars represent the quantity/frequency

useful in showing how a total quantity is distributed among a group of categories

the pieces of the pie represent the proportions/percentages of the total that fall in each category

graphical representation of data especially useful for showing trends over a period of time

way of representing statistical data using symbolic figures to match the frequencies of different kinds of data

each symbol represents a definite and uniform value

is a value at the center or middle of a data set, that is, the value where the data tend to cluster