Basic Concepts of Statistics

Statistics (etymology)

derived from the Latin word “status” meaning state

Statistics (Plural Sense)

it is defined as any set of numerical data

Statistics (Singular Sense)

It is defined as a branch of science that deals with the collection, presentation, analysis, and interpretation of data

Data

facts or figures from which conclusions may be drawn

Data Set

collection of facts and figures or data

Variable

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

Elements/Units

entities on which data are collected

Observation

set of measurements collected for a particular element study

Measurement

The process of determining the value or label of a particular variable for a particular experimental unit

Descriptive Statistics

These are the numerical, tabular, and graphical methods used to summarize data.

Inferential Statistics

These are methods for using sample data to make general conclusions (inferences) about populations.

Qualitative Variable

Outcomes of the variables are expressed non- numerically or categorically

Quantitative Variable

Outcomes of the variables are expressed numerically that are meaningful or indicate some sort of amount

Discrete Quantitative

• a variable which can assume finite, or at most

, countably infinite number of values

• usually measured by counting

Continuous Quantitative

• a variable which can assume infinitely many

values corresponding to a line interval

• gives rise to measurement

• answers the question “how much”

Nominal

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

Ordinal

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

Interval

• 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

Ratio

• 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

Population

It is the entire groups of individuals or subjects.

Sample

It is selected to represent the population in a research study.

Parameter

Any numerical measures that describe the population.

Statistic

Any numerical measures that describe the sample.

Subjective Data

• means “from someone’s point of view”

• commonly about perceptions, beliefs, feelings, and opinions

Objective Data

• measured or counted

• information is about publicly observable events, knowledge, or facts

Interview

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

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

Questionnaire

• data is 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

Experimental

• used when the objective is to determine the cause and effect

relationship of certain phenomena under controlled conditions

• experiment = an operation where there is actual human interference with the condition that can affect the variable under study

Observation

• The researcher observes the behavior of persons and their outcomes

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

Registration

This method of collecting data is enforced by certain laws information is kept systematized and made available to all because of the requirement of the law

Census/Complete Enumeration

process of gathering information from every unit of the population

Sampling/Survey Sampling

• process of obtaining a part or subset of the population

• the main reason sampling is used is that the population

is too large

Probability sampling

The process of selecting the sample from a population based on the principle of randomization or chance. The idea of randomization is to avoid selection bias so that reliable estimates can be produced, and we can make inferences about the population.

Random

Each person within the sampling frame has an equal chance of being selected.

Non-probability sampling

The process of selecting the sample from a population arbitrarily. Every unit of the population does not have the same probability of being included in the sample.

Simple Random Sampling

This involves selecting anybody from the sampling frame

entirely at random.

SRS with Replacement

A chosen element is always replaced before the next selection is made

SRS without Replacement

A chosen element is not replaced before the next selection is made

Systematic Sampling

Systematic sampling with a “random start” is a method of selecting a sample by taking every kth unit from an ordered population, where the first unit being selected at random

Stratified Random Sampling

The population is divided into two or more non-overlapping groups called strata, according to some criterion such as geographic location, grade level, age, or income.

Proportional allocation

The percentage of these sample taken from each stratum is

proportionate to the percentage that each stratum is within the

population.

Equal Allocation

Each stratum receives the same number of samples.

Cluster Sampling

The entire population is divided into pre-existing segments called clusters. Then the clusters will be randomly selected using simple random or systematic sampling, and every member of each selected cluster will be included in the sample.

Multi-stage Sampling

- This technique is essentially the process of taking random samples of preceding random samples.

- Complex form of cluster sampling in which two or more levels of units are embedded one in the other.

Purposive Sampling

Sampling with a “purpose” in mind.

Convenience Sampling

- Sample elements are selected for the convenience of the

researcher.

Quota Sampling

Sample elements are selected until the quota controls are satisfied.

Snowball sampling

Survey subjects are selected based on referral from other survey respondents.

Raw data

are collected data which have not been arranged numerically.

Array

Is the arrangement of data from highest to lowest or from lowest to highest. This arrangement, however, is not advisable because it gives little information as compared to the work entailed in its construction.

Textual Presentation

Collected data may be organized and presented in a narrative or ________form. It is the simplest method of presenting data.

Tabular Presentation

• _________ 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.

Heading

consists of table number, title, and

headnote

Caption

contains the column heads which describe the data

Stub

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

Field

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

Graphical method

is the presentation of data in the form of a graph or diagram.

Bar graph

uses bars to compare data cross categories of a variable.

Line graph

use to display the trend or pattern of values of a variable over

time wherein the data points are plotted or connected by a line in a “dot-to-dot” fashion

Pie Chart

use to show how part of the data compares in size to the whole circle. The circle is divided proportionally to the relative frequency (percentages) and portion of the circles are allocated to the different groups or categories.

Pictograph

is a way of showing data using images.