basic concept and terms

8/9/2019 Basic Concept and Terms

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PROBABILITY ANDSTATISTICS

Origin and History

Basic Concepts and TermsLevels of Measurement

Data Collection

Sampling


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ORIGIN

The original idea of Statistics" was the collection ofinformation about and for the "state". The wordstatistics derives directly, not from any classicalGreek or Latin roots, but from the Italian word for

state.

Probability has much longer history. Probability isderived from the verb to probe meaning to "find out"what is not too easily accessible or understandable.The word "proof" has the same origin that providesnecessary details to understand what is claimed to betrue.

http://www.statisticalforecasting.com/origin-statistics-probability.php


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ORIGIN

Probability originated from the study of games ofchance and gambling during the 16th century.Probability theory was a branch of mathematicsstudied by Blaise Pascal and Pierre de Fermat inthe seventeenth century. Currently in 21st

century, probabilistic modeling is used to controlthe flow of traffic through a highway system, atelephone interchange, or a computer processor;

find the genetic makeup of individuals orpopulations; quality control; insurance;investment; and other sectors of business andindustry.http://www.statisticalforecasting.com/origin-statistics-probability.php


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TIMELINE

1654 -- Pascal -- mathematics of probability, incorrespondence with Fermat

1662 -- William Petty and John Graunt -- firstdemographic studies

1713 -- Jakob Bernoulli -- Ars Conjectandi

1733 -- DeMoivre -- Approximatio; law of error(similar to standard deviation)

1763 -- Rev. Bayes -- An essay towards solving a

problem in the Doctrine of Chances,foundation for "Bayesian statistics"

1805 -- A-M Legendre -- least square method

1809 -- C. F. Gauss -- Theoria Motus CorporumCoelestium


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TIMELINE

1812 -- P. S. Laplace -- Thorie analytique desprobabilits

1834 -- Statistical Society of London established

1853 -- Adolphe Quetelet -- organized firstinternational statistics conference; appliedstatistics to biology; described the bell-shapedcurve

1877 -- F. Galton -- regression to the mean

1888 -- F. Galton -- correlation 1889 -- F. Galton -- Natural Inheritance

1900 -- Karl Pearson -- chi square; appliedcorrelation to natural selection


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TIMELINE

1904 -- Spearman -- rank (non-parametric)

correlation coefficient

1908 -- "Student" (W. S. Gossett) -- The probable

error of the mean; the t-test 1919 -- R. A. Fisher -- ANOVA; evolutionary

biology

1930's -- Jerzy Neyman and Egon Pearson (son of

Karl Pearson) -- type II errors, power of a test,confidence intervals


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NATURE OF STATISTICS

1. DESCRIPTIVE STATISTICS

Descriptive statistics are used to describe the basic

features of the data in a study. They provide simple

summaries about the sample and the measures.Together with simple graphics analysis, they form

the basis of virtually every quantitative analysis of

data. With descriptive statistics you are simply

describing what is or what the data shows.

http://www.socialresearchmethods.net/kb/statdesc.php


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NATURE OF STATISTICS

2. INFERENTIAL STATISTICS

With inferential statistics, you are trying to reach

conclusions that extend beyond the immediate data

alone. For instance, we use inferential statistics totry to infer from the sample data what the

population might think. Or, we use inferential

statistics to make judgments of the probability that

an observed difference between groups is a

dependable one or one that might have happenedby chance in this study.

http://www.socialresearchmethods.net/kb/statinf.php


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BASIC STATISTICAL TERMS

1. POPULATION is the set of all individuals or

entities under consideration or study. It may be

finite or infinite collection of objects, events, orindividuals, with specified class or characteristics

under consideration.

2.

VARIABLE is a characteristic of interestmeasureable on each and every individual in the

universe (population), denoted by any capital

letter in the English alphabet.


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TYPES OFVARIABLE

QUALITATIVE VARIABLE consists of categories or

attributes, which have non-numericalcharacteristics.

QUANTITATIVE VARIABLE consists of numbers

representing counts or measurements.


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TYPES OF QUANTITATIVEVARIABLE

DISCRETE QUANTITATIVE VARIABLE results

from either a finite number of possible values or acountable number of possible values.

CONTINUOUS QUANTITATIVE VARIABLE

results from infinitely many possible values thatcan be associated with points on a continuous

scale in such a way that there are no gaps or

interruptions.


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BASIC STATISTICAL TERMS

3. SAMPLE is a part of the population or a sub-collection of elements drawn from a population.

4. PARAMETER is a numerical measurementdescribing some characteristic of a population.

5. STATISTIC is a numerical measurement

describing some characteristic of a sample.

6. SURVEY is often conducted to gather opinions orfeedbacks about a variety of topics.


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LEVELS OF MEASUREMENT

1. NOMINAL is characterized by data that consist

of names, labels, or categories only. The data

cannot be arranged in an ordering scheme.

2. ORDINAL involves data that may be arranged in

some, but differences between data values either

cannot be determined or are meaningless


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LEVELS OF MEASUREMENT

3. INTERVAL is like ordinal level, with the

additional property that meaningful amounts of

differences between data can be determined.However, there is no inherent (natural) zero

starting point.

4. RATIO in the interval level modified to include

the inherent zero starting point. For values at this

level, differences and ratios are meaningful.


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DATA COLLECTION AND

PRESENTATION


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CHARACTERISTICS OF AGOOD QUESTION

1. A good question is unbiased.

Do you like classical music?

Do you like boring classical music?

2. A good question must be clear and simply stated.What is your average grade last semester?

What is your academic performance last semester?

3. Questions must be precise.

Do you think male and female are equal? (Vaguequestion)

4. Good questionnaires lend themselves to easy

analyses.


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TWO CATEGORIES OF SURVEYQUESTIONS

1. OPEN QUESTION allows free response

2. CLOSED QUESTION allows only fixedresponse


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TYPES OF DATA

1. PRIMARY DATA are information collected from

an original source of data, which is first-hand in

nature. Examples are data collected frominterviews and surveys.

2. SECONDARY DATA are information collected

from published or unpublished sources like

books, newspapers, and thesis.


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METHODS OF DATACOLLECTION

1. Direct or interview method

2. Indirect or questionnaire method

3. Registration method

4. Observation method

5. Experiment method


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SAMPLING

Sampling is the process of selecting units, likepeople, organizations, or objects from apopulation of interest in order to study and fairlygeneralize the results back to the population from

which the sample was chosen.

1. Probability Sampling and method of samplingthat utilizes some form of random selection

a) Simple random sampling a group of subjectsis selected for study from a larger group. Eachindividual is chosen entirely by chance andeach member of the population has an equalchance of being included in the sample.


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b.) Stratified random sampling involves

dividing the population into homogenoussubgroups and then taking a simple random

sample in each subgroup. The objective is to

divide the population into non-overlapping

groups

Equal allocation

Proportional allocation

c.) Systematic random sampling selects every

kth unit from an ordered population


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d.) Cluster random sampling divides the

population into clusters, usually alonggeographic boundaries, then randomly takingsamples of clusters and measuring all unitswithin sampled clusters

2. ) Non-probability Sampling doesnt involverandom selection of samples and thereforedoesnt represent the population well.

a) Accidental, haphazard or convenience isbased primarily on the convenience of theresearcher. Most common examples areinterviews done by television news programsto get a quick reading of public opinion.


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b.) Purposive sampling done with a purpose in

mind. Usually, one or more specific predefinedgroups are sought. It can be very useful in

situations where a target sample needs to be

reached quickly and where sampling for

proportionality is not the primary concern.

Subcategories of Purposive Sampling:

1.) Modal Instance sampling for specific groups

or types of people wherein sampling the most

frequent case or the typical case is sought for.

This method is commonly used in informal public

opinion polls.


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2.) Expert Sampling involves assembling of a sample

of persons with known or demonstrable experience

and expertise in some area.

3.) Quota Sampling respondents are selected non-

randomly according to some fixed quota.

4.) Heterogeneity - is performed when all opinions or

views about a specific topic are the primary concern

and representing these views proportionately is not of

major importance. This is also called diversity.

5.) Snowball Sampling starts by identifying someonewho meets the criteria for inclusion in the study. The

respondent is then asked to recommend others whom

they may know who also meet the criteria.


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EXERCISES

Identify the type of sampling used in the followingstatements.

_______1.) An engineer selects every 50th cell phonefrom the assembly line for careful testing and

analysis._______2.) A dean at DLSU D surveys all students

from each of 12 randomly selected classes.

_______3.) A reporter writes the names of each

senator on a separate card, shuffles the cards,and then draws five names.

_______4.) A reporter obtains sample data fromreaders who decide to mail in a questionnaireprinted in the latest issue.


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_______5.) A mathematics professor selects 18 men

and 18 women from each of four classes.

_______6.) In conducting research for a psychology

course, a student of DLSU D interviews

students who are leaving the SBC canteen.

_______7.) A reporter obtains numbered listing of

the1000 companies with the highest stock

market values, uses a computer to generate 20

random numbers between 1and 1000, and then

interviews the chief executive officers of the

companies corresponding to these numbers.


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_______8.) A medical student at DLSU HSC

interviews all diabetic patients in each of 15

randomly selected hospitals in the country.

_______9.) A researcher interviews every 45th

patient in the list of DLS UMC in-patients.

_______10.) Ms. Morales wants to give away 3

movie tickets. In order to remove bias, she wrote

the name of each of her students in a paper and

placed it in a hat. To determine the 3 winners,she picked 3 rolled papers from the hat.


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_________11.) To research consumer recognition of

Swerte Ko noodles, the researcher conducts a

survey of 2000 consumers in the Philippines by

interviewing typical class C and D consumers

coming out of the supermarket.

_________12.) A student interviews school

principals and classroom teachers about the

implementation of the 2002 Basic Education

Curriculum.

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