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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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