Statistics

StatisticsStatistics
• Is a scientific body of knowledgeIs a scientific body of knowledge
that deals with:that deals with:
 collection of datacollection of data
 organization or presentation oforganization or presentation of
datadata
 analysis and interpretation ofanalysis and interpretation of
datadata

• Is a statistical procedureIs a statistical procedure
concerned with describing theconcerned with describing the
characteristics and properties ofcharacteristics and properties of
group of persons, places orgroup of persons, places or
things; it is based on easilythings; it is based on easily
verifiable facts.verifiable facts.
Descriptive StatisticsDescriptive Statistics

• Is a statistical procedure used toIs a statistical procedure used to
draw inferences for thedraw inferences for the
population on the basis of thepopulation on the basis of the
information obtained from theinformation obtained from the
sample.sample.
Inferential StatisticsInferential Statistics

• Population.Population. It is the total collection ofIt is the total collection of
all the elements (people, events,all the elements (people, events,
objects, measurements, and so on)objects, measurements, and so on)
one wishes to investigate.one wishes to investigate.
• Sample.Sample. Subgroup obtained from aSubgroup obtained from a
population.population.
• Parameter.Parameter. A numerical value thatA numerical value that
describes a characteristic of adescribes a characteristic of a
population.population.
DefinitionsDefinitions

• Statistic.Statistic. It is a numerical value thatIt is a numerical value that
describes a particular sample.describes a particular sample.
• Data.Data. This are facts, or a set ofThis are facts, or a set of
information gathered or under study.information gathered or under study.
• Quantitative DataQuantitative Data are numerical inare numerical in
nature and therefore meaningfulnature and therefore meaningful
arithmetic can be done.arithmetic can be done.
Ex:Ex: ageage

• Qualitative DataQualitative Data are attributes whichare attributes which
cannot be subjected to meaningfulcannot be subjected to meaningful
arithmetic.arithmetic.
Ex:Ex: gendergender
• Discrete DataDiscrete Data assume exact valuesassume exact values
only and can be obtained by countingonly and can be obtained by counting
Ex:Ex: number of studentsnumber of students

• Continuous DataContinuous Data assume infiniteassume infinite
values within a specified interval andvalues within a specified interval and
can be obtained by measurement.can be obtained by measurement.
Ex:Ex: heightheight
• ConstantConstant is a characteristic oris a characteristic or
property of a population or sampleproperty of a population or sample
which makes the member similar towhich makes the member similar to
each other.each other.

• VariableVariable is a characteristic oris a characteristic or
property of a population or sampleproperty of a population or sample
which makes the members differentwhich makes the members different
from each other.from each other.
• Dependent.Dependent. A variable which isA variable which is
affected by another variable.affected by another variable.
Ex:Ex: test scorestest scores

• Independent.Independent. A variable whichA variable which
affects the dependent variable.affects the dependent variable.
Ex:Ex: number of hours spent innumber of hours spent in
studyingstudying

Levels of MeasurementsLevels of Measurements
• Nominal numbersNominal numbers do not meando not mean
anything; they just label.anything; they just label.
Ex:Ex: SSS NumberSSS Number
• Ordinal numbersOrdinal numbers are used to label +are used to label +
rank.rank.
Ex:Ex: size of t-shirtsize of t-shirt

Levels of MeasurementsLevels of Measurements
• Interval numbersInterval numbers are used to label +are used to label +
rank; do not have a true zero.rank; do not have a true zero.
Ex:Ex: temperaturetemperature
• Ratio numbersRatio numbers are used to label +are used to label +
rank + equal unit of interval; have arank + equal unit of interval; have a
true zerotrue zero
Ex:Ex: number of votesnumber of votes

Target PracticeTarget Practice
A. Determine whether the set of data isA. Determine whether the set of data is
qualitative or quantitative.qualitative or quantitative.
1.1. Models of cell phonesModels of cell phones
2.2. Number of subscribers to Philippine DailyNumber of subscribers to Philippine Daily
NewsNews
3.3. Weights of 1000 packs of a brand ofWeights of 1000 packs of a brand of
noodlesnoodles
4.4. Yes or No responses to survey questionYes or No responses to survey question
5.5. Telephone numberTelephone number

B. Which of the following numbers isB. Which of the following numbers is
discrete or continuous?discrete or continuous?
1.1. Distance from town A to town BDistance from town A to town B
2.2. Record of absent students in a class inRecord of absent students in a class in
StatisticsStatistics
3.3. Number of customers in a restaurantNumber of customers in a restaurant
4.4. Number of cars parked in the basement ofNumber of cars parked in the basement of
a buildinga building
5.5. Weights of all Grades 1 pupils in theWeights of all Grades 1 pupils in the
Library SchoolLibrary School

C.C. Identify the level of measurement:Identify the level of measurement:
nominal(N), ordinal(O), interval(I), or ratio(R)nominal(N), ordinal(O), interval(I), or ratio(R)
most appropriate for each of the followingmost appropriate for each of the following
data.data.
1.1. Color of the eyeColor of the eye
2.2. Number of votesNumber of votes
3.3. Rank of facultyRank of faculty
4.4. Exam scoreExam score
5.5. Temperature in Baguio last summerTemperature in Baguio last summer

Determining the Sample SizeDetermining the Sample Size
Slovin’s Formula:Slovin’s Formula:
2
1
N
n
Ne
=
+
nn is the sample size
NN is the population size
ee is the margin of error
TheThe margin of errormargin of error is a value whichis a value which
quantifies possible sampling errors.quantifies possible sampling errors.

Determining the Sample SizeDetermining the Sample Size
TheThe margin of errormargin of error can be interpretedcan be interpreted
by the use of ideas from the laws ofby the use of ideas from the laws of
probability. In reality, it is whatprobability. In reality, it is what
statisticians call astatisticians call a confidenceconfidence
interval.interval.
Sampling errorSampling error means that the resultsmeans that the results
in the sample differ from those of thein the sample differ from those of the
target population because of thetarget population because of the
“luck of the draw”.“luck of the draw”.

Sampling TechniquesSampling Techniques
SamplingSampling is the process of selectingis the process of selecting
samples from a given population.samples from a given population.
1.1. Probability SamplingProbability Sampling
2.2. Non-probability SamplingNon-probability Sampling
Types:Types:

A.A. Probability Sampling:Probability Sampling: Samples areSamples are
chosen in such a way that eachchosen in such a way that each
member of the population has amember of the population has a
known though not necessarily equalknown though not necessarily equal
chance of being included in thechance of being included in the
samples.samples.
- Avoids biasesAvoids biases
- It provides the basis for calculatingIt provides the basis for calculating
the margin of error.the margin of error.

1.1.Simple Random Sampling:Simple Random Sampling: SamplesSamples
are chosen at random with membersare chosen at random with members
of the population having a known orof the population having a known or
sometimes equal probability orsometimes equal probability or
chance of being included in thechance of being included in the
samples.samples.
a.a. LotteryLottery
b.b. Generation of random numbersGeneration of random numbers

2. Systematic Sampling:2. Systematic Sampling: Samples areSamples are
chosen following certain rules set bychosen following certain rules set by
the researchers. This involvesthe researchers. This involves
choosing the kchoosing the kthth
member of themember of the
population, with k=N/n, but therepopulation, with k=N/n, but there
should be a random start.should be a random start.

3. Cluster Sampling:3. Cluster Sampling: is sometimesis sometimes
calledcalled area samplingarea sampling because it isbecause it is
usually applied when the populationusually applied when the population
is large.is large.
In this technique, groups orIn this technique, groups or
clusters instead of individuals areclusters instead of individuals are
randomly chosen.randomly chosen.

4. Stratified Random Sampling:4. Stratified Random Sampling: ThisThis
method is used when the populationmethod is used when the population
is too big to handle, thus dividing Nis too big to handle, thus dividing N
into subgroups, calledinto subgroups, called stratastrata, is, is
necessary.necessary.
A process that can be used isA process that can be used is
proportional allocationproportional allocation..

B. Non Probability Sampling:B. Non Probability Sampling: EachEach
member of the population does notmember of the population does not
have a known chance of beinghave a known chance of being
included in the sample. Instead,included in the sample. Instead,
personal judgment plays a verypersonal judgment plays a very
important role in the selection.important role in the selection.
Non-probability sampling is oneNon-probability sampling is one
of the sources ofof the sources of errorserrors in research.in research.

Types:Types:
1.1.Convenience Sampling:Convenience Sampling: This type isThis type is
used because of the convenience itused because of the convenience it
offers to the researcher.offers to the researcher.
2.2.Quota Sampling:Quota Sampling: This is very similarThis is very similar
to the stratified random sampling.to the stratified random sampling.
The only difference is that theThe only difference is that the
selection of the members of theselection of the members of the
samples in stratified sampling issamples in stratified sampling is
done randomly.done randomly.

3. Purposive Sampling:3. Purposive Sampling: Choosing theChoosing the
respondents on the basis of pre-respondents on the basis of pre-
determined criteria set by thedetermined criteria set by the
researcher.researcher.

Data Gathering TechniquesData Gathering Techniques
1.1.The Direct or the Interview Method:The Direct or the Interview Method:
In this method, the researcher hasIn this method, the researcher has
direct contact with the researcher.direct contact with the researcher.
A: Clarification can be done easily.A: Clarification can be done easily.
D: Costly and time-consuming.D: Costly and time-consuming.

1.1.The Indirect or QuestionnaireThe Indirect or Questionnaire
Method:Method: The researcher gives orThe researcher gives or
distributes the questionnaire to thedistributes the questionnaire to the
respondents either by personalrespondents either by personal
delivery or by mail.delivery or by mail.
A: Saves time and money; largeA: Saves time and money; large
number of samples can be reached.number of samples can be reached.
D: Problem of retrievalD: Problem of retrieval

The QuestionnaireThe Questionnaire (charact erist ics)(charact erist ics)
1.1.

2. There is a descriptive title/name for2. There is a descriptive title/name for
the questionnaire.the questionnaire.
3. It is designed to achieve objectives.3. It is designed to achieve objectives.
4. The directions are clear4. The directions are clear
5. It is designed for easy tabulation.5. It is designed for easy tabulation.

6. It avoids the use of double6. It avoids the use of double
negatives.negatives.
7. It also avoids double barreled7. It also avoids double barreled
questions.questions.
8. It phrases questions well for all8. It phrases questions well for all
respondents.respondents.

Types of QuestionnaireTypes of Questionnaire
• OpenOpen – this type has an unlimited– this type has an unlimited
responsesresponses
• ClosedClosed – this type limits the scope of– this type limits the scope of
responsesresponses
• CombinationCombination – this type is a– this type is a
combination of open and closedcombination of open and closed
types of questionnairetypes of questionnaire

Types of QuestionsTypes of Questions
• Multiple choiceMultiple choice – allows respondent– allows respondent
to select answer/s from the listto select answer/s from the list
• RankingRanking – asks respondents ton rank– asks respondents ton rank
the given itemsthe given items
• ScalesScales – asks respondents to give– asks respondents to give
his/her degree of agreement to ahis/her degree of agreement to a
statement (Likert-scale)statement (Likert-scale)

3.The Registration Method:3.The Registration Method: ThisThis
method of gathering data is governedmethod of gathering data is governed
by laws.by laws.
A: Most reliable source of dataA: Most reliable source of data
D: Data are limited to what are listedD: Data are limited to what are listed
in the documentsin the documents

4. The Experimental Method:4. The Experimental Method: ThisThis
method of gathering data is used tomethod of gathering data is used to
find out cause and effectfind out cause and effect
relationships.relationships.
A: Can go beyond plain descriptionA: Can go beyond plain description
D: Lots of threats to internal andD: Lots of threats to internal and
external validityexternal validity

Presentation of DataPresentation of Data
Textual Form:Textual Form: Data are presented inData are presented in
paragraph or in sentences. Thisparagraph or in sentences. This
includes enumeration of importantincludes enumeration of important
characteristics, emphasizing thecharacteristics, emphasizing the
most significant features andmost significant features and
highlighting the most strikinghighlighting the most striking
attributes of the set of data.attributes of the set of data.

Tabular Form:Tabular Form: A more effective deviceA more effective device
of presenting data.of presenting data.
1. stem and leaf plots1. stem and leaf plots
2. frequency distribution table2. frequency distribution table
3. contingency table3. contingency table

Graphical/Pictorial Form:Graphical/Pictorial Form: A mostA most
effective device of presenting data.effective device of presenting data.
1. line graph (freq. polygon, ogive)1. line graph (freq. polygon, ogive)
2. bar graph (histogram)2. bar graph (histogram)
3. pie chart3. pie chart
4. pictograph4. pictograph
5. statistical maps5. statistical maps

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