Statistical Concepts: Introduction

IN STATISTICS
06/28/14 eccphd@yahoo.com

Think of these…Crime rate
Unemployment
figures
2010 BAR Passing rate
Mortality rates
Gasoline prices
Proportion of voters
favoring a candidate
Enrolment trend
Drop-out rate
• Number of Accident per
year
• Annual growth rate
• Monthly income
• Annual budget
• Shooting average
• Registered vehicles
annually
• Ratio of male teachers
to the female
• Average life span

Numerical descriptions…Numerical descriptions…
Statistics
ESTIMATES
PREDICTIONSPREDICTIONS
DECISIONS

 Statistics is a branch of
mathematics that deals with
the methods of collection,
presentation, analysis and
interpretation of data.
NATURE OF STATITICS

 Descriptive Statistics
 Inferential Statistics

 It is concerned with the
gathering, classification, and
presentation of data and
summarizing the values to
describe the group
characteristic.


 It pertains to the methods
dealing with making of inference,
estimate or prediction about a
large set of data (population) using
the information gathered from a
sample.

• Population refers to groups or
aggregate of people, animals, subjects,
materials, events, or things of any form.
• Samples are elements of the population
selected through a process. They have of the
same characteristics with the population.

POPULATION
SAMPLE

• Parameter – It is a descriptive measure of
the population. Greek letters are used to
represent parameters, e.g. population mean
μ, population standard deviation σ, etc.
• Statistic – It is a descriptive measure of the
sample. Roman letters are used for statistic,
e.g. sample mean x, sample standard
deviation s, etc.

•Raw Data
•Grouped Data
•Primary data
•Secondary Data
DataData are any bits or collection of
information, ideas, figures or concepts.

Try asking some Fourth Year students to give
you his age, date of birth, ethnic group,
religion, birth order, occupation of his
father, occupation of her mother,
educational background of his parents,
place of birth, ambition, favorite subject,
most liked Grade school teacher and
hobbies – any information he will feed you
are basically RAW DATA.

Grouped Data – those data placed in
tabular form characterized by category
or class intervals with the corresponding
frequency
Ethnic Groups Frequency
Ilongo 24
Ilocano 56
Cebuano 78
Tagalog 52
Bicolano 9
Maguindanaon 23
Maranao 21
Total 263

English Grades Frequency
75 – 79 4
80 – 84 16
85 – 89 27
90 – 94 5
95 - 99 2
Total 54
Age Bracket Frequency
10 – 19 40
20 – 29 26
30 – 39 17
40 – 49 52
50 - 59 20
Total 155
Grouped
Data
class
intervals

Primary Data – data are measured and
gathered by the researcher who published it
You submit a
statistical data to
your Professor
regarding the
educational profile
of the teachers in
your school which
you yourself had
gathered through
interview.
Educ'l Attainment Percentage
BSED 13%
BEED 26%
AB w/ Educ Units 10%
BEED w/ MA units 45%
Master's Degree Holder 3%
MA w/ doctoral units 3%
Total 100%
Table 1. Educational Profile of Teachers in
Balintong Elementary School, SY
2012-2013

Secondary Data – data being republished
by another researcher for agency
PNARUs Officers and EPs Percentage
NARF 5,622 53%
4TH
NCRes Bn 268 3%
30TH
NARG 1,107 10%
502ND
NRS 199 2%
503RD
NRS 125 1%
705TH
NRS 1,667 16%
706TH
NRS 1,561 15%
Total 10,549 100%
Table 4. Personnel Capability of the Philippine Navy Affiliated Reserve
Units (PNARUs)
Source: NAVRESCOM,
2010
This data is
lifted from
an original
source by Col
Robles (2011)
and aptly
included in
his study on
PNARUs.

Monthly Income Percent
below 7,500.00 47.60
7,501.00 - 10,000.00 18.80
10,001.00 - 12,500.00 14.70
12,501.00 - 15,000.00 5.80
above 15,000.00 13.10
Total 100.00
Table 6. Monthly Income of the Parents of the Senior High School
Students in Arakan Valley, Division of Cotabato, SY
2010-2011
Source:
Alpajando, 2011
Secondary DataSecondary Data
If this
data would
be used in
another
study, then
it turns
into a
secondary
data.

• It is a characteristic or attribute of the
experimental unit (persons, units or objects)
which assumes different values or labels.
• The process of assigning value or label of a
particular experimental unit is called
measurement.

 Qualitative
Variables
 Quantitative
Variables

Quantitative
Variables – When
measured from the
experimental units, they yield
numerical responses.
Examples
height, age, income, family size
Age - 15, 18, 29, 45, 54, 60
Family size – 2, 4, 5, 8
Height – 150 cms, 164 cms

• Discrete Variables
• Continuous Variables

Discrete variablesDiscrete variables
assume a finite or countable
infinite values such as 0, 1, 2,
3, etc.
Ex: number of studentsnumber of students
population of teacherspopulation of teachers
score in a testscore in a test
female Senatorsfemale Senators

Continuous variables
cannot take finite values.
These values are related with
points on an interval of the
real line.
Ex: Height - 23.3 cm, 23.456 m,
123.8 ft
Mass – 28.56 kgs, 8.36 lbs

• Nominal
• Ordinal
• Interval
• Ratio

Nominal Level is the crudest
form of measurement. The numbers
or symbols are used for the purpose
of categorizing forms into groups.
The categories are mutually
exclusive, that is, being in one
category automatically
excludes another.
Ex: Gender (F – Female; M – Male)
Faculty (1 – Tenured; 0 – Non-tenured)
Response (1- Yes, 0 - No)

Student Attitude
1 – Strongly Disagree
2 – Slightly Disagree
3 – Disagree
4 – Moderately Agree
5 – Strongly Agree
Ordinal Level is a sort of
improvement of nominal level because
data are ranked from the “bottom to
the top” or from the “low to high”
manner.
 Statements such as “greater than” or
“lesser than” may be used in this level.
Administrative
Performance
• Excellent -1
• Very Satisfactory - 2
• Good - 3
• Fair - 4
• Poor - 5
Examples:

Interval Level possesses both
the properties of the nominal and
ordinal levels. The distances between
any two numbers on the scale are
known and it does not have a stable
standing point (or an absolute zero).
Ex: temperature

Ratio Level possesses all the properties
of nominal, ordinal and interval levels.
 In addition, it has an absolute zero point
and data can be classified and placed in
a proper order to compare their
magnitudes. ZeroZero stands for of
something or absence absolutely nothing.
Ex: grades
income
tuition fees

Sampling
techniques are used to
economize (on the part of
the researcher) the
following:
 Time
 Effort
 Money

Sampling techniquesSampling techniques
are classified into:are classified into:
• probability
sampling
• non-probability
sampling

PROBABILITY SAMPLING
 It is a method of selecting a sample (n)
from a universe (N) such that each
member of the population has an equal
chance of being included in the sample
and all possible combinations of size (n)
have an equal chance of being chosen
as the sample.

NON-PROBABILTY SAMPLING
It is a method wherein the
manner of selecting a sample
(n) from a universe (N)
depends on some inclusioninclusion
rulerule as specified by the
researcher.

• Simple Random (Lottery) Sampling
• Systematic Sampling
• Stratified Sampling
• Cluster or Area Sampling
• Multi-stage Sampling

Ex: N = 100, n = 25
N/n = 100/25
= 4
• This means every 4th
element in a series should be
taken as a sample.
This method still
uses the concept of
random sampling
and involves the
selection of the nth
element of a series
representing the
population.

1 11 21 31 41 51 61 71 81 91
2 12 22 32 42 52 62 72 82 92
3 13 23 33 43 53 63 73 83 93
4 14 24 34 44 54 64 74 84 94
5 15 25 35 45 55 65 75 85 95
6 16 26 36 46 56 66 76 86 96
7 17 27 37 47 57 67 77 87 97
8 18 28 38 48 58 68 78 88 98
9 19 29 39 49 59 69 79 89 99
10 20 30 40 50 60 70 80 90 100

 This is a random sampling
technique in which the
population is divided into
non-overlapping
subpopulations called strata.

Respondents n
Administrators 10
Teachers 50
Students 100
Parents 50
STRATIFIED SAMPLES
Gender n
Female 170
Male 250
Schools n
Public 20
Private non-sectarian 10
Private sectarian 10

 barangays in a municipality
 municipalities in a province
This is a random sampling technique in which
the populationis divided into non-
overlapping clusters or area.

Ex: Region – 1st
level
Province – 2nd
Level
City – 3rd
Level
Barangay – 4th
A technique that considers
different stages orphases
in sampling.

MULTI-STAGE SAMPLING

• Purposive SamplingPurposive Sampling
 It is based on a criteria orIt is based on a criteria or
qualifications given by thequalifications given by the
researcher. Those who willresearcher. Those who will
satisfy the criteria are included.satisfy the criteria are included.

• Quota Sampling
 It is quick and cheap since the interviewer
is given a definite instruction and quota
about the section of the population he is to
work on.
 The final choice of the actual person is left
to his preference.
NON-PROBABILITY SAMPLING
TECHNIQUES

• Convenience SamplingConvenience Sampling
 It uses some instruments or equipment that
provide convenience like the telephone or hand
set to pick his samples units.
 That means, people with no telephones can
not be given a chance at all.

 How many samples do weHow many samples do we
need to use sufficiently inneed to use sufficiently in
our study?our study?
Is this number enough forIs this number enough for
the study?the study?
Will it give a valid resultWill it give a valid result
for the study?for the study?

This equation is
commonly used
by statisticians
to determine
the samples
when the
population is
equal ormore
than 500.
N
n = -----------------
(1 + e2
N)
wherewhere
n = the desired number ofn = the desired number of
samplessamples
N = total populationN = total population
e = sampling errore = sampling error
e = 0.05, 0.02 or 0.01 (arbitrary)e = 0.05, 0.02 or 0.01 (arbitrary)

Case 1:
A study is to be conducted in a big School
Division of 25,000 students. Determine the
appropriate sample using a 5% sampling error.
Solution:
n = [N/1 + e2
N]
= {25,000/[1 + (0.05)(.05)(25,000)]}
= 393.7 or
≈ 394 students

 Descriptive Research –Descriptive Research –
10% of the population (20% for smaller N)10% of the population (20% for smaller N)
 Correlational Research -Correlational Research - 30 subjects30 subjects
Ex-post Facto Research -Ex-post Facto Research - 15 per group15 per group
 Experimental Research -Experimental Research - 15 subjects per group15 subjects per group

Where Zα/2 is the confidence level value
 At 99% confidence level, Zα/2 = 2.58
, N = population
n = desired sample size
p = largest possible proportion (0.50)
e = sampling error
e = 0.01 for 99% confidence level

1000 (1.96) 2
[0.50 (1 – 0.50)]
n = ---------------------------------------------------
1000 (.05)2
+ (1.96)2
[0.05(1 – 0.05)]
= 277.54 or278

where Zα/2 is the confidence level value
E = allowable error (±E) in the estimate
of the true value of μ
n = desired sample size
SAMPLE SIZE FROM THE ESTIMATION OFSAMPLE SIZE FROM THE ESTIMATION OF μμ
THIS CAN BE USED
WHEN THE
POPULATION IS NOT
KNOWN.

(1.96) (.05) 2
n = ---------------------
.01
= 96.04 or 96

NN11
nnii = -------- x n; for i = 1, 2, 3,..= -------- x n; for i = 1, 2, 3,..
NN
where n = the total size of the
stratified random sample
N = total population
N1 = number of the 1st
stratum elements
N2 = number of the 2nd
stratum elements
N3 = number of the 3rd
stratum elements

PROPORTIONAL ALLOCATION
n1 = [119/1000](286)
= 34 (seniors)
n2 = [210/1000](286)
= 60 (juniors)
And so with n3, n4, and n5.
Strata Population (N)
Seniors 119
Juniors 210
Sophomores 325
Freshmen 346
Total 1000
n = 286 (desired samples)

Strata Population (N) Sample (n)
Seniors 119 34
Juniors 210 60
Sophomores 325 93
Freshmen 346 99
Total 1000 286
PROPORTIONAL ALLOCATION

The choice of the appropriate methods to
be used in gathering of data depends mainly
on some factors. These include:
 the nature of the problem
 the population under investigation
 the time
the material factors

 Direct or Interview Method
 Indirect or Questionnaire Method
 Registration Method
Other MethodsOther Methods
 ObservationObservation
 Phone interviewPhone interview
 ExperimentsExperiments

Direct or
Interview Method

It is one of the easiest methods of
data gathering.
It takes time to prepare because
questionnaires need to be
attractive.
The content of a typical
questionnaire, directions included,
must be precise, clear and self-
explanatory.

Examples:Examples:
 MarriageMarriage
registrationregistration
 birth certificatesbirth certificates
 vehicle registrationsvehicle registrations
 firearms licenses ,firearms licenses ,
Registration Method

Observation
• It is utilized to gatherIt is utilized to gather
data regardingdata regarding
attitudes, behavior,attitudes, behavior,
values, and culturalvalues, and cultural
patterns of the samplespatterns of the samples
under investigation.under investigation.

Phone Interview
It is employed if the
questions to be
asked are brief and
few.

Experiments
 It is applied to collect or
gather data if the investigator
wants to control the factors
affecting the variable being
studied.

Data needs to beData needs to be
organized to showorganized to show
important propertiesimportant properties
that may help in thethat may help in the
analysis andanalysis and
interpretation.interpretation.

 Textual
 Tabular
• Graphical

• In this form, the presentation is in
narrative or paragraph mode.
•The data are within the text of the
paragraph.
• In most cases, it cannot not get the
immediate interest of the reader but it can
present a more comprehensive picture of
the data because of its written explanation.

• The data shows the grades of a student in the FirstThe data shows the grades of a student in the First
Quarter. As indicated, he got an excellent grade inQuarter. As indicated, he got an excellent grade in
Values Education (96). On the other hand, heValues Education (96). On the other hand, he
achieved the same level of performance in bothachieved the same level of performance in both
Filipino and English (90). As shown also, he gained fairFilipino and English (90). As shown also, he gained fair
performance in Science and Social Studies where heperformance in Science and Social Studies where he
got 89 and 86, respectively. With a grade of 80, it onlygot 89 and 86, respectively. With a grade of 80, it only
suggests that he finds Math a difficult subject.suggests that he finds Math a difficult subject.

• In this form, the presentation
makes use of rows and columnsrows and columns like
a frequency table or distribution.
• The data are presented in a
systematic and orderly manner
which catches one’s attention and
may facilitate the comprehension
and analysis of the data presented.

Subject Areas
First Quarter
Grades
Math 80
English 90
Science 89
Social Studies 86
Filipino 90
Values Education 94
Average 88.17
ILLUSTRATIVE EXAMPLEILLUSTRATIVE EXAMPLE

TABULAR PRESENTATION
Gender Frequency Percent
Male 20 40%
Female 30 60%
Total 50 100%

• In this form, the numerical data
in a frequency distribution can be
made more interesting and easier
to understand when presented in
pictures or geometrical
representations.

GRAPHICAL PRESENTATION (Pie Graph)

GRAPHICAL PRESENTATION (Cylindrical
Graph)

Figure 1. The Ethnic Profile of PhD Students in SKSUFigure 1. The Ethnic Profile of PhD Students in SKSU
Graduate Studies Program iGraduate Studies Program i
06/28/14

Ethnic Groups Frequency
Ilongo 20
Bicolano 5
Tagalog 2
Ilocano 3
Total 30
Table 1. The Ethnic Profile of PhD Students at SKSU
Graduate Extension Program in Iloilo City
Category or labelCategory or label

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