statistical concepts: introduction

IN STATISTICS

04/10/23 [email protected]

Think of these…Crime rate Unemployment

figures2010 BAR Passing

rateMortality ratesGasoline pricesProportion of voters

favoring a candidateEnrolment trendDrop-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 Numerical descriptions…descriptions…

Statistics04/10/23 [email protected]

ESTIMATES

PREDICTIONSPREDICTIONSDECISIONS

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 04/10/23 [email protected]

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.

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 FrequencyIlongo 24Ilocano 56Cebuano 78Tagalog 52Bicolano 9Maguindanaon 23Maranao 21Total 26304/10/23 [email protected]

English Grades Frequency75 – 79 480 – 84 1685 – 89 2790 – 94 595 - 99 2Total 54

Age Bracket Frequency10 – 19 4020 – 29 2630 – 39 1740 – 49 5250 - 59 20Total 155

Grouped Data

class interva

ls


Primary Data – data are measured and gathered by the

researcher who published itYou 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 PercentageBSED 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 13.10Total 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, 8Height – 150 cms, 164 cms04/10/23 [email protected]


• Discrete Variables • Continuous Variables

Discrete variablesDiscrete variables assume a finite or countable infinite values such as 0, 1, 2, 3, etc.

Ex: number of students number of students population of teachers population of teachers

score in a testscore in a test

female Senators female 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 lbs04/10/23 [email protected]


• 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

POPULATION

SAMPLE


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 inclusion ruleinclusion rule as specified by the researcher. 04/10/23 [email protected]


• Simple Random (Lottery) Sampling

• Systematic Sampling• Stratified Sampling

• Cluster or Area Sampling• Multi-stage Sampling


Ex: N = 100, n = 25N/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 50Students 100Parents 50

STRATIFIED SAMPLESSTRATIFIED SAMPLES

Gender n

Female 170

Male 250

Schools nPublic 20Private non-sectarian 10Private sectarian 10



barangays in a municipality municipalities in a province

This is a random sampling technique in which

the population is divided into

non-overlapping clusters or area.


Ex: Region – 1st levelProvince – 2nd

LevelCity – 3rd Level Barangay – 4th

Level

A technique that considers different stages or phases in sampling.


MULTI-STAGE SAMPLINGMULTI-STAGE SAMPLING


• Purposive SamplingPurposive Sampling

It is based on a criteria It is based on a criteria or qualifications given by or qualifications given by the researcher. Those who the researcher. Those who will satisfy the criteria are will satisfy the criteria are included. 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

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 How many samples do we need to use we need to use sufficiently in our sufficiently in our study?study?

Is this number enough Is this number enough for the study?for the study?

Will it give a valid Will it give a valid result for the study? result for the study?


This equation is commonly used by statisticians to determine the samples when the population is equal or more than 500.

Nn = ----------------- (1 + e2 N)

wherewhere

n = the desired number of n = 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 + e2N]

= {25,000/[1 + (0.05)(.05)

(25,000)]}

= 393.7 or

≈ 394 students 04/10/23 [email protected]


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 or 278

where Zα/2 is the confidence level value At 99% confidence level, Zα/2 = 2.58 At 95% confidence level, Zα/2 = 1.96 At 90% confidence level, Zα/2 = 1.65

E = allowable error (±E) in the estimate of the true value of μn = desired sample size


SAMPLE SIZE FROM THE ESTIMATION OF SAMPLE SIZE FROM THE ESTIMATION OF μμTHIS 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,..

NNwhere 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 ALLOCATIONPROPORTIONAL ALLOCATIONn1 = [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

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 Methods Other 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: Marriage Marriage registrationregistration birth certificatesbirth certificates vehicle vehicle registrationsregistrations firearms licenses , firearms licenses , etcetc

Registration Method


Observation• It is utilized to It is utilized to gather data gather data regarding regarding attitudes, behavior, attitudes, behavior, values, and cultural values, and cultural patterns of the patterns of the samples under samples under investigation.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 be Data needs to be organized to show organized to show important properties important properties that may help in the that may help in the analysis and analysis 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 data shows the grades of a student in

the First Quarter. As indicated, he got an the First Quarter. As indicated, he got an

excellent grade in Values Education (96). On excellent grade in Values Education (96). On

the other hand, he achieved the same level of the other hand, he achieved the same level of

performance in both Filipino and English (90). performance in both Filipino and English (90).

As shown also, he gained fair performance in As shown also, he gained fair performance in

Science and Social Studies where he got 89 Science and Social Studies where he got 89

and 86, respectively. With a grade of 80, it and 86, respectively. With a grade of 80, it

only suggests that he finds Math a difficult only suggests that he finds Math a difficult

subject. 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 80English 90Science 89Social Studies 86Filipino 90Values Education 94


Average 88.17

ILLUSTRATIVE EXAMPLEILLUSTRATIVE EXAMPLE

TABULAR PRESENTATIONTABULAR 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 (Pie Graph)


GRAPHICAL PRESENTATION (Cylindrical Graph)GRAPHICAL PRESENTATION (Cylindrical Graph)


Figure 1. The Ethnic Profile of PhD Students in SKSU Figure 1. The Ethnic Profile of PhD Students in SKSU Graduate Studies Program iGraduate Studies Program i

04/10/23

[email protected]

Ethnic Groups FrequencyIlongo 20Bicolano 5Tagalog 2Ilocano 3

Total 30

Table 1. The Ethnic Profile of PhD Students at SKSU Graduate Extension Program in Iloilo City

Category or label Category or label


statistical concepts: introduction

Education

primary data data

presentation of data

raw data

interpretation of data

statistical data

secondary datasecondary

large set of data population

population sample