STATISTICS
STATISTICS
A paper
Presented to fulfill
the requirment of Statistics
CHAPTER I
INTRODUCTION
A.
Background of study
Statistics is a branch
of mathematics that deals with the collection, analysis and interpretation of
data. Data can be defined as groups of
information that represent the qualitative or quantitative attributes of a
variable or set of variables. In layman's terms, data in statistics can be any
set of information that describes a given entity. An example of data can be the
ages of the students in a given class. When you collect those ages, that
becomes your data.
A set in
statistics is referred to as a population. Though this term is commonly used to
refer to the number of people in a given place, in statistics, a population
refers to any entire set from which you collect data.
Today, statistics has become an important tool in the
work of many academic disciplines such as medicine, psychology, education,
sociology, engineering and physics, just to name a few. Statistics is also
important in many aspects of society such as business, industry and government.
Because of the increasing use of statistics in so many areas of our lives, it
has become very desirable to understand and practise statistical thinking. This
is important even if you do not use statistical methods directly.
B.
The Formulation of the problem
In this paper the writer explains about the formulation of the problem,
that are:
1.
What are the definition of
statistics, educational statistics, and Classification of Statistics?
2.
How the way to use and the functions of statistics in
education
3.
What are the definition of statistics data and Kinds
of statistics
4.
What
are the principles of collecting statistics data
5. How the way of collecting
statistics data
6. What are the tool
of collecting data
C.
The purpose of the writing
1.
To know what are the
definition of statistics, educational statistics, and Classification of
Statistics.
2.
The way how to use and the functions of statistics in
education
3.
To know what are the definition of statistics data and
Kinds of statistics.
4.
To
know what are the principles of collecting statistics data
5.
The
way How to collect statistics data
6.
To
know what are the tool of collecting data
CHAPTER I
DISCUSSION
A.
Statistic and educational Statistics
1.
Definition of Statistic
Statistics, in short, is the
study of data. It
includes descriptive statistics (the study of methods and tools for collecting
data, and mathematical models to describe and interpret data) and inferential
statistics (the systems and techniques for making probability-based decisions
and accurate predictions.
From Entomology Side, the name
is implies. Statistics has its roots in the idea of "the state of
things". The word itself comes from the ancient Latin term statisticum
collegium, meaning "a lecture on the state of affairs".
Eventually, this evolved into the Italian word statista, meaning
"statesman", and the German word Statistic, meaning
"collection of data involving the State". Gradually, the term came to
be used to describe the collection of any sort of data.
Statistics is also as a subset
of mathematics. As one would expect, statistics is largely grounded in mathematics, and the
study of statistics has lent itself to many major concepts in mathematics:
probability, distributions, samples and populations, the bell curve,
estimation, and data analysis[1].
According the oxford dictionary, Statistics
is a collection of information shows in numbers. Then Ir. M. Iqbal Hasan,. MM said,
Statistics is the study of the ins and outs of the data, namely
regarding the collection, processing,
analyzers, interpretation and conclusion of the
data in the form of numbers.
Besides that, according Irianto
, Statistics basically a tool to provide an
overview of an event through
a simple form, either
in the form of numbers - numbers and graphs
- graphs, given its
role as a tool, it is necessary
to realize that the key to
the success of the statistical analysis
is still lies in its
use[2].
Statistics is the study of the collection, analysis, interpretation, presentation,
and organization of data.
In applying statistics, e.g. a scientific,
industrial, or societal problem, it is necessary to begin with a population or process to be studied. Populations can be diverse topics such as
"all persons living in a country" or "every atom composing a
crystal". It deals with all aspects of data including the planning of data
collection in terms of the design of surveys and experiments[3].
In case census data cannot be collected, statisticians collect data by developing
specific experiment designs and survey samples.
Representative sampling assures that inferences and conclusions can safely
extend from the sample to the population as a whole. An experimental study involves
taking measurements of the system under study, manipulating the system, and
then taking additional measurements using the same procedure to determine if
the manipulation has modified the values of the measurements. In contrast, an observational study does not
involve experimental manipulation.
Statistics can be said to have
begun in ancient civilization, going back at least to the 5th century BC, but
it was not until the 18th century that it started to draw more heavily from calculus and probability theory. Statistics
continues to be an area of active research, for example on the problem of how
to analyze Big data[4].
Statistics basically a tool to provide an overview of
an event through a simple form, either in the
form of figures and graphs. Originally statistical
terms only a set of numbers that
describe the state of the population, people's income, the level of agricultural production at any given time. in a statistical sense
here just to give
an idea of the past until now in the
picture[5].
Statistics is concerned with scientific methods for collecting,
organising, summarizing, presenting and analyzing data as well as deriving
valid conclusions and making reasonable decisions on the basis of this
analysis. Statistics is concerned with the systematic collection of numerical
data and its interpretation. The word ‘statistic’ is used to refer to:
1.
Numerical
facts, such as the number of people living in particular area.
2.
Definition
of Educational Statistics.
Statistics education is the practice of teaching and learning of statistics, along with the associated scholarly research.
Statistics is both a formal science and a practical theory of scientific
inquiry, and both aspects are considered in statistics education. Education in
statistics has similar concerns as does education in other mathematical
sciences, like logic, mathematics, and computer science. At the same time, statistics is concerned
with evidence-based reasoning, particularly with the analysis of data.
Therefore education in statistics has strong similarities to education in
empirical disciplines like psychology and chemistry, in which education is closely tied to
"hands-on" experimentation.
Mathematicians and statisticians often work in a department of mathematical sciences
(particularly at colleges and small universities). Statistics courses have been
sometimes taught by non-statisticians, against the recommendations of some
professional organizations of statisticians and of mathematicians.
Statistics education research is an emerging field that grew out of
different disciplines and is currently establishing itself as a unique field
that is devoted to the improvement of teaching and learning statistics at all
educational levels[7].
Statistics educators have cognitive and non-cognitive goals for
students. For example, former American
Statistical Association (ASA) President Katherine Wallman defined statistical
literacy as including the cognitive abilities of understanding and critically
evaluating statistical results as well as appreciating the contributions
statistical thinking can make.
One of the goals of the American Statistical Association is to improve
statistics education at all levels. Through the Statistics Education Web
(STEW), the ASA is reaching out to K-12 mathematics and science teachers who
teach statistics concepts in their classrooms. STEW is an online resource for peer-reviewed
lesson plans for K-12 teachers. The web site is maintained by the ASA and accessible
to K-12 teachers throughout the world.
Statistics and probability concepts are included in K-12 curriculum
standards, in particular the Common Core State Standards, and on state and
national exams; however, few K-12 teachers have formal training or applied
experience with statistical concepts. K-12 teachers need a place where they can
find peer-reviewed teaching materials available in a standard format. Teachers
also can benefit from guidance toward activities that are appropriate for their
students' maturity levels and from the ability to select relevant, useful, and
meaningful applications. The ASA is the logical entity to host a resource to
support teachers in their efforts to master the content and incorporate it into
their classrooms[8].
IASE, the International
Association for Statistical Education, seeks to promote, support and improve
statistical education at all levels everywhere around the world. It is the
international umbrella organization for statistics education. It fosters
international cooperation, and stimulates discussion and research. It
disseminates ideas, strategies, research findings, materials and information
using publications, international conferences, and increasingly, this website.
IASE is the education section
of the International Statistical Institute (ISI), but may also be joined
independently by those who wish to participate in IASE’s activities, or simply
to support the work on improving statistics education and extending its
outreach[9].
In other explanation, Education Statistics is the science that
discuss or learn and develop principles
- principles, methods
and procedures to be used in the context of data
collection, presentation, analysis
of materials in the form of numeric information about
things - things related to education
and drawing conclusions, making of estimates in
the forecast and scientific[10].
3.
Classification
of Statistics
1)
Classification
Statistics For analysis method:
a)
Descriptive Statistics
Descriptive statistics is the science of statistics
relating to the activities of recording and summarizing the results of
observations of events or human characteristics, place and so on, quantitative,
or statistical study ways of collecting, and preparing, and presenting and
describing data has been collected to a study.
The activities included in this category, such as data
collection, data grouping, the determination of the value and statistical
functions, create graphs, diagrams and drawings. Records of births, deaths and
marriages per year are called statistics. Similarly descriptive regarding age,
education level, as well as enrich composition of the population living in an
area.
The main purpose of the operation of descriptive
statistics is easier for people to read and understand the meaning of data. The
scope includes descriptive statistics:
Ø The
frequency distribution
Ø Measurement
of central values (mean, mode, median and standard deviation), dispersion, skewers
and kurtosis.
Ø Presentation
of data in the form of graphs (histograms, polygons, ogive)
Ø Figures
Index
Ø The time
series or time series
b)
Inferential Statistics
Inferential statistics is the science that studies the
statistical procedures for drawing conclusions about the entire population
based on existing data (sample) or statistics relating to the activities of drawing
conclusions from the facts, and making decisions based on facts.
In the inferential statistic contain parameter
estimation, hypothesis testing, prediction and calculation of the degree of
association between variables. The scope of inferential statistics includes:
Ø Probability
Ø Data
Distribution
Ø Estimation
of parameters
Ø Test the
hypothesis included chi-square test and analysis of variance
Ø Regression
Analysis
Ø Correlation
Analysis
2)
Classification
of Statistics According to the How It Works:
In the inferential statistics / Inductive, various
statistical tests that can be used basically be divided into two groups, namely
the Test Statistic Parametric and Non-Parametric Test Statistics.
a)
Statistical Parametric
Parametric
Statistics is a statistical test that is already known in advance that the data
scale and ratio scale interval data, the distribution (distribution) that is
normally distributed data. When viewed from the amount of data, usually large
amounts of data, at least great than or equal to 30 data. The larger the data,
it will be close to normal assumptions.
b)
Non-Parametric Statistics
Non-Parametric Statistics is a statistical test of the
unknown distribution of data and need not normally distributed population where
quantities are not known or assumptions are required in the population (in
parametric statistics) are not met. Thus these statistics can be regarded as
statistical tests assume free[11].
4.
The Use and
The functions of Statistics in Education
A
function held by the statistics in the world of education is becoming a
tool in the teaching-learning process.
In assessing the activities
of the educational outcomes, an educator wearing
certain norms; The
norm is essentially a kind of size. The
assessment results are usually expressed in a variety of ways. But the most common way
is to put it
in the form of numbers (numbers). It is assessed itself is progress
or development of students as they
go through the process of education in a given
period of time. Actually is
qualitative, but converted into quantitative data. In
other words, the results of the
assessment conducted quantification. Quantification reason it is certainly
vary, but the
most important reason is to
make changes to the material information that is not
of a figure into the material particulars of the figures, educators will be able to be more straightforward to obtain an overview of the progress or development which
has been achieved by students, after
they undergo the
process of education. By using quantitative
data an education will be able to obtain
certainty, rather than using qualitative data. Because the educational
outcomes assessment activities most common way is to use the data quantitative.
An
important function as a tool, which
is a tool to process, analyzes,
and summarizes the results that have been achieved in the assessment activities.
For a professional
educator, statistics also has a sizable usability.
Because by the use of statistics as a tool, it
is based on the data that he
will be able to exact:
a.
Getting a picture, either
specifically or picture
a general description of a symptom, condition or
event.
b.
Following the development or tidal
regarding symptoms, circumstances
or events that,
from time to
time.
c.
Testing, if the symptoms are different from one another symptom or not. If
there are differences, whether those differences are significant differences or differences
occurred simply by chance alone.
d.
Know if the problem has to do with
one another symptom.
e.
Prepare a report in the form of quantitative data with regular,
clear and concise.
f.
Logically draw conclusions, make decisions accurately and steadily, and
can estimate or
predict things that may happen in the
future, and what concrete steps that may be performed by an educator[12].
B.
Statistics
Data
1.
Definition
of statistics data
Data statistic is something
that does not have any meaning for the recipient and is still in need of
a treatment. Data
may manifest a state, pictures, sounds, letters,
numbers, math, language or other symbols that
can be used as an
ingredient to look at the environment, objects, events, or a concept[13]. Then,
statistical data is a collection of
information or facts
that describes a problem.
Data is a
representation of real-world facts
that represent an object as a value that is recorded
in the form of numbers, letters,
symbols, text, images,
sounds or combinations
thereof[14].
Data can be defined as groups
of information that represent the qualitative or quantitative attributes of a
variable or set of variables, which is the same as saying that data can be any
set of information that describes a given entity. Data in statistics can be
classified into grouped data and ungrouped data.
Any data that you first gather
is ungrouped data. Ungrouped data is data in the raw. An example of ungrouped
data is a any list of numbers that you can think of.
In the statistics there is
also called as Grouped Data. Grouped data is data that has been
organized into groups known as classes. Grouped data has been 'classified' and
thus some level of data analysis has taken place, which means that the data is
no longer raw.
A data class is group of data
which is related by some user defined property. For example, if you were
collecting the ages of the people you met as you walked down the street, you
could group them into classes as those in their teens, twenties, thirties,
forties and so on. Each of those groups is called a class.
Each of those classes is of a
certain width and this is referred to as the Class Interval or Class
Size. This class interval is very important when it comes to drawing
Histograms and Frequency diagrams. All the classes may have the same class size
or they may have different classes sizes depending on how you group your data.
The class interval is always a whole number[15].
Below is an example of grouped
data where the classes have the same class interval.
|
Age
(years)
|
Frequency
|
|
0 - 9
|
12
|
|
10 - 19
|
30
|
|
20 - 29
|
18
|
|
30 - 39
|
12
|
|
40 - 49
|
9
|
|
50 - 59
|
6
|
|
0
- 69
|
Solution:
Below is an example of grouped
data where the classes have different class interval.
|
Age
(years)
|
Frequency
|
Class
Interval
|
|
0 - 9
|
15
|
10
|
|
10 - 19
|
18
|
10
|
|
20 - 29
|
17
|
10
|
|
30 - 49
|
35
|
20
|
|
50
- 79
|
2.
Kinds of
Statistics Data
When a given data set is numerical in nature, it is necessary to
carefully distinguish the actual nature of the variable being quantified.
Statistical tests are generally specific for the kind of data being handled.
1)
Data on a nominal (or categorical) scale
Identifying the true nature of numerals
applied to attributes that are not "measures" is usually
straightforward and apparent. Examples in everyday use include road, car,
house, and book and telephone numbers. A simple test would be to ask if
re-assigning the numbers among the set would alter the nature of the
collection. If the plates on a car are changed, for example, it still remains
the same car in reality.
2)
Data on an Ordinal Scale
An ordinal scale is a scale with ranks. Those ranks only have sense in
that they are ordered, that is what makes it ordinal scale. The distance [rank n]
minus [rank n-1] is not guaranteed to be equal to [rank n-1]
minus [rank n-2], but [rank n] will be greater than [rank n-1]
in the same way [rank n-1] is greater than [rank n-2] for all n
where [rank n], [rank n-1], and [rank n-2] exist. Ranks of
an ordinal scale may be represented by a system with numbers or names and an
agreed order.
We can illustrate this with a common example: the Likert scale. Consider
five possible responses to a question, perhaps Our president is a great man,
with answers on this scale
|
Response:
|
Strongly
Disagree
|
Disagree
|
Neither
Agree nor Disagree
|
Agree
|
Strongly
Agree
|
|
Code:
|
1
|
2
|
3
|
4
|
5
|
Here the answers are a ranked scale reflected in the choice of numeric
code. There is however no sense in which the distance between Strongly agree
and Agree is the same as between Strongly disagree and Disagree.
Numerical ranked data should be distinguished from measurement data.
3)
Measurement data
Numerical measurements exist in two forms, Meristic and continuous, and
may present themselves in three kinds of scale: interval, ratio and circular.
a.
Meristic or discrete
variables are generally counts and can take on only discrete values. Normally
they are represented by natural numbers. The number of plants found in a
botanist's quadrant would be an example. (Note that if the edge of the quadrant
falls partially over one or more plants, the investigator may choose to include
these as halves, but the data will still be meristic as doubling the total will
remove any fraction).
b.
Continuous
variables are those whose measurement precision is limited only by the
investigator and his equipment. The length of a leaf measured by a botanist
with a ruler will be less precise than the same measurement taken by
micrometer. (Notionally, at least, the leaf could be measured even more
precisely using a microscope with a gratitude.)
c.
Interval Scale
Variables measured on an interval scale have values in which differences are
uniform and meaningful but ratios will not be so. An oft quoted example is that
of the Celsius scale of temperature. A difference between 5° and 10° is
equivalent to a difference between 10° and 15°, but the ratio between 15° and
5° does not imply that the former is three times as warm as the latter.
d.
Ratio Scale
Variables on a ratio scale have a meaningful zero point. In keeping with the
above example one might cite the Kelvin temperature scale. Because there is an
absolute zero, it is true to say that 400°K is twice as warm as 200°K, though
one should do so with tongue in cheek. A better day-to-day example would be to
say that a 180 kg Sumo wrestler is three times heavier than his 60 kg wife.
e.
Circular Scale
When one measures annual dates, clock times and a few other forms of data, a
circular scale is in use. It can happen that neither differences nor ratios of
such variables are sensible derivatives, and special methods have to be
employed for such data.
C.
Collecting Statistic
Data
1.
Principles
of Collecting statistic Data
Data collection is the process
of gathering and measuring information on variables of interest, in an
established systematic fashion that enables one to answer stated research
questions, test hypotheses, and evaluate outcomes. The data collection
component of research is common to all fields of study including physical and social sciences, humanities, business, etc. While methods vary by discipline, the emphasis
on ensuring accurate and honest collection remains the same. The goal for all
data collection is to capture quality evidence that then translates to rich
data analysis and allows the building of a convincing and credible answer to
questions that have been posed.
Regardless of the field of
study or preference for defining data (quantitative, qualitative), accurate
data collection is essential to maintaining the integrity of research. Both the
selection of appropriate data collection instruments (existing, modified, or
newly developed) and clearly delineated instructions for their correct use
reduce the likelihood of errors occurring.
A formal data collection
process is necessary as it ensures that data gathered are both defined and
accurate and that subsequent decisions based on arguments embodied in the
findings are valid.[2] The process provides both a baseline from which to measure and in certain
cases a target on what to improve.
Consequences from improperly
collected data include: Generally there are three types of data collection and
they are:
1)
Surveys:
Standardized paper-and-pencil or phone questionnaires that ask predetermined
questions.
2)
Interviews:
Structured or unstructured one-on-one directed conversations with key
individuals or leaders in a community.
3)
Focus
groups: Structured interviews with small groups of like individuals using
standardized questions, follow-up questions, and exploration of other topics
that arise to better understand participants.
ü Inability to answer research questions accurately.
Distorted findings result in wasted resources and can mislead other
researchers to pursue fruitless avenues of investigation. This compromises
decisions for public policy, and causes harm to human participants and animal subjects.
2.
The Way of
Collecting Statistics data
As we have seen in the
definition of statistics, data collection is a fundamental aspect and as a
consequence, there are different methods of collecting data which when used on
one particular set will result in different kinds of data. Let's move on to
look at these individual methods of collection in order to better understand
the types of data that will result.
1)
Census Data
Collection
Census data collection is a
method of collecting data whereby all the data from each and every member of
the population is collected.
For example, when you collect
the ages of all the students in a given class, you are using the census data
collection method since you are including all the members of the population
(which is the class in this case).
This method of data collection
is very expensive (tedious, time consuming and costly) if the number of
elements (population size) is very large. To understand the scope of how
expensive it is, think of trying to count all the ten year old boys in the
country. That would take a lot of time and resources, which you may not have.
2)
Sample Data
Collection
Sample data collection, which
is commonly just referred to as sampling that is a
method which collects data from only a chosen portion of the population.
Sampling assumes that the
portion that is chosen to be sampled is a good estimate of the entire
population. Thus one can save resources and time by only collecting data from a
small part of the population. But this raises the question of whether sampling
is accurate or not. The answer is that for the most part, sampling is
approximately accurate. This is only true if you choose your sample carefully
to be able to closely approximate what the true population consists of.
Sampling is used commonly in
everyday life, for example, all the different research polls that are conducted
before elections. Pollsters don't ask all the people in a given state who
they'll vote for, but they choose a small sample and assume that these people
represent how the entire population of the state is likely to vote. History has
shown that these polls are almost always close to accuracy, and as such
sampling is a very powerful tool in statistics.
3)
Experimental
Data Collection
Experimental data collection
involves one performing an experiment and then collecting the data to be
further analyzed. Experiments involve tests and the results of these tests are
your data.
An example of experimental
data collection is rolling a die one hundred times while recording the outcomes.
Your data would be the results you get in each roll. The experiment could
involve rolling the die in different ways and recording the results for each of
those different ways.
Experimental data collection
is useful in testing theories and different products and is a very fundamental
aspect of mathematics and all science as a whole.
4)
Observational
Data Collection
Observational data collection
method involves not carrying out an experiment but observing without
influencing the population at all. Observational data collection is popular in
studying trends and behaviours of society where, for example, the lives of a
bunch of people are observed and data is collected for the different aspects of
their lives.
Based Pros and Cons, Each method of data collection has advantages
and disadvantages.
1)
Resources.
When the population is large,
a sample survey has a big resource advantage over a census. A well-designed
sample survey can provide very precise estimates of population parameters -
quicker, cheaper, and with less manpower than a census.
2)
Generalizability
Generalizability refers to the
appropriateness of applying findings from a study to a larger population.
Generalizability requires random selection. If participants in a study are
randomly selected from a larger population, it is appropriate to generalize
study results to the larger population; if not, it is not appropriate to
generalize.
Observational studies do not
feature random selection; so generalizing from the results of an observational
study to a larger population can be a problem.
3)
Causal
inference
Cause-and-effect relationships
can be teased out when subjects are randomly assigned to groups. Therefore,
experiments, which allow the researcher to control assignment of subjects to
treatment groups, are the best method for investigating causal relationships.
3.
The tool of
Collecting Data
Among the tools that
can be used in the educational
work of collecting statistical data can be
pointed out here for example:
a.
List or check (check list)
b.
A graduated scale (Rating Scale)
c.
Guidelines for the interview (interview gulde)
d.
Questionnaire (list of questions that every
question has been resolved in the answer
to select or
provide a place to fill in the answer[16].
REFERENCES
Moses, Lincoln E. (1986) Think and Explain
with Statistics, Addison-Wesley, ISBN 978-0-201-15619-5 . pp. 1–3
Dr.H Agus Irianto,(2004)Statistik(Konsep dasar, Aplikasi, dan Pengembangannya),
Jakarta, Kencana.
Hays, William Lee, (1973) Statistics for the Social Sciences, Holt,
Rinehart and Winston, p.xii, ISBN 978-0-03-077945-9
http://en.wikipedia.org/wiki/Statistics (was taken on december, 04, 2014)
http://arlingsapri.blogspot.com/2014/03/pengertian-statistik-pendidikan.html
Moses, Lincoln E. (1986) Think and Explain
with Statistics, Addison-Wesley, ISBN 978-0-201-15619-5 . pp. 1–3
Dr.H
Agus Irianto,(2004)Statistik(Konsep dasar, Aplikasi, dan Pengembangannya),
Jakarta, Kencana.
ChairpersonDr. J. Jothikumar,(2005),Statistik Higher secondary-first
year,Tamilnadu, Governman
http://en.wikipedia.org/wiki/Statistics_education ( Nonember, 04,2014)
Journal of statistics education, 2014, Statistics
Education Web (STEW), North washington, American statistical education.
http://iase-web.org/ Journal International Association for
statistical education,
http://yuni-elf.blogspot.com/2012/12/tugas-ii-statistik.html
http://yuni-elf.blogspot.com/2012/12/tugas-ii-statistik.html
Hays, William Lee, (1973) Statistics for the
Social Sciences, Holt, Rinehart and Winston, p.xii, ISBN 978-0-03-077945-9
http://fisikaiain2010.blogspot.com/2012/06/vbehaviorurldefaultvmlo_15.html (November, 12, 2014)
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