COLLECTION AND PRESENTATION OF DATA
Types of data :
1.
Qualitative data are categorical
data taking the form of attributes or categories such as sex, course, race,
religion, blood type, etc. This type of
data can only be categorized but cannot be quantified.
2.
Quantitative
data
or numerical data are obtained from measurements like weights, ages, heights,
temperatures, score and other measurable quantities.
Measurement is a process to
convert qualitative data to quantitative data. By measurement, numbers are used
to code objects or items so that they can be treated statistically.
Measurement
scales
1.
Nominal
measurement
is used merely for identification or classification purposes.
Example. A group
of students maybe classified according to their courses:
1 – BSED 4
– BSBA 7 – BSIS
2 – BEED
5 –
BSIT 8
– BSA
3 – BSCS 6
– BSN 9
– BSCpE
2.
Ordinal
measurement.
The ordinal measurement does not only classify items but also give the order or
rank of classes, items or objects.
Example. a) Ranks as 1st, 2nd, 3rd in an oratorical contest
b) Ranks as 1st, 2nd, 3rd in a poster making contest
3.
Interval
measurement.
In the interval measurement, numbers assigned to the items or objects not only
identify and rank the objects but also measure the degree of differences
between two classes.
Example. Height, mass, temperature, score
a)
If Jay has a mass of 48 kg and Claire is 54 kg, the mass difference of 6 kg implies
that Claire is 6 kg heavier than Jay.
b)
If
water from the faucet is 22 degrees Celcius, and that coming from the well
is 27 degrees Celcius, the temperature
difference of 5 degrees implies that water from the well is warmer than the
water from the faucet.
c)
If John has a height of 5’ 8” and
Jim stands 5’ 4”, then the
difference of 4 inches implies that John is taller than Jim by 4 inches.
4.
Ratio
measurement. For ratio measurement, the ratio of the
numbers assigned in the measurement reflects the ratio in the amount of
property being measured. Multiplication and division have meaning in ratio
measurements.
Thus, if Rezzie is 18 years old and Stephen is 24 years old, then their
ages can expressed
in the ratio of 3 : 4.
If a motorcycle moves 80 km/hr and a car moves with a speed of 100 km/hr, then their
speeds can be expressed in the ratio of
4 : 5.
SAMPLING TECHNIQUES
Sampling
techniques
are use to ensure the validity of conclusions or inferences from the sample to
the population.
Common types of sampling techniques:
1. Simple random sampling
2. Stratified random sampling
3. Systematic random sampling
4. Cluster sampling
5. Multi-stage sampling
Samples can either be a Judgment sample, Convenience sample or a Random
sample.
* Judgment
sample
is one in which the individual selecting the sample items uses experience as
the basis for choosing the items to be included in the sample with the
objective to make the sample as representative of the population as possible.
An example is an auditor who chooses only few records necessary for sample
audit base on the judgment that these records are representative of the records
in general.
* Convenience
sample
includes the most easily accessible measurement or observations. An example is
taking an opinion poll from students passing by the Plaza Madonna entrance
gate.
* Random
sample
is a sampling procedure by which every element in the population has a known
and usually equal chance of being chosen for inclusion in the sample.
* Simple random sampling.
A
random sample has limited number of individuals chosen from the population.
Before the selection is done every individual has an equal chance of being
selected in the sample.
Lottery is the simplest method of random sampling. To illustrate the process,
consider a population of 356 CITE students. Obtain a coded or numbered list of
all the students. Write the numbers or codes in a small slip of paper, roll the
papers and place in a container. Jumble it thoroughly; and without looking at
the slip of papers draw, i.e. 160 slips representing 160 students, the desired
sample size. The process ensures a representative sample because each item has
the same chance of getting into the sample.
If the population is large, the table of random numbers can be used.
This allows us to select the desired sample on a purely chance basis.
1.
Identify
the population and determine the sample size.
2.
Make
a list of all members of the population and number them consecutively from zero
to the last number of the population.
3.
Using
the table of random number, point at any number without looking at the table.
Since the code numbers is composed of 3 digits, just look at the last three
digits of the number pointed out in the table. If the last three digits is a
number in the list, then the member corresponding to that number is selected to
be included in the sample.
4.
Using
this number as reference, read the table horizontally whether to the left or to
the right; or vertically up or down or diagonally. Continue recording those
numbers found in the population ignoring those numbers which are not found. Discard
duplicate numbers and continue until the required sample size is completed.
*
Stratified Random sampling
- is used to avoid biasedness. This
sampling technique is done by dividing the population into categories or strata
and drawing the members to be included in the sample at random proportionate to
its stratum or subgroup. T select a stratified random sample, the researcher
must possess a clear understanding of the problem in order to determine the
strata into which the population should be divided.
Example. a) A college has a
population of 2000 students of which 1200 are females and 800 are males. Here,
the strata is the male and the female group of students. After the categories or strata have been
determined, a random sample is selected from each stratum which is proportional
to its sample size. This avoids the error of selecting too few or too many
members from each stratum. A sample of 400 students is required. To obtain a sample proportional to the given
members in each stratum, compute first for the proportion of the sample to the
population. Then multiply the result to the number of males and to the number
of females.
400/2000 = 0.20
( 0.20 ) * ( 1200 ) = 240 females in the sample
( 0.20 ) * ( 800 ) = 160
males in the sample
The last step is to draw the required
random sample size of 400 students either by lottery or by the use of table of
random numbers from the 240 females and 160 males.
*
Systematic random sampling
- is a process of selecting every nth element of the
population until the desired sample size is obtained. The members or elements
maybe arranged alphabetically or in any systematic fashion. To obtain n, divide
the population size by the sample size. In the above example, 2000/400 = 5,
which implies that every 5th element of the given population is
chosen to be included in the sample.
To know where to start from the
population list, use the table of random numbers. Without looking, point at any
number in the table and get the last digit. Supposed that the last digit in the
number pointed is 3, it means that the 3rd member in the list is
included. From the number 3, take every 5th element in the
population as belonging to the sample. This means in the list 3, 8, 13, 18, 23,
28, 33, 38, 43, 48, 53, etc. are included in the sample.
*
Cluster sampling
Cluster is an intact group
possessing common characteristics.
Cluster sampling is an advantageous procedure if the population is
spread out over a wide geographical area. It is also a practical sampling
technique used if the complete list of members of the population is not
available. An example is a population consisting of 600 teachers in the 30
public schools of Midsayap. To illustrate how the desired sample size of 140
teachers could be selected from the given population, the steps are as follows :
1. Prepare a list of the cluster comprising the
population and determine the sample size. The logical cluster is by school.
Prepare a list of all the 30 public schools.
2. Estimate the average number of
members per cluster in the population. Assume that the average number of
teachers per school is 20.
3. Divide the required sample
size by the average number of teacher per cluster to get the number of clusters
to be selected. Since, the sample size is 140 and the average teacher per
school is 20, the number of clusters shall be : 140/ 20 = 7
4. Select the needed number of
clusters. By using the table of random numbers, select the 7 public schools
from the 30 population schools. Include all the members in the selected
clusters. Since there is an average of 20 teachers per school, and 7 clustered
school, the sample size of 140 teachers is completed.
Summary :
Number of public schools : N = 30
Average number of
teachers per school : x = 20
Desired sample size : n = 140
Required
cluster : y = n/x = 140/20 = 7
Hence, there are 7 clusters.
*
Multi stage sampling
This
is a more complex sampling technique which involves the following steps :
1. Divide the population into
strata.
2. Divide each stratum into
clusters.
3. Draw a sample from each
cluster using the simple random sampling technique.
To illustrate, take a random sampling of
all first year high schools in the island of Mindanao. Mindanao is divided into
6 regions which forms our stratum. From each stratum, we choose a private and a
public high school which again forms a stratum. From these public and private
high school, we select first year high school classes forming our clusters.
From these clusters, we select first year students from each class by using the
simple random sampling technique.
METHODS OF COLLECTING DATA
There are several methods of collecting
data. There is however, no best method to obtain the desired information under
investigation. The choice of appropriate methods to be used depends on the
following factors :
1.
Nature
of the problem.
2.
The
population under investigation, and
3.
The
time and the material factors.
The
methods of collecting data are :
1.
The
direct interview method
2.
The
indirect or questionnaire method.
3.
The
registration method, and
4.
Other
methods such as;
a)
Observation
b)
Telephone
interview
c)
Experiments
*
The direct or interview method
This is considered as one of the most effective methods of collecting
original data. To obtain accurate responses, the maybe conducted by
well-trained interviewers. The interviewers maybe of great help to the
respondents in answering questions which the respondents could not understand.
Advantages
of the interview
method
1.
It
can give complete information needed in the study.
2.
It
can yield precise and consistent information since the interview can
immediately clarify any misinterpretation made by the respondents.
Limitations
of the interview
1. It is more expensive and time
consuming.
2. It may yield inaccurate
information since the interviewer can
influence the respondent’s
through his facial expression, tone
of voice or wording the question.
3. The interviewer may cheat by turning in dishonest responses if their
expected or desired responses
are not obtained.
* Indirect
or Questionnaire method
- is one of the earliest method of
data gathering. It takes time to prepare because questionnaires need to be
attractive. It can include illustrations, pictures and sketches. Its content
especially the instructions, must be precise, clear, and self-explanatory.
Advantages
of the questionnaire method
1.
It
is less expensive since questionnaires can be distributed personally or by
mail.
2.
It
is less-time-consuming since it can be distributed over a wider geographical
area in a shorter time.
3.
It
can give confidential responses since the respondents can answer the
questionnaire privately.
4.
The
answers obtained are free from any influence from the interviewer.
Limitations
of the questionnaire method
1.
It
cannot be accomplished by illiterates.
2.
It
has a high proportion of non-response or non-return.
3.
It
tends to yield wrong information since answers cannot be corrected right away.
4.
It
tends to give incomplete information.
* The Registration method
By registration method, the respondents give information in compliance
with certain laws, policies, rules, regulations, decrees or standard practices.
Data which can be collected by registration method are as follows : marriage
contracts, birth certificates, motor vehicle registration, license of firearms,
registration of corporations, real estates, voters, etc.
Other
methods
:
* Observation method is used to gather
data regarding attitudes, behaviour, values, and cultural pattern of the sample
under investigation.
*
Telephone interview are
employed if the questions to be asked are brief and few. An example is the
checks made on listeners to certain radio programs, like asking what programs
his radio is turned on to. This method is used to find the most popular Radio
or TV programs.
*
Experiment is employed to
collect data if the investigator wishes to control the factors affecting the variables being studied. An example is when the researcher wants to
determine the different factors affecting the academic performance of the
students such as IQ methods or approaches used in teaching.
METHODS
OF PRESENTING DATA
1.
Textual
or Textular method
2.
Tabular
method
3.
Semi-tabular
method
4.
Graphical
method
*
Textual presentation – the
data is presented in paragraph form. The reader gets information by reading the
gathered data in the paragraph.
*
Tabular presentation – the
data is presented in rows and columns. This is more effective way of showing
relationships or comparison of numerical data. It gives more precise,
systematic and orderly presentation of data in rows and columns. This method
makes comparison of figures easy and comprehensible.
*
Semi-tabular presentation –
employs both the textual and the tabular methods. This method is used only if
there are a few figures to be tabulated. The tables are followed by narrative
explanations to make he facts more understandable.
*
Graphical presentation. The
use of graphs is the most effective method of presenting statistical results or
findings. It gives the relationship of data in pictorial form. Presentation of
facts are made attractive and meaningful especially if colors are made and
pictures re used, making it easy for important information to be grasped by the
reader.
** Advantages of Graphical presentation
1.
Graphs
enable students, readers and the busy executive to easily understand the
essential facts that numerical data intend to convey. Private and government agencies
use charts and graphs in their reports.
2.
They
can easily attract attention and are more readily understood. It is easier to
go through graphs than through quantitative data.
3.
Graphs
simplify concepts that would otherwise have been expressed in so many words.
** Limitations of graph
1. Graphs are not as precise as tables.
2. Graphs require more skill and time to
prepare.
3. Graphs can only be made after the data have
been presented in tabular form.
Parts
of a Statistical Table
1. Table heading – consist of a
table number and the title.
2. Stub – are found at the left
side of the body of the table which are categories or
classifications.
3. Box head – The box head
identifies what are contained in the column. Included in the Box
head are the stub head, master caption and column caption.
4. Body – main part of the table.
This contains the substance or the figures of one’s data.
Table number
Title
Stub
Head
|
Master Caption
|
||
Column Caption
|
Column Caption
|
Column Caption
|
|
Row Caption
|
|||
Row Caption
|
|||
Row Caption
|
B O D Y
|
of the
|
Table
|
Row Caption
|
|||
Row Caption
|
|||
Footnote
Source of data
Example
Table 1.1
College Student Population of XYZ University
S. Y. 2007 – 2012
School Year
|
BSCS*
|
BSIT*
|
BSED*
|
BEED*
|
BSBA*
|
AS*
|
BSN*
|
2007 – 2008
|
75
|
150
|
45
|
60
|
290
|
130
|
56
|
2008 – 2009
|
70
|
140
|
34
|
50
|
285
|
108
|
45
|
2009 – 2010
|
50
|
120
|
30
|
45
|
270
|
62
|
34
|
2010 – 2011
|
48
|
85
|
28
|
43
|
225
|
48
|
23
|
2011 – 2012
|
30
|
75
|
22
|
38
|
213
|
44
|
18
|
*
Summer enrolment is not included
Source of data : Registrar’s Office
TYPES OF GRAPHS COMMONLY USE
1.
Linear graph ( Line graph )
2. Bar graph
3.
Hundred percent
chart
( Pie chart or Circle graph )
4.
Pictogram ( Pictograph )
5. Statistical maps
*
Linear graph is a practical
device uniquely suited to portray changes in values effectively over successive
periods of time. Variations in the data are indicated by the variation in the
movement of linear curves.
** Advantages of linear graph
1.
The
curves shows data as a continuous line; hence, it is continuous in its effect.
2.
The
wandering line of the curve tells the whole story. At a glance one can see just
what the situation is and what is likely to happen.
3.
Its
preparation requires less time and skill.
* Bar
graph – is one of the most common and widely used graphical devices. This
consists of bars of equal width either all vertical or all horizontal. The
length of each bar represents the frequency of each class. The bars must be of
the same width and is arbitrary. The space between bars is about one-half of
the width of the bars itself.
*
Pie chart ( circle graph ) –
is use to represent quantities that make up a whole. It consists of a circle
subdivided into sectors which look like pieces of a pie whose sizes are
proportional to the magnitudes or percentages they represent. The pie chart
aims to show per cent distribution of a whole into its component parts.
** Construction of a Pie chart
1.
Express
each component part as a certain per cent of the whole and multiply the result
by 3.6 since 1 % of the circumference is
equal to 3.6 degrees.
2.
Mark
off the desired number of degrees on the circumference of the circle using a
protractor; connect this points to the center of the circle in order to produce
pie-shaped areas which make-up the whole circle.
3.
Label
the various segments horizontally whenever possible with the percentages
indicated.
4.
Arrange
the sector clockwise according to size.
5.
Use
cross-hatching, coloring, shading, etc. to increase the effectiveness of a pie
chart.
6.
Avoid
overloading the chart by showing too many categories; simplicity is a
fundamental characteristics of all charts.
*
Pictogram ( pictograph )
An excellent device for portraying data is by means of pictures or
symbols. Its chief purpose is to catch the reader’s attention to convey to him
in a vivid manner basic numerical facts. It does not attempt to show details;
it simply tries to facilitate comparison of approximate quantities.
The symbol or picture should suggest the nature of the data being
presented. For instance
a) corn production can be
represented by a picture of a sack of corn;
b) truck
importation can be represented by a picture of a truck;
c) population in
one’s place can be represented by a person, etc.
*
Statistical maps
One of the best ways to present data is through statistical maps. A map can be drawn and divided into desired
regions. Each region maybe distinguished from the other by use of shades, dots
or cross-hatching. A statistical map is always accompanied by a legend which
tells the meaning of the lines, colors or other symbols used.
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