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7/27/2019 learning task 2 final.docx
1/12
De La Salle University2401 Taft Avenue, Manila 1004
Science Education Department
College of Education
Statistics for Science Education SCE500M
Roxanne Diane R. Uy Learning Task 2 2ND TERM S.Y.2013-2014
A statistical analysis, properly conducted, is a delicate dissection of uncertainties, a
surgery of suppositions. ~M.J. Moroney
QUESTIONS
1.
a. What is statistics?
The word statistics was derived from the Italian word statistica meaning statesman. This
was first used by Gottried Achenwall in 1749 (Parcel, 1966). But Achenwalls meaning of
statistics is not what it is today.
Today, statistics is defined in three meanings, namely; singular, plural, and general. In its
singular sense, the word statistics refers to the branch of mathematics which deals with the
systematic collection tabulation, presentation, analysis, and interpretation if quantitative
data, which are collected in a methodical manner without bias.
In its plural sense, statistics means a set of quantitative data or facts.
Generally, statistics is divided into statistical methods and statistical theory or
mathematical statistics. Statistical methods refer to those procedure and techniques used in
the collection, presentation, analysis and interpretation of quantitative data. Likewise,
statistical theory or mathematical statistics deals with the development and exposition of
theories which constitutes the bases of the statistical methods (Parcel, 1966)
Calmorin & Calmorin (1997) referred to it as the tool of all sciences and the language of
research.
To sum up, statistics is a scientific body of knowledge that deals with the collection,
organization or presentation, analysis and interpretation of data. (Acelajado, Blay, &
Belecina, 1999)
7/27/2019 learning task 2 final.docx
2/12
De La Salle University2401 Taft Avenue, Manila 1004
Science Education Department
College of Education
Statistics for Science Education SCE500M
Roxanne Diane R. Uy Learning Task 2 2ND TERM S.Y.2013-2014
b.Why is there a need to study statistics?
There is a need to study statistics due to its application to various fields and discipline like
business, education, psychology, politics and government, medicine, agriculture,
entertainment, in our everyday life. (Acelajado et al., 1999)
A knowledge of statistics is essential for both understanding and conducting research in
any of the health professions according to Polit & Beck (2006). Statistics can be used to
analyze the data and help decide if the new idea is worthy of being incorporated into ones
life because fact and fiction can be discriminated.
In 1997, Calmorin & Calmorin identified 4 functions of statistics: 1.) To provide
investigators means of measuring scientifically the conditions that may be involved in a
given problem and assessing the way in which they are related. 2.) To show the laws
underlying facts and events that cannot be determined by individual observations. 3.) To
show relations of cause and effect that otherwise may remain unknown. 4.) To find out
trends and behavior in related conditions which otherwise may remain ambiguous.
c. What is the role of statistics in the field of educational research?
Zieffler, Garfield, Alt, Dupuis, Holleque, & Chang (2008) pointed out that education
research, being an interdisciplinary field of inquiry, relied on various research questions,
methodologies, and outcome variables studied. Participants in the studies have ranged from
young children to high school and college students to research professionals. It is evident
that there are different theoretical and research backgrounds for the studies, differentresearch methods as well as different foci for the studies.
Another area of research is in the development of student assessments that provide valid
and reliable measurements on important student outcomes such as statistical reasoning or
thinking. (National Research Council, 2001)
7/27/2019 learning task 2 final.docx
3/12
De La Salle University2401 Taft Avenue, Manila 1004
Science Education Department
College of Education
Statistics for Science Education SCE500M
Roxanne Diane R. Uy Learning Task 2 2ND TERM S.Y.2013-2014
With the above being said, Calmorin & Calmorin (1997) performs the following roles in
research: permits the most exact kind of description, forces the researchers to be definite
and exact in his procedures and in his thinking, enables the researcher to summarize results
in a meaningful and convenient form, enables the researcher to draw general conclusions:
the process of extracting conclusions is carried out according to accepted rules, enables the
researcher to predict how much of a thing will happen under conditions he knows and
has measured.
2. Compare and contrast the following
a. population and sample
A population is a set of persons (or objects) having a common observable, defining
characteristic. (Acelajado et al., 1999; Polit & Beck, 2006). Thorndike & Dinnel (2001)
definedpopulation as a set of all people or objects to which, one wish to generalize the
conclusions by applying statistical methods. Population is theoretically an infinitely large
group. (Welkowitz, Ewen, & Cohen, 1976).
Sample is a small portion or part of a population drawn from a specified population
(Welkowitz et al., 1976), which could also be defined as a subgroup, subset, or
representative of a population. (Acelajado et al., 1999; Polit & Beck, 2006;Thorndike &
Dinnel, 2001)
b. quantitative data and categorical data
Quantitative data are data which are numerical in nature. These are data obtained from
counting or measuring. In addition, meaningful arithmetic operations can be done with thistype of data because it has Numeric information such as actual values of the study
variables. (Acelajado et al., 1999; Polit & Beck, 2006). Test scores, length, weight and
height are quantitative data.
Categorical data (also referred to as frequency or qualitative data) are data which can
7/27/2019 learning task 2 final.docx
4/12
De La Salle University2401 Taft Avenue, Manila 1004
Science Education Department
College of Education
Statistics for Science Education SCE500M
Roxanne Diane R. Uy Learning Task 2 2ND TERM S.Y.2013-2014
assume values that manifest the concept of attributes, having a narrative description. Data
falling in this category cannot be subjected to meaningful arithmetic operations. They
cannot be added, subtracted, or divided. Things are grouped according to some common
property(ies) and the number of members of the group are recorded. Gender and nationality
are qualitative data. (Acelajado et al., 1999; Polit & Beck, 2006 )
c. descriptive statistics and inferential statistics
Descriptive statistics is a statistical procedure concerned with describing the characteristics
and properties of a group of persons, places, or things. (Acelajado et al., 1999).
Descriptive statistics deals with the enumeration, organization, and graphical representation
of data. (Kuzma & Bohnenblust, 2004). It is used to synthesize and describe data such as
averages and percentages. They are useful for summarizing data. Polit & Beck, 2006 )
Descriptive statistics are procedures for summarizing a body of information into one or a
few numbers. (Thorndike & Dinnel, 2001)
Inferential statistics is a statistical procedure that is used to draw inferences or information
about properties or characteristics by a large group of people, places, or things on the basis
of the information obtained from a small portion of a large group. (Acelajado et al., 1999).
Based on the laws of probability and mathematical and logical principles, they provide a
means for drawing conclusion about a population, given data from a sample, generalizing
from the specific. (Kuzma & Bohnenblust 2004; Polit & Beck, 2006; Thorndike & Dinnel,
2001)
d. research hypothesis and statistical hypothesisStatistical hypotheses, or null hypotheses, state that there is no relationship between the
independent variables and dependent variables. (Polit & Beck, 2006). It shows equality
or no significant differences or relationship between variables. (Acelajado et al., 1999).
Null hypothesis H0, is the hypothesis to be tested which one hopes to reject because it is a
7/27/2019 learning task 2 final.docx
5/12
De La Salle University2401 Taft Avenue, Manila 1004
Science Education Department
College of Education
Statistics for Science Education SCE500M
Roxanne Diane R. Uy Learning Task 2 2ND TERM S.Y.2013-2014
denial phenomenon when there is no difference at all among the variables. It is
formulated for the purpose of being rejected. (Calmorin & Calmorin, 1997)
Research hypothesis, also referred to as alternative, substantive or scientific hypotheses,
are statements of actual expected relationships between variables. All hypotheses
presented thus far are research hypotheses that indicate researchers true expectations.
(Polit & Beck, 2006). Alternative hypothesis generally represents the idea which the
researcher wants to prove. (Acelajado et al., 1999). The alternative hypothesis is an
affirmative existence of an observed phenomenon. It established the statement of
acceptance if the null hypothesis is rejected. (Calmorin & Calmorin, 1997)
3. Describe the four levels of measurement scales. Give at least one example for each level.
Nominal measurement, the lowest or most primitive level, involves using numbers
simply to categorize attributes. The numbers assigned in nominal measurement do not
have quantitative meaning. It provides information only about categorical equivalence
and nonequivalence and so the numbers cannot be treated mathematically. Examples are
qualitative variables such as zip code, hair color, gender, blood type, name of college or
university. (Acelajado et al., 1999; Kuzma & Bohnenblust 2004; Polit & Beck, 2006)
Ordinal measurement ranks objects based on their relative standing on an attribute.
Ordinals represent an ordered series of relationships. (e.g., first, second, third, and so
on). When objects are measured in this level, one can say that one is better or greater
than the other . It does not, however, tell us how much greater one level is than another.
As with nominal meaures, the mathematical operations permissible with ordinal-level arerestricted. In the ordinal level of measurement, data are arranged in some specified rank
or order. , but we cannot tell how much more or how much less of the characteristic one
object has than the other. The ranking of contestants in a beauty contests, of siblings in
the family, or of honor students in the class, the five leading causes of death are all in the
ordinal scale. (Acelajado et al., 1999; Kuzma & Bohnenblust 2004; Polit & Beck, 2006)
7/27/2019 learning task 2 final.docx
6/12
De La Salle University2401 Taft Avenue, Manila 1004
Science Education Department
College of Education
Statistics for Science Education SCE500M
Roxanne Diane R. Uy Learning Task 2 2ND TERM S.Y.2013-2014
Interval measurement occurs when researchers can specify ranking of objects on an
attribute and the distance between those objects. Most educational and psychological
tests are based on interval scales. For example, the Stanford-Binet Intelligence Scale-a
standardized intelligence (IQ) test used in many countries-is an interval measure.
Interval scales expand analytic possibilities because they convey information not only
about order but also about magnitudes of differences: Interval-level data can be averaged
meaningfully, for example. Many sophisticated statistical procedures require interval
measurements. (Acelajado et al., 1999; Kuzma & Bohnenblust 2004; Polit & Beck,
2006)
Ratio measurement is the highest level of measurement. Ratio scales, unlike interval
scales, have a rational, meaningful zero, therefore provide information about the absolute
magnitude of an attribute. Many physical measures, are ratio measures with a real zero.
A persons weight, for example, is a ratio measure. The statistical procedures suitable for
interval data are also appropriate for ratio-level data. (Acelajado et al., 1999; Kuzma &
Bohnenblust 2004; Polit & Beck, 2006). Thus, ratio scales provide the most
sophisticated measurement and are found in the most well-developed sciences.
(Thorndike & Dinnel, 2001)
4. What are the most commonly used measures of central tendency? Describe each.
Mean is equal to the sum of all values divided by the number of
participants/measurements-what people refer to as the average. It is the most frequently
used measure of central tendency because it is the most generally recognized measure; it
is also easily calculated. It is the appropriate measure when the data are in the interval orratio scale. Also, it is the best measure for regular distribution, since it provides
reliability and stability by having the least probable error. However, it is easily
influenced by extreme values because all values contribute to the average. It does not
supply information about the homogeneity of the group, thus, the more homogenous the
set of observations or group of individuals is, the less satisfactory is the mean as measure
7/27/2019 learning task 2 final.docx
7/12
De La Salle University2401 Taft Avenue, Manila 1004
Science Education Department
College of Education
Statistics for Science Education SCE500M
Roxanne Diane R. Uy Learning Task 2 2ND TERM S.Y.2013-2014
of central tendency. (Acelajado et al., 1999; Calmorin & Calmorin,1997; Kuzma &
Bohnenblust 2004; Polit & Beck, 2006; Thorndike & Dinnel, 2001).
Median is the point in a distribution that divides scores in half. It is the middle point
value on the score scale of a given set of measurements, provided that the values or
measurements are arranged in an array (arrangement of values in increasing or decreasing
order). It is the most appropriate measure for interval data and is the best measure when
the distribution is irregular or skewed. However, its position is not stable if the data do
not cluster at the center of the distribution. It also does not lend itself to algebraic
manipulation. Thus, it has a larger probable error than the mean. (Acelajado et al., 1999;
Calmorin & Calmorin,1997; Kuzma & Bohnenblust 2004; Polit & Beck, 2006;
Thorndike & Dinnel, 2001).
Mode is the number that occurs most frequently in a distribution. It is the most
appropriate measure of central tendency when the data are in nominal scale. It is the least
reliable among the three measures of central tendency because its value is undefined in
some distribution. It does not lend itself any algebraic manipulation, which makes it
inapplicable to a small number of cases when the values may not be repeated and is
inapplicable to irregular distribution. However, it is simple to approximate, does not
necessitate the arrangement of values, and is always the real value since it does not fall
on zero. It is the quick approximation of the average, referred to as an inspection
average. (Acelajado et al., 1999; Calmorin & Calmorin,1997; Kuzma & Bohnenblust
2004; Polit & Beck, 2006; Thorndike & Dinnel, 2001).
5. How is the arithmetic mean affected when each raw data is
(a)added with constant value?
(b)multiplied by a constant value?
Provide proof/justification to your answer
7/27/2019 learning task 2 final.docx
8/12
De La Salle University2401 Taft Avenue, Manila 1004
Science Education Department
College of Education
Statistics for Science Education SCE500M
Roxanne Diane R. Uy Learning Task 2 2ND TERM S.Y.2013-2014
A linear transformation of a data set is one where each element is increased by or
multiplied by a constant.
In addition, if a constant c is added to each member of a set, the mean will be c more than
it was before the constant was added; this can be proved by letting be the mean, before
adding c, and t be the mean after the transformation. Finally, let the original set be {a1,
a2, . . . , an}, so that the transformed set is {a1 + c, a2 + c, . . . , an + c}.
t = (a1 + c) + (a2+ c) + + (an + c) a1 + a2+ + an + n.c
n = nt = a1 + a2+ + an cn
n + n = + c
Another type of transformation is multiplication. If each member of a set is multiplied by
a constant c, then the mean will be c times its value before the constant was multiplied;
Using the same notation as before, the equation would be:
t = (a1c) + (a2c) + + (anc) (a1 + a2+ + an) .c
n = nt = a1 + a2+ + an . c
n = . c
To give an example, let us refer to the following table:
Data Mean Mode Median
Original Data Set:6, 7, 8, 10, 12, 14, 14, 15, 16,
2012.2 14 13
Add 3 to each data value
9, 10, 11, 13, 15, 17, 17, 18,
19, 23 15.2 17 16
Multiply 2 times each data
value
12, 14, 16, 20, 24, 28, 28, 30,
32, 4024.4 28 26
7/27/2019 learning task 2 final.docx
9/12
De La Salle University2401 Taft Avenue, Manila 1004
Science Education Department
College of Education
Statistics for Science Education SCE500M
Roxanne Diane R. Uy Learning Task 2 2ND TERM S.Y.2013-2014
When added: Since all values are shifted the same amount, the measures of central tendency all
shifted by the same amount. If you add 3 to each data value, you will add 3 to the mean, mode
and median.
When multiplied: Since all values are affected by the same multiplicative values, the measures
of central tendency will feel the same affect. If you multiply each data value by 2, you will
multiply the mean, mode and median by 2.
6. A class Methods of Research consisting of 34 students were given a 20-pt quiz. The
scores are given below:
Female Male
8 10 20 14 13 17 17 12 14 14
9 12 10 9 18
10 10 13 10 14 15 8 17 14 15 13
17 16 8 18 14 6 16 10
Formulas/Steps Used:
Mean Computation : _
X= XN
where
_
X=mean
X= sum of the measurements or values
N= number of measurements
Median Computation:
Arrange the measurements in an array then locate the middlemost scores. If there are two
middlemost scores, divide them by two.
Mode Computation:
Locate the value or measurement which occurs the most number of times.
7/27/2019 learning task 2 final.docx
10/12
De La Salle University2401 Taft Avenue, Manila 1004
Science Education Department
College of Education
Statistics for Science Education SCE500M
Roxanne Diane R. Uy Learning Task 2 2ND TERM S.Y.2013-2014
a. Considering the whole class, compute the mean, the median, and the mode.
Measure of Central TendencyComputation
Mean X= 441
N= 34
Median Array:
6,8,8,8,9,9,10,10,10,10,10,10,12,12,13,13,
13,14,14,14,14,14,14,15,15,16,16,17,17,
17,17,18,18,20
Mode 6 10s
6 14s
Measure of Central Tendency Whole Class
Mean 12.97
Median 13.5
Mode 10,14
b. For each group (male and female), compute the mean, median and mode.
Compare the results in each group.
Measure
of
Central Tendency
Computation
Male Female
Mean X= 244
N= 19
X= 197
N= 15
Median Array:
6 8 8 10 10 10 10 13 13 14
14 14 15 15 16 16 17 17 18
Array:
8 9 9 10 10 12 12 13 14
14 14 17 17 18 20
Mode 4 10s 3 14s
7/27/2019 learning task 2 final.docx
11/12
De La Salle University2401 Taft Avenue, Manila 1004
Science Education Department
College of Education
Statistics for Science Education SCE500M
Roxanne Diane R. Uy Learning Task 2 2ND TERM S.Y.2013-2014
Measure of Central Tendency Male Female
Mean 12.84 13.3
Median 14 13
Mode 10 14
Mean and mode of females is higher than males. Median on the other hand is higher
in males.
c. Compare each groups results with the results for the whole class.
Measure of Central Tendency Whole Class Male Female
Mean 12.97 12.84 13.13
Median 13.5 14 13Mode 10,14 10 14
Comparing the three groups, the female has the highest median while the males have
the highest median. Mode for the three groups is evenly distributed since the mode of
the class is also the mode of each gender.
In terms of comparing the females and the malesscores to that of the classscores,
mean of males is closer to the mean of the whole class compared to the females. The
difference in median and mode of the female and male to the whole class is the equal.
d. Write a brief explanation about the results obtained.
In terms of mean, females performed better than males, having a mean of 13.13,
compared to the 12.84 of the males. However, the males mean is closer to the
trend mean of the class
Looking into the median, both the males and females median has only a 0.5
difference with the class median. But the males median is higher than that of
the females.
Lastly, the mode of both the females and the males is similar to that of the class.
But if to compare the females and the males mode, most of the girls got a higher
mode to most of the boys mode.
7/27/2019 learning task 2 final.docx
12/12
De La Salle University2401 Taft Avenue, Manila 1004
Science Education Department
College of Education
Statistics for Science Education SCE500M
Roxanne Diane R. Uy Learning Task 2 2ND TERM S.Y.2013-2014
References
Acelajado, M., Belecina, R., & Blay, B. (1999). Mathematics for the new millennium. Makati,
Philippines: Diwa Scholastic Press.
Calmorin, L. P., & Calmorin, M. A. (1997). Statistics in education and the sciences. Manila,
Philippines: Rex Book Store.
Hon, K. (2013). An introduction to statistics. Retrieved from
http://www.artofproblemsolving.com/LaTeX/Examples/statistics_firstfive.pdf
Kuzma, J. W., & Bohnenblust, S. E. (2004).Basic statistics for the health sciences (5th ed.). Los
Angeles, California: McGraw-Hill Education.
Polit, D. F., & Beck, C. T. (2006). Essentials of nursing research: Methods, appraisal, and
utilization (6th ed.). Philadelphia, USA: Lippincott Williams & Wilkins.
Thorndike, R. M., & Dinnel, D. L. (2001). Basic statistics for the behavioral sciences. Upper
Saddle River, N.J: Merrill Prentice Hall.
Welkowitz, J., Ewen, R. B., & Cohen, J. (1976). Introductory statistics for the behavioral
sciences (2nd ed.). New York, New York: Academic Press.