122 Best Practices for Education Professionals
Figure 9.2. The normal curve.
As one can see in Fig. 9.2, almost all scores in a normal distribution will fall
between three standard deviations above and below the mean score. One will nd
approximately 68% of the scores between one standard deviation above and below
the mean. For the sample data in Table 9.1, the mean was calculated to be 13.5. To
determine where over two-thirds of the class’s test scores fell, the teacher would add
and subtract the standard deviation (2.16) to and from the mean. For this set of data,
approximately 68% of the test scores will fall between 11.34 (one standard deviation
below the mean) and 15.66 (one standard deviation above the mean).
Calculating the mean and standard deviation can help an educator begin to understand
the overall picture found in a set of scores such as test scores, which represent one of
the most commonly used forms of data collected in educational settings (Connolly,
2007). Taken one step further, educators can use a student’s raw score, the mean, and
the standard deviation to calculate a student’s z-score. To compute a z-score, one sub-
tracts the mean from the raw score and then divides by the standard deviation.
A z-score is an example of what is known as a standard score; the z-scores for the
ctional students can be seen in Table 9.3. Standard scores are used to show exactly
how one individual’s score compares to the entire set of scores from which it is calcu-
lated. Z-scores correspond directly to standard deviations, as can be seen in the normal
distribution of scores (under the normal curve). Z-scores have a mean of zero and a
standard deviation of one. A z-score of 1.0 is exactly one standard deviation above the
mean. A z-score of –2.0 is equal to two standard deviations below the mean. Looking
more closely at one ctional student’s z-score, one may be able to better comprehend
how a z-score helps to show the relationship of that student’s score as compared to the
entire groups’ scores. For instance, if one were to look closely at Andrew’s z-score,
one nds Andrew’s z-score falls a little more than half-way between the mean and one
standard deviation above the mean. Another commonly used standard score is known
as the T-score. A T-score has a mean of 50 and a standard deviation of 10. T-scores
are sometimes used over z-scores as they are represented using no negative numbers.
Table 9.3. Sample Students’ Z-scores.
Score on Test z-score
Other standard scores which are familiar to most educators are those found in com-
monly used assessment instruments. One such well known instrument is the Scholastic
Aptitude Test or the SAT, (College Board, 2010), which almost all college-bound high
Understanding and Utilizing Quantitative Research 123
124 Best Practices for Education Professionals
school students in the United States take as part of the collegiate application process.
The SAT verbal and math tests have a mean of 500 and a standard deviation of 110;
the standard deviation prior to the 1995 recentering was 100, (College Board, 2010).
Percentiles represent another statistical term commonly used by educators. As many
of the other statistical measures mentioned here, percentiles allow educators to state
where one student’s scores fall in relation to the other students assessed. Percentiles
are also easily recognized when found in a normal distribution or normal curve as
shown in Fig. 9.2. If one adds the percentage of scores found under portions of the
normal curve, one can determine the percentile into which a student’s score would fall.
For instance, if a student’s score fell exactly one standard deviation above the mean,
the student’s score would fall at approximately the 85th percentile. In other words, this
student scored higher than 84% of the other students on this particular assessment.
By establishing a rm foundation in basic statistical methods and terminology,
educators will be better able to utilize quantitative research in their professional prac-
tice. Educators and education students often do not understand the need to learn quan-
titative research methods or how those methods may apply to their real-world settings
(Murtonen, 2005; Pan & Tang, 2004; Papanastasiou & Zembylas, 2008). There are, in
fact, many ways that quantitative research skills enter the lives of professional educators.
DISCUSSING AND REPORTING TEST SCORES
One of the ways educators use quantitative research is for reporting results. Reports
are provided for many stakeholders in education. Reports of student or institutional
progress are given on a regular basis to parents/guardians, school administrators, and
Parents/guardians are the “front line” stakeholders who receive much of the quan-
titative data produced in schools; they also represent the stakeholders who may be
least likely to understand those quantitative reports. When discussing test scores with
parents, it is vital for an educator to be able to explain what a student’s test score says
about a student’s performance, not about the student himself/herself. So often test
scores become a label, which can undermine a student’s condence and further hinder
future academic performance. How would a teacher or administrator report a student’s
test score to a parent/guardian? Having a detailed understanding of what test scores
truly mean is an excellent rst step. A teacher may also want to show a parent/guardian
a student’s progress over time.
Reports of student progress for administrators and agencies are more often pre-
pared in group formats, rather than reporting the progress of individual students.
Knowledge of central tendency and variability are essential when preparing reports
on class or school-wide progress. In the current age of “accountability” being able
to show how a group of students is improving (quantitatively) will be instrumental.
Results from the collection of quantitative research are being used more and more
frequently in the decision-making process of educational administration (Hodges &
Mid-Atlantic Lab. for Student Success, 1995; Roderick, Easton, & Sebring, 2009).
Education professionals who hone their quantitative research skills may be better
aligned to aid in this decision-making process.
Learning is not only to use quantitative data helpful in reporting results, but also by
establishing a solid foundation in understanding the basics of research methodology
and statistics, an educator can begin to read relevant literature with a critical eye. He/
she will be better able to identify the key pieces of research articles which may play a
part in his/her professional life. As students, future educators are encouraged to read
journal articles relevant to current educational practice. It is the hope of faculty who
prepare education professionals to instill a culture of life-long learning and the pursuit
of further knowledge and skill improvement in their students through the regular men-
tal ingestion of professional literature.
Unfortunately, perusing the latest professional literature is not enough. One must
be able to read journal articles with a critical eye, combining an understanding of
research methodology, statistics, and real-world application. By critically reading
relevant literature, an educator links research to practice. Quality, relevant literature
should be utilized to inform and improve educational practices (Cruickshank & Phi
Delta Kappa, 1990; Fleischman, 2006; Greenwood & Maheady, 2001). Through criti-
cal reading of journals, one can deduce which pieces of professional research will be
most likely to help improve one’s real-world work as an educator.
It is very likely that quantitative research methods will never be the favorite topic sur-
rounding the water-cooler in educational institutions. Hopefully, a regular refresher in
the basics of statistics and a reminder of the usefulness of quantitative research will
make the topic a bit less scary and taboo. Gaining an understanding and appreciation
of quantitative research methods can help educators utilize their inner scholars and
researchers to inform and improve their professional practice.
• Average deviation
• Standard deviation
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