Effect Size and Meta-Analysis. ERIC Digest.
by Boston, Carol
Given the growing demand for "evidenced-based research" to guide educational
interventions, interest in the research technique of meta-analysis has
surged. Developed by Gene Glass in the mid-1970s, meta-analysis is a statistical
technique that enables the results from a number of studies to be combined
to determine the average effect of a given technique. Comparisons can then
be made about the relative effectiveness of various techniques for increasing
Where traditional literature reviews often present a narrative, chronological
look at a small subset of studies deemed by an author to be relevant to
the question at hand, meta-analysis is a more exacting and objective process
that involves identifying, collecting, reviewing, coding, and interpreting
scientific research studies. Studies are typically coded according to such
categories as publication in a peer-reviewed journal, sample size and composition,
control group, use of randomization, research methodology, type of intervention,
and length of intervention. Study outcomes are translated to a common metric,
called an effect size, to allow results to be compared.
This Digest provides a review and applications of the concepts of normal
distribution, standard deviation, effect size, and translation of effect
size into percentile gain foundations for the understanding of meta-analytic
results. It also includes resources for further exploration.
BASICS OF RESEARCH SYNTHESIS
Statistically, students' achievement scores tend to be distributed according
to the well-known "bell curve," also known as normal distribution. In other
words, the majority of scores are clustered around the mid-point of the
scale, or distributed symmetrically around the mean, with fewer scores
occurring as the distance from the mean increases according to a specific
mathematical equation. Standard deviation is the measurement of how scores
are clustered or dispersed in relation to the mean. It is a measure of
variability, something akin to an average distance from the mean.
Normal distribution has a range of about three standard deviations above
the mean and three standard deviations below the mean. In graphic terms,
envision a bell-shaped curve divided in half at the highest part (the mean
score), then add two more vertical lines at equal intervals on each side.
About 68 percent of the population can be expected to lie within the first
standard deviation on either side of the mean (34 percent on each side).
About 95 percent of the population will lie within +/- two standard deviations,
and 99 percent of the population will lie within +/- three standard deviations.
To give an extremely simplified example, assume subject knowledge is normally
distributed among 100 students, on a test of 100 items with a mean of 50
and a standard deviation of 20. About 34 students would be expected to
score between 50 and 70, about 14 students would score between 71 and 90,
and about 2 would score between 91 and 100. Fifty of the students would,
of course, score below the mean, with 34 scoring between 30 and 50, 14
scoring between 10 and 29, and two students scoring between 0 and 9 points.
In order to show whether a particular technique or intervention helps
raise student achievement on a test, a researcher would translate the results
of a given study into a unit of measurement referred to as an effect size.
An effect size expresses the increase or decrease in achievement of the
experimental group (the group of students who are exposed to a specific
instructional technique) in standard deviation units.
For example, suppose that the effect size computed for a specific study
is 1.0. This means that the average score for students in the experimental
group is 1.0 standard deviation higher than the average scores of students
in the control group. In other words, a student at the 50th percentile
in the experimental group would be one standard deviation higher than a
student at the 50th percentile in the control group. A study that shows
an effect size of 1.0 thus means a percentile gain of 34 points one standard
deviation above the mean encompasses 34 percent of the scores provided
one can assume the average for the group is the 50th percentile.
As Marzano, Pickering, and Pollock (2001) note, "Being able to translate
effect sizes into percentile gains provides for a dramatic interpretation
of the possible benefits of a given instructiona strategy." By way of example,
they report that Redfield and Rousseau (1981) analyzed 14 studies on the
classroom use of higher level questions and computed the average effect
size of those studies to be .73. This means that the average student who
was exposed to higher level questioning strategies scored .73 standard
deviations above the scores of the average student who was not exposed
to higher level questioning strategies. Transforming effect sizes to percentile
gains through statistical conversion shows that an effect size of .73 represents
a percentile gain of about 27 points (p. 6).
Another way of interpreting effect size is to consider an effect size
of .20 as small, an effect size of .50 as medium, and an effect size of
.80 as large (Cohen, 1988). While these are accepted rules of thumb, the
importance of an effect size magnitude is, in the end, a judgment call.
IDENTIFYING EFFECTIVE INSTRUCTIONAL TECHNIQUES THROUGH META-ANALYSES
Meta-analysis is a widely accepted technique for summarizing studies
and exploring relationships. The National Reading Panel convened by the
National Institute of Child Health and Human Development and the U.S. Department
of Education, for example, used the technique to assess the state of research-based
knowledge about teaching children to read (NICHHD, 2000).
Researchers at the Mid-Continent Regional Educational Laboratory undertook
a study to identify broad strategies with a high probability of enhancing
student achievement for all students in all subject areas at all grade
levels. A detailed look at these instructional strategies, their basis
in research, and their classroom application, is provided in the handbook,
Classroom Instruction That Works: Research-Based Strategies for Increasing
Student Achievement (Marzano, Pickering, and Pollock, 2001). In the area
of homework and practice, for example, the average effect size was .77
for a percentile gain of 28--based on 134 studies. The reported standard
deviation of .36 tells how different those 134 studies were. One meta-analysis
of homework involving research up to 1988 reported effect sizes of homework
to be .15 for grades 4 to 6, .31 for grades 7 to 9, and .64 for grades
10 to 12 (Cooper, 1989). According to this study, whereas homework in high
school produces a gain of about 24 percentile points, homework in the middle
grades produces a gain of only 12 percentile points, and homework in grades
4 to 6 has a relatively small effect a percentile gain of 6 points on student
achievement. More recent studies have shown beneficial results for elementary
school students as young as second grade (see, for example, Cooper, Lindsay,
Nye, and Greathouse, 1998; Cooper, Valentine, Nye, and Lindsay, 1999).
Walberg (1999) found that the effects of homework vary greatly, depending
on the feedback a teacher provides. Homework assigned but not graded or
commented on generates an effect size of only .28; however, the effect
size increases to .78 when homework is graded, and to .83 (a percentile
gain of 30 points), when the teacher provides written comments.
Readers who wish to locate more meta-analyses may wish to search the
ERIC database for relevant citations by using the terms META ANALYSIS OR
EFFECT SIZE in one set, and an intervention or instructional technique
(e.g., COOPERATIVE LEARNING, COMPUTER ASSISTED INSTRUCTION) in another.
The technique of meta-analysis injects useful scientific rigor into
reviews of educational research, but it also has some limitations. For
example, a synthesis of research studies may provide evidence about the
overall effectiveness of a method, but not the specific details that would
help guide implementation, such as the following raised by Marzano, Pickering,
and Pollock (2001): * Are some instructional strategies more effective
in certain subject areas? * Are some instructional strategies more effective
at certain grade levels? * Are some instructional strategies more effective
with students from different backgrounds? * Are some instructional strategies
more effective with students of different aptitude? (p. 9)
A good meta-analysis may point to the need for more focused and refined
research studies to answer those questions. It's also important to remember
that it is provisional representing the best evidence at the time it was
conducted, but subject to change in the face of the evolution of the knowledge
Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences,
2nd ed. Hillsdale, NJ: Erlbaum.
Cooper, H. (1989). Synthesis of research on homework. Educational Leadership,
47 (3): 85-91.
Cooper, H., Lindsay, J.J., Nye, B., & Greathouse, S. (1998). Relationships
among attitudes about homework, amount of homework assigned and completed,
and student achievement. Journal of Educational Psychology, 90 (1): 70-83.
Cooper, H., Valentine, J.C., Nye, B., & Lindsay, J.J. (1999). Relationship
between five after-school activities and academic achievement. Journal
of Educational Psychology, 91 (2): 369-378.
Glass, G. (1976). Primary, secondary, and meta-analysis of research.
Educational Research, 5: 3-8.
Glass, G. (1977). Integrating findings: The meta-analysis of research.
Review of Research in Education, 5: 351-379.
Marzano, R.J., Pickering, D.J., and Pollock, J.E. (2001). Classroom
Instruction That Works: Research-Based Strategies for Increasing Student
Achievement. Alexandria, VA: Association for Supervision and Curriculum
National Institute of Child Health and Human Development (2000). Report
of the National Reading Panel. Teaching Children to Read: An Evidence-Based
Assessment of the Scientific Research Literature on Reading and Its Implications
for Reading Instruction: Reports of the Subgroups (NIH Publication No.
00-4754). Washington, DC: U.S. Government Printing Office. [Online]. Available:
Redfield, D.L., and Rousseau, E.W. (1981). A meta-analysis of experimental
research on teacher questioning behavior. Review of Educational Research,
Walberg, H.J. (1999). Productive teaching. In H.C. Waxman and H.J. Walberg,
eds. New Directions for Teaching Practice and Research, 75-104. Berkeley,
CA: McCutchen Publishing Corporation.