by Boston, Carol Given the growing demand for "evidencedbased research" to guide educational interventions, interest in the research technique of metaanalysis has surged. Developed by Gene Glass in the mid1970s, metaanalysis 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 student achievement. 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, metaanalysis 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 peerreviewed 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 metaanalytic results. It also includes resources for further exploration. BASICS OF RESEARCH SYNTHESIS Statistically, students' achievement scores tend to be distributed according to the wellknown "bell curve," also known as normal distribution. In other words, the majority of scores are clustered around the midpoint 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 bellshaped 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 METAANALYSES Metaanalysis 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 researchbased knowledge about teaching children to read (NICHHD, 2000). Researchers at the MidContinent 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: ResearchBased 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 28based on 134 studies. The reported standard deviation of .36 tells how different those 134 studies were. One metaanalysis 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 metaanalyses 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. SOME CAVEATS The technique of metaanalysis 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 metaanalysis 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 base. REFERENCES 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): 8591. 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): 7083. Cooper, H., Valentine, J.C., Nye, B., & Lindsay, J.J. (1999). Relationship between five afterschool activities and academic achievement. Journal of Educational Psychology, 91 (2): 369378. Glass, G. (1976). Primary, secondary, and metaanalysis of research. Educational Research, 5: 38. Glass, G. (1977). Integrating findings: The metaanalysis of research. Review of Research in Education, 5: 351379. Marzano, R.J., Pickering, D.J., and Pollock, J.E. (2001). Classroom Instruction That Works: ResearchBased Strategies for Increasing Student Achievement. Alexandria, VA: Association for Supervision and Curriculum Development. National Institute of Child Health and Human Development (2000). Report of the National Reading Panel. Teaching Children to Read: An EvidenceBased Assessment of the Scientific Research Literature on Reading and Its Implications for Reading Instruction: Reports of the Subgroups (NIH Publication No. 004754). Washington, DC: U.S. Government Printing Office. [Online]. Available: http://www.nichd.nih.gov/publications/nrp/report.htm Redfield, D.L., and Rousseau, E.W. (1981). A metaanalysis of experimental research on teacher questioning behavior. Review of Educational Research, 51(2): 237245. Walberg, H.J. (1999). Productive teaching. In H.C. Waxman and H.J. Walberg,
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