# READ MORE READ BETTER? A META-ANALYSIS OF THE LITERATURE ON THE RELATIONSHIP BETWEEN EXPOSURE TO READING AND READING ACHIEVEMENT M. Lewis S. J.

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1 READ MORE READ BETTER? A META-ANALYSIS OF THE LITERATURE ON THE RELATIONSHIP BETWEEN EXPOSURE TO READING AND READING ACHIEVEMENT M. Lewis S. J. Samuels University of Minnesota 1

9 researchers made valid assumptions of independence and normal distribution when they reported test results, to justify doing a meta-analysis on those studies. Effect size computation The d-index effect size, was calculated for each study that reported means and standard deviations, t-tests, or F tests with one degree of freedom in the numerator. Multiple effect sizes on the same construct are a potential problem in meta-analysis. They are statistically dependent and violate the assumption of independence of data points. A single effect size can be selected, or an average of the effect sizes can be calculated to produce one single effect size for each construct measured (Cooper, 1998). There were no consistent or especially suitable criteria to justify choosing one measure over another, therefore, multiple effect sizes on the same construct were averaged to contribute one effect size for each sample for each reading achievement construct measured. Another complicating factor in estimating effect size occurs when studies compare more than two groups. A sample may compare two experimental conditions to a single control. The three d-indexes from these comparisons are not statistically independent. According to Cooper (1998), using multiple effect sizes is preferable to using multiple inference tests. When several comparisons were made between sample groups, we included all comparisons of interest. The r-index effect size is the Pearson product-moment correlation coefficient that describes the relationship between two continuous variables in terms of degree and direction. In combining correlations in a meta-analysis, sampling distributions become non-normal as values approach the limits of and For this reason, several statisticians ( Cooper, 1998; Lipsey & Wilson, 2000; Rosenthal, 1995) recommend converting r-indexes to their corresponding z-scores, which have no limiting value and a normal distribution. Once the average z-score has been calculated, it can be converted back to r for interpretation. For overall analysis of all studies, the r-index was chosen as the effect size metric. Although different effect size metrics can be easily converted, it is important to choose one to describe results. The 9

10 confidence interval around the effect size statistic was calculated to provide a test of the null hypothesis that there is no relationship in the population between reading exposure and reading achievement. Homogeneity analysis was used to compare observed effect size variance to expected variance, testing whether they come from the same population. Homogeneity is calculated using the Q statistic. Q has a chi-square distribution with k-1 degrees of freedom, where k = the number of effect sizes. If the observed variance is significantly different from expected variance, we reject the null hypothesis that the variation among effect sizes is due to sampling error alone. We then need to examine whether other characteristics might be associated with variations in effect size. These potential moderator variables were also examined using homogeneity analysis. Studies were grouped according to various characteristics and the average effect size tested. A significant Q value indicates that particular characteristics are possible explanations for observed variations in effect size. A meta-analysis involves assumptions about the population represented by the included studies; these may be fixed or random. A fixed effects model assumes that all the comparisons come from the same population, so observed effect size differences are a result of sampling variability. This model is appropriate if an exhaustive search for and examination of moderator variables can be and is done. It is also considered appropriate in situations where the inferences made are conditional and concern only the observed studies (Hedges & Vevea, 1998). A random effects model assumes other sources of variability in addition to sampling error. If these factors are believed to be a potentially significant source of error, then a random effects model is appropriate. It is also appropriate when one wishes to make inferences that are generalizable beyond the observed studies, implying that the set of observed studies may reveal something about a larger presumed set of studies that are the real object of interest (Hedges & Vevea, 1998). Random effects models typically yield a more conservative analysis than fixed effects models. In examining reading performance, individual differences may be related to a variety of influences beyond reading exposure. Some of these factors were not reported and so could not be analyzed. It is also true that inferences would be made to the larger population of all students. Therefore, we chose to apply both fixed and random effects models, running all analyses twice. 10

11 Sample of studies Two search strategies were used to locate studies. Primary searches were done through ERIC, PsychINFO, Education Abstracts, Dissertations Online and Dissertation Abstracts. The reference section of every article retrieved was also examined for additional articles missed through direct search. Search terms were initially entered using the keyword index. This turned up thousands of articles. Search terms were therefore indexed in the abstract first, and if no articles were found then searches were done through the subject and major descriptor indexes. Table 1 reports the overall search results. After eliminating duplications, 1306 articles were found. The abstract of each of these was examined. Of the 251 studies retrieved, 97 were coded, 48 studies in the directional analysis and 49 in the meta-analysis. A second search was made shortly before the final analysis was done. This search turned up 33 additional reports; none were suitable for inclusion (insert table 1 here ) Coding Format and Database All reported information related to reading was coded. Information was classified by design type; sample selection criteria and group equivalence; student and teacher characteristics; school environment; reading instruction methods and materials; pretests administered and results; reading practice measures; and outcome measures. A brief description of the researcher s findings was provided, statistical analyses done and results, and researcher conclusions. It was noted whether or not the study satisfied the hypothesis and if not, why not. Effect size magnitude and direction was computed for each outcome measure. The r-index, was coded as reported. Space was provided for any additional information readers felt was important, and to note limitations, design flaws, or other factors that might have affected results. Both a directional summary and a meta-analysis were planned because of the disparity in type of data reported across studies. A sorting sheet was developed to identify studies for inclusion in the meta- 11

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