Meta-Analysis: Statistical Conversion to Common Metric

Conversion to a common metric in meta-analysis is the process whereby researchers aggregate certain statistics of many separate research findings and translate them into the same metric so treatment effects can be estimated. Meta-analysis is a type of study whereby research studies are used as data points instead of individuals. Meta-analysis statistically synthesizes the results from an accumulation of research reports. This is fundamentally different from narrative reviews of research literatures, which although quite useful for describing many details about a body of literature, are unable to apply statistics to evaluate a series of studies. Quantitative research synthesis like meta-analysis is important because not all research studies agree, and the conclusions of narrative reviews may reflect hopeful myths instead of empirically accurate realities of research literatures. In fact, the first meta-analysis resulted from precisely the type of conflicting narrative reviews described here, resolving a debate that began in the 1950s but that was not settled until the 1970s concerning the benefits of psychiatry. After a literature search has been conducted, and defensible criteria for including studies in the analysis has been decided, the step of converting to a common metric can begin.

Conceptually, conversion to a common metric is analogous to what one does when one wants to compare sometimes (e.g., the price of gas during one’s summer travels). In this example, it is easy to compare state to state in the United States, because all U.S. states charge in the same units for gas (U.S. dollars/gallon), but it gets trickier when one goes to Puerto Rico (U.S. dollars/liter) or London (pounds/liter) or Germany (Euros/liter). In order to do this, one applies a mathematical formula to convert the data into common metrics: Pounds and Euros can be converted into U.S. dollars if one knows the exchange rates at the time of purchase, and liters can be converted into gallons (3.78541 liters = 1 gallon). Note one can also convert U.S. dollars to other currencies and also gallons to liters. Once one has converted the disparate information about units of gasoline and units of money into a common metric, one can compare where gas was cheapest and/or most expensive on a trip regardless of the measurement units of the place one was traveling.

This entry details a variety of issues central to understanding common metric conversions in meta-analysis. First, a brief discussion of the importance of comparison in meta-analysis is provided. Second, the common metrics, known as effect sizes, are explained in the context of their importance for meta-analysis. Third, the main effect sizes used in communication research are introduced and the formulas for calculating them provided. The main effect sizes discussed include the standardized mean difference, the correlation coefficient, and the odds ratio. Fourth, the methods for converting from one effect size into another are explained and relevant equations are provided. Throughout this entry, examples of meta-analysis from the field of communication dealing with the effectiveness of inoculation treatments are provided to help demonstrate the concepts under consideration. Finally, this entry offers some practical considerations regarding conversion to a common metric in meta-analysis.

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