Statistical models attempt to describe and quantify relationships between variables. In the models presented in this chapter, there is a response variable (sometimes called dependent variable) and at least one predictor variable (sometimes called independent or explanatory variable). When investigating a possible cause-and-effect type of relationship, the response variable is the putative effect and the predictors are the hypothesized causes. Typically, there is a main predictor variable of interest; other predictors in the model are called covariates. Unknown covariates or other independent variables not controlled in an experiment or analysis can affect the dependent or outcome variable and mislead the conclusions made from the inquiry (Bock, Velleman, & De Veaux, 2009). A p value (p) measures the statistical significance of the observed relationship; given the model, p is the probability that a relationship is seen by mere chance. The smaller the p value, the more confident we can be that the pattern seen in the data 2 is not random. In the type of models examined here, the R measures the prop- tion of the variation in the response variable that is explained by the predictors 2 specified in the model; if R is close to 1, then almost all the variation in the response variable has been explained. This measure is also known as the multiple correlation coefficient. Statistical studies can be grouped into two types: experimental and observational.

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This book addresses implications for "Gold Standards" of education research―especially in science education and literacy. These standards are meant to provide evidence-based educational outcomes found effective in randomized controlled trials, following patterns of evidence used in medical research. Similar expectations have emerged in other countries―from education ministries, for researchers working with U.S. colleagues, and for researchers with multinational and non-profit support.

The current "Gold Standard" policy, developed in the United States through the 2001 "No Child Left Behind" [NCLB] Act and the 2002 Education Sciences Reform Act, attempts to improve the effects of schooling and enhance educational research. The contributions to this book explore perspectives on how best to implement multiple standards of education research.

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