A meta-analysis of the relationship between density and travel behavior

Moreover, these two studies examined more causal elements of urban form than density, a proxy for the elements (Ewing and Cervero 2010; Handy 2005a).

Considering a variety of density and travel measures, the post-test might have controlled for all variables used in previous two tests. However, the sample size was not sufficient for a single meta-regression model to include all the variables. Meta-regression needs at least five cases per characteristic to be investigated. In this vein, similar to earlier meta-regression (e.g., Brander et al. 2006; Furnée et al. 2008), this study developed a parsimonious post-test model in which only significant variables in the previous tests were controlled for. Based on 26 studies, the post-test included the maximum number of variables allowed: one variable found to be significant in the previous tests and four new variables (=5 ≈ 26/5). Parsimonious modeling is also beneficial in reducing the likelihood of a Type I error.

Possibly, the insignificance might be because the variables, particularly several control-level dummy variables, were estimated on a small number of studies (see Table 1). From this perspective, in addition to the full model with regard to control structures, this study developed alternative models based on six different groupings of the structures. The first grouping reflected the three-stage evolution of the control levels (see the section “Control levels”): F (neither sociodemographic nor attitudinal controls), the combination of D and F + D (sociodemographic but not attitudinal controls), and the combination of D + P and F + D + P (both sociodemographic and attitudinal controls) (base = F). The other five groupings were employed to estimate the effect of each control structure alone or as combined: (1) with and without F, (2) with and without D, (3) with and without P (or D + P), (4) with and without F + D, and (5) with and without F + P (or F + D + P) (base = without the control structure). [According to each of the five groupings, the control structures were dichotomized as follows: (1′) F, F + D, and F + D + P versus D and D + P (with versus without F); (2′) D, F + D, D + P, and F + D + P versus F (with versus without D); (3′) D + P and F + D + P versus F, D, and F + D (with versus without P or D + P); (4′) F + D and F + D + P versus F, D, and D + P (with versus without F + D); and (5′) F + D + P versus F, D, F + D, and D + P (with versus without F + P or F + D + P).] In none of the six cases were dummy variables found to be significant.

The variable of the difference between composite travel measures and the others (i.e., travel measure 1) could have been deemed significant (Z = 1.5949; p = 0.1107), choosing a higher significance level than 0.1. Such a choice is justifiable because this study is based on a small sample (n = 26). Small-sample studies tend to produce insignificant outcomes, compared to large-sample studies (see the section “Variable selection for the post-test”). In this sense, this study recognizes the validity of Ewing and Cervero’s meta-analysis (2010) that separated elasticities according to travel measures.

This formula is based on the g-to-r conversion equation: r = \( \sqrt {\frac{{g^{2} }}{{g^{2} + 4}}} \) (where g = Hedges’ g) (Lipsey and Wilson 2001).