Funnel plot for "Differences in Helping Whites and Blacks"

I happened across the Saucier et al. 2005 meta-analysis "Differences in Helping Whites and Blacks: A Meta-Analysis" (ungated), and I decided to plot the effect size against the standard error in a funnel plot to assess the possibility of publication bias.The funnel plot is below.

Funnel plot asymmetry was not detected in Begg's test (p=0.486) but was detected in the higher-powered Egger's test (p=0.009)

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NOTE:

1. Saucier et al. 2005 reported sample sizes but not effect sizes standard errors for each study, so I estimated the standard errors with formula 7.30 of Hunter and Schmidt (2004: 286).

2. Code here.