This was the reason for me. The statsdata module uses array shorthands, which are incompatible with PHP < 5.4
If you use PHP 5.3, replace line 108 in modules/statsdata/statsdata.php:
$this->context->controller->registerJavascript('modules-plugindetect', 'modules/'.$this->name.'/js/plugindetect.js', ['position' => 'bottom', 'priority' => 150]);
with:
$this->context->controller->registerJavascript('modules-plugindetect', 'modules/'.$this->name.'/js/plugindetect.js', array('position' => 'bottom', 'priority' => 150));
The bug seems fixed in latest development branch on github.
(In other news, this module compares versions using lte instead of version_compare, which will break the conditionals on 1.6.10)