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[R-meta] About whether to delete the outliers from the dataset

I have a question concerning whether to delete some of the data or not. I
have a dataset of 56 studies with a pooled effect size of g=1.25. Yet,
there are 4 data that reported an incredibly high effect size (8.15, 6.63,
4.14, 4.10 respectively). Statistically, they should be considered as
outliers and be removed from the dataset. But since these data went through
the inclusion and exclusion criteria, they should be staying in the dataset
since they met all the requirements of my selection. So if we excluded the
4 data, wouldn't that be miss-reporting some data in the dataset? What
should I do? Should I excluded the 4 seemingly influential cases or keep
them for a complete list of research?
*Name*: Nick Chen (Ping-Cheng, Chen)
*School*:National Taiwan Normal University (NTNU) English Department
(Master)
*Email*: wow99308008 at gmail.com
*Phone number*: +886 909 663 963