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"by statistics" is a correct and usable phrase in written English.
It is typically used to indicate that something is supported or backed by data. Example: By statistics, it can be seen that the majority of people prefer pizza over pasta.
Exact(49)
CRICKET is a game dominated by statistics.
Slew's views are borne out by statistics.
This is borne out by statistics.
The alarmists will not be dissuaded by statistics.
But these reports are backed up by statistics.
Sometimes it is right to be enthralled by statistics.
Similar(11)
Data were collected by Statistics Sweden.
The surveys were administered by Statistics Sweden.
Consent for the data was given by Statistics Netherlands.
The sample was drawn by Statistics South Africa.
The data were made available by Statistics Netherlands.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com