Looking on the internet deeply has found these results:

to that end is the most popular phrase on the web.

to that effect 1544,000 results on the web	to that end 15,480,000,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
something like that just mentioned. She said she wouldn't be available until after three, or something to that effect. I was told to keep out of the house�or�... With that basic or general meaning, as in He said he was very worried, or words to that effect. This term is also put as to the effect that when introducing a clause, �... ods.un.org. home � Anglais britannique et international; to that effect ... result, purpose, or meaning: she thought it a foolish rule and put a notice to that effect in a newspaper. our friends who are judges and lawyers, or words to that effect. www2.parl.gc.ca ... Information on obstacles to that effect may be provided. daccess	And Lebensborn is... an early attempt to that end. Mrs Bennet will dedicate herself to that end. It is therefore appropriate to provide that the proof of origin contains a clarification to that end. You seem to have all sorts of schemes to that end. The coordinator's powers have been widened to that end. Election involves both the elect's salvation and the means to that end. Member States are invited to contribute actively to that end. It will consider all proposals to that end.

to that effect

1544,000 results on the web

to that end

15,480,000,000 results on the web

More popular!

something like that just mentioned. She said she wouldn't be available until after three, or something to that effect. I was told to keep out of the house�or�...
With that basic or general meaning, as in He said he was very worried, or words to that effect. This term is also put as to the effect that when introducing a clause, �...
ods.un.org.
home � Anglais britannique et international; to that effect ... result, purpose, or meaning: she thought it a foolish rule and put a notice to that effect in a newspaper.
our friends who are judges and lawyers, or words to that effect. www2.parl.gc.ca ... Information on obstacles to that effect may be provided. daccess

And Lebensborn is... an early attempt to that end.
Mrs Bennet will dedicate herself to that end.
It is therefore appropriate to provide that the proof of origin contains a clarification to that end.
You seem to have all sorts of schemes to that end.
The coordinator's powers have been widened to that end.
Election involves both the elect's salvation and the means to that end.
Member States are invited to contribute actively to that end.
It will consider all proposals to that end.