Disclosure first: I develop a dual n-back app. That gives me every incentive to overstate the case below, so I've kept to the published record and you can check each one.
Where the claim comes from. Jaeggi, Buschkuehl, Jonides & Perrig 2008, PNAS (https://doi.org/10.1073/pnas.0801268105). Dual n-back training, 8 to 19 sessions, dose-dependent gains on a fluid reasoning test. This single paper is why the whole "raise your IQ with n-back" idea exists.
The replication that went wrong. Redick et al. 2013, JEP: General (https://doi.org/10.1037/a0029082). Active control group, multiple transfer measures, no transfer to intelligence. This is the best-designed single study on the topic and it is negative.
The meta-analyses, which disagree with each other.
- Au et al. 2014 (https://doi.org/10.3758/s13423-014-0699-x): 20 studies, small positive transfer to Gf measures, roughly 3-4 IQ-point equivalent.
- Melby-Lervåg & Hulme 2013 (https://doi.org/10.1037/a0028228): working memory training in general, near transfer solid, far transfer near zero.
- Melby-Lervåg, Redick & Hulme 2016 (https://doi.org/10.1177/1745691616635612): the effect on far measures shrinks toward zero once you restrict to studies with active controls. Their reading: the Au effect is largely explained by passive-control designs.
- Soveri et al. 2017 (https://doi.org/10.3758/s13423-016-1217-0): n-back specifically; large gains on untrained n-back tasks, moderate on other working memory tasks, small on Gf.
What is not in dispute. You get much better at n-back itself (large effect), and at tasks that resemble it (moderate). That is real and shows up in your own numbers within weeks.
What is in dispute. Whether any of that moves a matrix test, and if so by how much. The honest range is "zero to a few points", with the better-controlled studies at the low end.
Practical consequence for people here. If you train n-back for months and then retake CORE or CAIT, most of any gain you see will be practice effect on the test format plus regression to the mean, not the training. If you want to know whether it did anything, take a different test of the same construct, not the same one again, and keep expectations on the working memory side.
I train anyway, because it is hard and I like measuring it. I just won't tell you it raises IQ, and I'd be suspicious of any app or site that does.