TL; DR summary: no.
Someone at Statistics Brain copied data from an unreliable source, introduced an error while copying it, and misattributed it to a reliable source. Now articles all over the Internet use the wrong data, attribute it to the reliable source (that never said anything like it), and don't do any verification on their own.
The real source of the 8% number appears to be a survey conducted by Stephen Shapiro, a management consultant, author, and speaker, and published in an article on his website. According to him,
Only 8% of people are always successful in achieving their resolutions. 19% achieve their resolutions every other year. 49% have infrequent success. 24% (one in four people) NEVER succeed and have failed on every resolution every year. That means that 3 out of 4 people almost never succeed.
Of course, "Only 8% of people are always successful in achieving their resolutions" is not the same as "8% of People Achieve Their New Year's Resolutions". The study by Shapiro has not been published in a scientific journal.
In general, the numbers on the Statistics Brain page come from multiple sources:
The "News Years Resolution Statistics" table, "Age Success Rates" table, and "Type of Resolutions" table on Statistics Brain come from the Stephen Shapiro article (but sometimes with errors, e.g. leaving out the "always" in the statement regarding the 8% number.)
Statistics Brain cites "University of Scranton. Journal of Clinical Psychology" as the source for the entire page. This is likely a reference to the paper published by University of Scranton researchers in the Journal of Clinical Psychology:
Norcross, J. C., Mrykalo, M. S., & Blagys, M. D. (2002). Auld lang Syne: Success predictors, change processes, and self‐reported outcomes of New Year's resolvers and nonresolvers. Journal of Clinical Psychology, 58(4), 397-405.
(The "Length of Resolutions" table on Statistics Brain comes from the Norcross paper, as does the statement that "People who explicitly make resolutions are 10 times more likely to attain their goals than people who don't explicitly make resolutions".)
Other websites using this 8% number also cite Norcross, Mrykalo, and Blagys, e.g. New Year, New You? How to use Behavioral Principles to actually stick to those resolutions:
University of Scranton research shows that approximately 45% of individuals in the United States make New Year’s Resolutions, unfortunately, this research also suggests that just 8% of people achieve their New Year’s goals by the end of the calendar year (Norcross, Mrykalo, & Blagys, 2002).
Norcross, J. C., Mrykalo, M. S., & Blagys, M. D. (2002). Auld lang Syne: Success predictors, change processes, and self-reported outcomes of New Year’s resolvers and nonresolvers. Journal of Clinical Psychology, 58 (4), 397-405. DOI: 10.1002/clp.1151
However, the paper by Norcross, Mrykalo, and Blagys concludes that many New Years' resolutions are successful:
Contrary to widespread public opinion, a considerable proportion of New Year resolvers do in fact succeed, at least in the short run. This and previous longitudinal research can counterbalance the ubiquitous contention that “resolutions never succeed” (Goll-witzer, 1999) or, in the words of Oscar Wilde (1909) in The Picture of Dorian Gray, the origin of resolutions “is pure vanity. Their result is absolutely nil.” Although the success rates of New Year’s resolutions obviously depend on the interval and criteria considered,the proportion of self-reported continuous success was 46% at six months.
(This 46% number is reflected on the Statistics Brain page under "Resolution maintained... Past six months).
They do, however, note:
The success rates reported in this study are probably overestimates for several reasons. First, although we tried to recruit an unbiased community sample via telephone, the sample is nonetheless composed of volunteers. Only 31% of those contacted agreed to participate, and those who volunteered may have been more likely to be successful in their resolutions. Second, the self-report outcomes of resolvers (and perhaps nonresolvers) may be inflated. This observation is supported by the quantitative data, which shows a modest reduction in the target behaviors (average reduction of 23 to 15 cigarettes per day and an average weight loss of 8 lb from January to July). Third, all of the data are
based on self-report without independent verification. And fourth, our criteria of “mostly successful” and “totally successful” may be too lenient. The demand characteristics of the study probably pose the most serious threat to its validity.
It's also plausible that disclosing their resolution to a researchers, and knowing that the researcher would follow up, affected the success rate of the resolvers.
The Forbes article with the 8% number later links to an interview Norcross did on NPR. In that NPR interview, he said
FLATOW: I was surprised in reading your paper about actually how many people are successful in...
NORCROSS: Oh, yes. We say the glass is proverbial, half-empty or half-full, here.
NORCROSS: In two of our longitudinal studies, 40 to 46 percent of New Year's resolvers will be successful at six months. So, the half empty is, it's true, most people fail. But 40 to 46 percent is pretty impressive. Particularly when you compare it to the people who don't try and therefore have, in our research, 0 to 4 percent chance.
Marist has been collecting data on New Years' resolutions since the 90s. They found the following self-reported success rates:
(The Statistics Brain page has been online since at least January 2012, per archive.org.)