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Anyone with a brain, common sense, or training in Science or Statistics would tell you: you throw it out as an aberration.

Not for this topic!  Quite the contrary!  Anyone with "training in Science or Statistics" should quickly "tell you" that "throw[ing] it out" instead shows readers how little you really learned from "training in [...] Statistics".  That's because it's highly important to understand the relationship between statistical samples, the (real-world-by-definition) populations from which they're taken, and the statistical methods that apply to them--and those that do not.

When you have a single datum which is ridiculously above the norm, and has never been even close to repeated, you cast it out as an anomaly or an aberration.

What's with your "single datum [...] never been even close to repeated"? 
The U.S.A. completed flights at least as far as Lunar orbit on at least 8 occasions: Apollo 8, 11, 12, 13, 14, 15, 16, 17.  Plus (I think) another for testing undocking & rendezvous between the command module and Lunar-excursion module.  Of those identified by number, 6 successfully landed "on the Moon" and were "returned safely to Earth".

It's a law of experimental science, as well as Statistics, that when you have a far-and-above exception to 99% of the data, it must be considered an aberration to be dismissed.  I didn't come up with this argument, but man is it rock-solid and the most compelling argument why the Moon Landings were a hoax.  The truth of it resonated with me, and burrowed deep into my brain.

"Rock-solid"?  Really, now?

Anyone with "training in Science or Statistics" should recognize that the distances travelled during individual flights in the "Space Race" and for subsequent "Moon Landings" are obviously not simple data-points [#] for which it's valid to apply your "law of experimental science, as well as Statistics" whose indiscriminate use you're promoting.

We have years of history to prove it now--that the so-called moon landings in the early 1970's never happened.

Fascinating!  Being determined to use historical records not to prove the real occurrence (thus reality) of disputed events, but instead, to prove the nonoccurrence (thus unreality) of those same events!

You're telling me no other country has managed to go there in almost 50 years?

Yes, that is what I'm telling you, as confirmed by the intervening "years of history".

There are a lot of advanced countries that should have the technology to do so [...]. Russia, Japan, China, Europe just for starters.

You have invoked "years of history", but seem completely unaware of what "history" shows as having happened during those "years".  You've completely failed to present any "history" that was relevant to the "Space Race" and "Moon Landings".  Perhaps that apparent ignorance should be expected from someone who wasn't born until roughly a decade after the return of Apollo 17 (Dec. 19, 1972) ended the flights of Project Apollo--prematurely at that.

Each of the "advanced countries" or regions you listed has made its own decisions on outer space while experiencing changes in political or technical leadership, wrestling with competing or contrary goals of opposition parties or factions, enjoying increased national prosperity or enduring national deprivation, benefitting from technical discoveries or developments, carrying on despite the loss of key people, and sometimes   often  unpredictable changes in national priorities.

You do understand that for a democratic republic to participate in a "Space Race" or strive for "Moon Landings" ultimately requires the assent of "we the people", don't you?  The representative office-holders in a republic are really keen on continuing to enjoy their perks of power by continuing to be reëlected.  They can only survive whatever is their next election by being attentive to their constituents, and recognizing, i.a., when their support has dwindled to election-jeopardizing levels for any national program that was once too popular to risk opposing, e.g., exploration or colonization of outer space.

Not even the exalted leader of a 20th-Century communist dictatorship had the autocratic power wielded by the Russian tsar of any earlier century, not even those communist leaders who combined the 2 top offices of premier and general secretary of the Party.  The judgmental attention of high-ranking Party leaders didn't end when they elevated such a man to either top office.  The Party repeatedly demonstrated that altho' they can "giveth great power", they themselves reserve the power to "taketh it away"[†].

So what does the "history" of the 20th Century tell us about what happened to exploration or colonization of outer space?  Stay tuned to this topic [*].

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Note #: It's valid for the kind of "experimental science" in which the sampling is, e.g., counts of inanimate objects, measurements of sedated wildlife, or periodic output from sensors (e.g., wind velocity).

Note †: Nikita Khruschëv, e.g., was fortunate to be the first combined premier and general secretary who was removed from office simply by being involuntarily retired, instead of by being αssαssιnαtҽd.

Note *: I already have written a 1st draft of my implied future posting.

How about the interview talking about how NASA "destroyed" the technology to go to the Moon, and now they have to re-discover it? They also put forth "travelling through the Van Allen Belts" as another obstacle they need to overcome.

Really?

How does any science type perform the mental gymnastics necessary to swallow THAT whopper? I mean, give me a break!

To a layman such as myself the explanation here sounds reasonable.

The answer, simply, and which has been explained in detail elsewhere, is that the Apollo astronauts were not in the Van Allen belt for long enough to have to deal with dangerous levels of exposure to radiation.

The Apollo astronauts did return to Earth having been exposed to significant radiation - but not more than is allowed by US law for workers at nuclear power stations, for instance.

So what's different with Orion EFT-1? Put simply, two things: equipment and time.

First, Orion contains much more complex and complicated electronic equipment than the Apollo systems, which could potentially be damaged by radiation and so has to be tested before humans are allowed to fly inside it.

Second, Orion isn't just intended to go through the Van Allen belt and back in a few short days. It's designed for missions up to 21 days long, and perhaps even longer if it forms part of a mission to Mars. As a result it would face exposure to vast amounts of radiation in space, for months on end, and so testing its shields and how much radiation gets through is prooobably a good idea.

So no, NASA did not accidentally leak that the Apollo missions were fake in its own promotional videos.

If you don't believe any so-called "conspiracy theories", then why the ____ are you on CathInfo to begin with?

Like a moth to a flame, eh?

Or more likely you are a troll that is just here to start trouble and be contrary for lulz?

Don't tell me you're here for Traditional Catholic news, because virtually all your posts are on the topic of science of some sort. I'm really wondering if you belong here on a "Traditional Catholic" forum at all. If I deleted all your posts about Flat Earth or the Moon Landing, you would literally have 6 posts left in your posting history -- but those posts would all be almost 2 years old!

For all we know, based on your posting history, you apostatized 1.5 years ago. Since June 2016, you haven't said a single thing on CathInfo specifically Catholic, or anything that your average atheist or agnostic professor wouldn't say to a group of Traditional Catholics whom they considered to be "nut jobs".

Thanks much Matthew for trying so hard to keep things in proper check.   It's certainly no easy job and perhaps not nearly as appreciated as it should be.  It's great that you can pick up on certain patterns that fly under the radar for many of us.  P.S.  Sorry for my 2 somewhat off topic and silly WalMart posts today.