There were studies in the early Cold War on public reactions to false alarms. I do not know of any for the 1971 alert. But in the 1950s there were several false alarms in different cities, and there were sociologists who looked closely at what people did, what they reported they thought, and how that changed based on the type of person they were.

The three false alarms from the 1950s that were studied closely were:

• On May 5, 1955, the USAF could not identify a bomber squadron that was headed towards central California from the ocean. They sounded air raid sirens in Berkeley and Oakland. The squadron was an American one, in the end, and they stopped the sirens after about 10 minutes.

• On November 25, 1958, while doing routine repair work on telephone lines in Washington, DC, workers accidentally activated the Civil Defense warning system, leading to air raid warnings in many parts of downtown Washington, DC.

• On September 22, 1959, after the Chicago White Sox won the American League championship, the fire commissioner, who was also the Civil Defense officer for Chicago, decided that running the air raid alarm as a form of celebration was a valid activity (he informed police and fire departments that he was doing this only minutes before).

(In my notes that I took when I first read this study, I listed the causes of the air raids as "legitimate fear; wires crossed; complete asshole.")

So what happened? To summarize a lot of research succinctly, the researchers found that people regarded the warnings differently depending on who they were. Highly-educated people, especially men, tended to ignore them; they rationalized why they couldn't be real attacks (which is in fact a very irrational way to proceed in the face of a warning like that). The researchers in the early 1960s hypothesized (per the social/psychological theories of the time) that they were unconsciously rejecting of the idea of their own deaths and loss of social status. Women, esp. with children, tended to respond more consistently like they were real warnings and did the appropriate actions (got inside, took shelter, etc.). People who were highly-educated or un-educated both tended to ignore the warnings for different reasons (the highly-educated, again, rationalized them; the un-educated did not understand them). In many cases people sought external confirmation of the warning, before acting: they asked other people what to do, if the warning was real; they checked the radio for additional information.

There are many more details in the full 1961 study, and differences between the different events and cities; this is just an impressionist overview to give you a gist of it and the kinds of things the researchers looked at.

I bring this all up because arguably 1955-1958 was a much more "heated" time of the Cold War than 1971 (which is still during detente), when nuclear fears were much more palpable to the general public (even though, in objective terms, in 1971 the threat to Americans was higher, because the nuclear capabilities of the Soviets were far more capable of hitting the US, and there were many computer-related mishaps possible in the 1970s that were not possible in the pre-computerized 1950s). And yet even in the 1950s there was a large percentage of people who were exposed to these "take cover immediately" warnings that essentially ignored them.

In the case of the 1971 error, news accounts don't really give any details about anybody doing anything. The fact that it just went off the air, without any other information or instructions, probably means that most people didn't do that much. Many stations confirmed quickly with the White House that no emergency order was issued, apparently, and rescinded the radio silence. Certainly a weird thing. But probably not the same impact of an actual air raid warning. But the response would likely have varied on the type of person who perceived it.

It is frustrating to me that these kinds of things have not been studied more closely. The 1961 study I took my examples from (which has a terrible title: "The occasion instant: The structure of social responses to unanticipated air raid warnings") is one of the only studies I have seen that even try to do this, and it has many inadequacies (a lot of the study was too late after the fact, and not large-enough). I came across this work while looking into the Hawaiian false alert from 2018; there has been barely any research into the behavior of people after that, from what I can tell, despite it being one of the few "natural experiments" we have to inform us about how people will react in the event of a mass warning like that.

I went to Hawaii a year after the alert and talked with many people who were there for the alert — not in a scientific way, just as anecdotes — and saw the full spectrum of responses including "rationalizing it away one way or another" (which, again, is not actually a rational response — if you get a warning telling you to take cover immediately, you should do what it says, because you are not going to be in possession of the facts you need to know to evaluate its seriousness, unless you like literally work at NORAD), "taking it seriously but being fatalistic about it" (assume death is coming, sit back and wait for it), "taking it seriously but having no idea what exactly to do and doing something not that helpful" ("I got into the bathtub," which seems to be a confusion about the utility of running some water in the bathtub to use if the water supply gets disrupted), "taking it seriously but being able to figure out what to do" ("I Googled it and saw that I should take shelter in a basement of a big building so I did that"). My favorite response was from an octogenarian Japanese-American taxi driver who told me that he allowed himself a cup of coffee a day normally, but after he heard the warning, he decided he was entitled to two cups, since he was going to die soon anyway. Anyway, I just bring this up as an anecdote, and a reflection of my own interests in this, and my frustrations that our ability to mobilize social scientists on a large scale for this kind of important work is currently pretty meager from what I can tell.

To add some details on what happened in 1971 to /u/restricteddata's general comments:

Part of the reason the 1971 message was not widespread is that there was an actual scheduled test that people knew about. (Widespread enough, that it was cheekily noted that 9:33 AM on a Saturday was a perfect time for the Russians to attack.) They used the "real" code word for that time -- HATEFULNESS -- as opposed to a test one, which was the indicator the message was real. So the fact the non-test came at the specified time for a test left some of the stations confused; some called the White House press office directly for confirmation, as the order would have needed to come from the President. Some of the teletypes jammed, sometimes the messages were ignored, and apparently some stations just went off the air entirely without making the announcement.

(There was admittedly antiquated rules about stations not being on air during an actual nuclear attack, with the notion that missiles could use the broadcasts themselves as a method of localization.)

Additionally, while the retraction was broadcast "40 minutes later" there were in fact attempts to retract, but they accidentally resent the HATEFULLNESS code word again rather than the retraction word (IMPISH). While these retractions were supposed to be only accepted with the real code word, given the questionable circumstances some stations took the retraction as is (including the WOWO broadcast you linked, where the broadcaster Bob Sieger mentioned the "longest five minutes" of his life -- not 40).

The upshot is that only some of the stations broadcast the message, and the ones that did often included a message to turn into your local station for more updates (as in the WOWO message). However, this led to confusion as people would expect an emergency broadcast on all stations and spinning the dial led to music instead.

However, there were some newspaper accounts of some people who did believe the initial broadcast. Mrs. Peter Ori in Chicago:

I was absolutely terrified. It was so authentic. I just knew we were at war and the President would come on and say what had happened ... that some enemy had attacked this country ... but the President never came on.

An unnamed woman in Melbourne, Florida, was listening in the car and pulled over:

I didn't do anything. I just sat there being scared.

Skepticism was of course possible. One person working at a station in Texas who kept the actual teletypes that you can see scans of called the station manager to let him know about making arrangements, and he "just laughed it off" and that it "had to be a mistake". The retraction (with the wrong code word) came a few minutes later.

It could have been worse. The actual circumstances is that there were three tapes next to each other, one with the test, two with actual alerts. W.S. Eberhardt (who did not suffer any consequences for what happened) pulled off an actual alert tape which is how it ended up on the air. You can see a picture of the setup here.

The fortunate thing is, as I said, there were three tapes. The one that was actually played only said there was some kind of emergency.

The third tape, the one left untouched, was to broadcast specifically that there was an attack.

Afterwards, the real tapes were moved to another part of the room where they could not be confused for the test tape.