The testicle is not "large" for the purposes mentioned, but rather so that the gamete producing organs of the male can adjust to external factors in ways that protect the organs.
In the female the gamete-producing organs, full at birth of already-produced gametes ready to be matured and released at intervals throughout life, are located in a protected position within the body.
In the male the gamete-producing organs must descend to the outside of the body, as temperatures within are too high for sperm formation processes. For protection of the gametes/production of gametes, the scrotum is able to adjust according to temperatures, allowing the male to function in the world without having to consciously constantly adjust the location of the scrotal sac for best sperm production temperatures.
In other words, balls are sometimes larger in appearance: in hotter temperatures the sac expands and lowers the testicles for better cooling. The same man's balls are sometimes smaller in appearance: in cold weather the sac automatically brings the gamete-producing organs closer to the warmth of the body. It may also be noted that the sac often will draw toward the body in extreme shock or fear response, another auto-protective
feature.
It is also very well recognized that a penis varies in size according to arousal. (I do hope I need not link this particular statement to scientific studies.) Also, when the scrotum draws inward toward the body in cold/fear response, the flaccid penis will often appear smaller than when temperatures are warm, primarily because the drawing in of the nearby tissues results in a slight drawing in of the upper penile tissues as well. An entirely protective mechanism.
Just as the scrotum and associated musculature draw in the scrotum, and to a lesser degree, the penis, in defense against cold or in fear, the opposite occurs when the male is both unafraid and warm. That which draws in against cold or fear, relaxes when cold and fear are abated, taking the gametes and gamete-production away from excessive heat of the male's own body, and providing better cooling air circulation around the scrotum.
Psychologists are definitely not biologists, and it seems from both articles, that any "research" on this subject was likely done before a mirror rather than in a research facility or library, and is therefore not well informed.
Neither size of male human scrota (which is very variable even in a single male in the course of any day or year) nor shape of male human scrota (which is designed primarily for function and protection) has much to do with attracting human females.
Women are likely to confirm that size and shape of scrota is not a primary factor in sexual attraction: generally, by the time they see these organs, the attraction has already been confirmed. Another evidence for the UN-likelihood of human female attraction being based on appearance of scrota: how many women would likely subscribe to an erotic magazine featuring photography solely of scrota? Why not ask this question in column and take a poll?
A psychologist who wishes to argue these points, might wish to do another mirror-based study outdoors in very cold temperatures where wolves and grizzlies abound.

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