Sci-fi short story involving the scientific method being rediscovered in a medieval tribe of humans from stranded spacemen

Question

My dad had given me a book of short sci-fi stories before he left. I remember reading one around 2004 that has stuck with me but I cannot find it. Hopefully some of the old school sci-fi readers will see this, and point me in the right direction. So I'm going to try to be very specific with the plot.
PLOT:
4 or 5 Human ships crash unto an alien planet populated with alien life similar to Native American level knowledge (I remember them biologically being like frogmen.) and after generations each crashed ship is turned into a fortress and the offspring from the captains each rule their respective ship fortress kingdoms separately.
Science has been largely forgotten and what little weapons and technology from the past is relegated to the noble class. The ship based weapons had been kept pristine outwardly by constant cleaning and worship. They were believed to be functional but in fact the inward components had been destroyed and rusted away through generations of neglect.
A mage class assisted each "Captain". With several supposedly commanding giant metal beasts that would assist the mage and their captains in battle. These metal beasts were made real psychologically through psychosomatic suggestion and rumors/stories told through the human population.
They also had a physical representation sometimes that was little more then animatronic like statues that rolled along with them into battle. In one scene a siege occurs. A metal beast statue breaths fire and lights dummies wearing the enemies uniform on fire. Causing the defenders to panic and believe that they too were "magically" burning.
Another scene introduced a mage that would summon demons to possess his warriors, which manifested as a psychotic rage and sent them into battle capable of losing limbs with no regard. This was achieved by burning a mixed incense into an enclosed room filled with 20-40 warriors, while said mage would chant wearing an ancient gas mask (It was heavily implied the incense contained drugs). Those who breathed the incense would die an hour after initial inhalation.
The technological level of the human descendants were medieval and while magic and metal monsters existed culturally. Their perceived existence was maintained through tricks and psychological manipulation by the mage class of society.
In the end an apprentice mage who seeks the secrets to "real magic" rediscovers the scientific method which saves the humans from a horde of angry alien frogmen attacking the kingdom.
Sorry for the grammar/formatting appreciate any help you can give. The book this short story was in also contained stories by Robert Heinlein and a few others

FuzzyBoots · Answer

The story is likely Jack Vance's "The Miracle Workers".

The story is about a colony of human space voyagers founded when they took refuge on the Earth-like planet of Pangborn 1,600 years ago during a space war. The first colonists were still worried about the risk of attack, so they built huge fortresses and mounted heavy weapons from the spaceships on the ramparts. At the time of the story, the society has lost all of their knowledge of modern science, except for a small number of still-functioning air-cars.
They use a Medieval level of technology, such as horse-drawn carriages and simple tools. The planet is divided into feudal territories that are defended by mounted knights and foot soldiers carrying crossbows, swords and spears. To supplement these weapons, they have developed a type of telepathy which is used as a battle weapon. The telepathy is done by skilled “Jinxmen”, who cast spells and manipulate enemy troops using wooden cabinets filled with small voodoo dolls representing their opponents.
The "First Folk" (also called "autochthon") are indigenous hominids who live in the forested areas. They were brutally hunted down by the initial human colonists. While the human colonists gradually lost their scientific knowledge, the First Folk took up the scientific method that the first colonists showed them and continued to develop it over the centuries.

....

A young apprentice of Lord Faide’s head Jinxman has been experimenting with scientific approaches to defeating the First Folk. The apprentice has been studying the ancient scientific texts from their space-faring ancestors. After Lorde Faide wins the battle against Lord Ballant, he is for a time the overlord of the planet. However, the peace does not last long, as the First Folk launch a guerrilla war against the colonists using the First Folk's scientifically-bred army of arthropod creatures, which they are producing as bioweapons on an industrial scale.

According to ISFDB, it's been in a lot of collections, so we need more information about the time period to figure out which one, but I think a likely case is The Arbor House Treasury of Great Science Fiction Short Novels, which also includes "By his Bootstraps" by Heinlein.

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Sci-fi short story involving the scientific method being rediscovered in a medieval tribe of humans from stranded spacemen

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