To test the hypothesis that all treatments have exactly the same effect, the F-test's p-values closely approximate the permutation test's p-values: The approximation is particularly close when the design is balanced.

In game theory and economic theory, a zero – sum game is a mathematical representation of a situation in which a participant's gain ( or loss ) of utility is exactly balanced by the losses ( or gains ) of the utility of the other participant ( s ).

The entropy increase of the radiation field scattered from a directional laser into a random direction is exactly balanced by the entropy reduction of the atoms as they are trapped with the one-way wall.

Although Greg argued that an editor should be free to use his judgment to choose between competing substantive readings, he suggested that an editor should defer to the copy-text when " the claims of two readings ... appear to be exactly balanced.

If the two slices are placed together at distance 1 from the fulcrum, their total weight would be exactly balanced by a circle of area at a distance x from the fulcrum on the other side.

Zero sum is a situation in which a participant's gain or loss is exactly balanced by the losses or gains of the other participants.

It is unclear why Murphy would advocate for the execution of his son-in-law, especially in light of the balanced approach Murphy was known to have during the conflict, which calls into question exactly what his role in these events may have been.

A zero length spring can be attached to a mass on a hinged boom in such a way that the force on the mass is almost exactly balanced by the vertical component of the force from the spring, whatever the position of the boom.

The lasing threshold is reached when the optical gain of the laser medium is exactly balanced by the sum of all the losses experienced by light in one round trip of the laser's optical cavity.

The result is that the weight of the camera is almost exactly balanced by the tension force throughout the entire range of vertical movement, so even when the operator jumps vertically, the camera will retain its vertical position due to inertia, but remain balanced, just with the armature at a different angle.

First is a statement of hydrostatic equilibrium: the outward force due to the pressure gradient within the star is exactly balanced by the inward force due to gravity.

If S − I and NX are exactly zero, we are said to have balanced trade because the value of imports exactly equals the value of our exports.

Since the book is not accelerating, these forces must be exactly balanced, according to Newton's First or Second law.

i. e., when the two attractive forces — Newtonian gravity ( first term ) and the attraction unique to general relativity ( third term ) — are exactly balanced by the repulsive centrifugal force ( second term ).

I have a balanced hand and exactly 12 HCP

Suppose that the semiconductor initially is charge neutral, with the charge due to holes exactly balanced by the negative charge due to acceptor doping impurities.

Automatic redial, which is essentially exactly the same thing, but for modems, and included in most telecommunications programs that use modems, including all variants of Dial-up networking ever included in the Windows operating system.

At first based almost exactly on the military-type design, variants of the standard truck line were eventually given 4WD and the same “ Power Wagon ” name.

Many extensions and variants of the original Backus – Naur notation are used ; some are exactly defined, including Extended Backus – Naur Form ( EBNF ) and Augmented Backus – Naur Form ( ABNF ).

The name " Chernobyl Virus " was coined some time after the virus was already well known as CIH, and refers to the complete coincidence of the payload trigger date in some variants of the virus ( actually the virus creation date in 1998, to trigger exactly a year later ) and the Chernobyl accident, which happened in the Ukrainian SSR on April 26, 1986.

All of the variants are pronounced in the same or almost exactly the same manner regardless of the language and alphabet.

The games do not follow these landscape variants exactly, but still are recurring themes in the Mario series.

It is now almost exactly the same dimensions as the first and second Subaru Legacy ( 1990-1999 ). The third generation high-performance WRX variants will continue on in production until new versions will be released in 2013.

They do not appear under that name exactly in ancient history, however, but rather come on stage boldly and abruptly in the Germania ( Chapter 42 ) of Tacitus as the Naristi, with manuscript variants of Narisci and Varisti.

What exactly are we trying to prove??

It is difficult to tabulate exactly what was meant in each individual situation, but the conclusion may be drawn that 21 towns do not assess movable personal property, and of the remainder only certain types are valued for tax purposes.

We want to know when the Potlatches telephone exactly how many they are planning to bring, so that we won't end up with a splashing mob that looks like Coney Island in August.

a marvelous arrangement, for it provides exactly what the bee queens need to make their beebread, a combination of honey and pollen with which the young of all species are fed.

If a litigant chooses to enforce a Federal right in a State court, he cannot be heard to object if he is treated exactly as are plaintiffs who press like claims arising under State law with regard to the form in which the claim must be stated -- the particularity, for instance, with which a cause of action must be described.

Many years later ( on August 3, 1915 ), Lucy Upton wrote Winslow's daughter soon to be graduated from Smith College: `` While I love botany which, after dabbling in for years, I studied according to the methods of that day exactly forty years ago in a summer school, it must be fascinating to take up zoology in the way you are doing.

A school of thought has it that those attributes are exactly what this concerto needs.

The charges of the electron and proton are believed to be exactly equal and opposite, but Dr. Lyttleton is not so sure.

The axioms are referred to as " 4 + 1 " because for nearly two millennia the fifth ( parallel ) postulate (" through a point outside a line there is exactly one parallel ") was suspected of being derivable from the first four.

This choice gives us two alternative forms of geometry in which the interior angles of a triangle add up to exactly 180 degrees or less, respectively, and are known as Euclidean and hyperbolic geometries.

The Agriculturalists supported the fixing of prices, in which all similar goods, regardless of differences in quality and demand, are set at exactly the same, unchanging price.

Many of Alan ’ s writings are unable to be exactly dated, and the circumstances and details surrounding his writing are often unknown as well.

* A half pint ( 284 ml ) of beer with 3. 5 % ABV contains almost exactly one unit ; however, most beers are stronger.

semantics are very strong: they guarantee that the read and write operations to the variable behave exactly as if they happened instantaneously in some point in time which is within the actual time where the operation took place.

Many members of the movement are also aware of this, and argue that, as long as they have a common opponent, they should march together-even if they don't share exactly the same political vision.

For a first order predicate calculus, with no (" proper ") axioms, Gödel's completeness theorem states that the theorems ( provable statements ) are exactly the logically valid well-formed formulas, so identifying valid formulas is recursively enumerable: given unbounded resources, any valid formula can eventually be proven.

The boundaries of the present council area are exactly the same as those of the old county minus the City of Dundee.

: Athene's garments and ægis were borrowed by the Greeks from the Libyan women, who are dressed in exactly the same way, except that their leather garments are fringed with thongs, not serpents.

Decryption is exactly the same as encryption, except that P1, P2 ,..., P18 are used in the reverse order.

Here, two points on a sphere are called antipodal if they are in exactly opposite directions from the sphere's center.

Chapters 4-10 contain a series of oracles, or prophetic sermons, showing exactly why God is rejecting the Northern Kingdom ( what the grounds are for the divorce ).

Because arcs of circles and ellipses cannot be exactly represented by Bézier curves, they are first approximated by Bézier curves, which are in turn approximated by arcs of circles.