Control variable method(English: control variables)Monte Carlo methodFor reducingvarianceOne oftechnical method 。This method reduces the error of unknown quantity estimation by knowing the known quantity.
variableOr variable refers to the number that can be changed without fixed value.Variables are expressed in non numeric symbols, usually withlatin alphabet。Variables are the opposite of constants.The use of variables is to generalize the way instructions are described.If only true values can be used, the instruction can only be applied in some cases.Variables can be used as retainers for any of the values of a particular kind.
Variables are used in open sentences to indicate values that are not yet clear (i.e. variables), or a value that can be substituted (see function).These variables are usually expressed in one English letter. If more than one English letter is used, it is easy to confuse them into the multiplication of two variables.n. M, x, y, z are common variable names, in which n and m are often integers.
Physics
For the problem of multi factors (multi variables) in physics, the method of controlling factors (variables) is often used to turn the problem of multi factors into the problem of multiple single factors.Each time, only one of the factors is changed, while the other factors remain unchanged, so as to study the influence of the changed factor on things, study them separately, and finally solve them comprehensively. This method is called control variable method.It is an important method of thinking in scientific exploration, and is widely used in various scientific exploration and scientific experimental research.[1]
1. Independent variable, that is, a quantity change will not cause divisiondependent variableOther quantity changes.Only when a physical quantity is expressed by an independent variableFunctional relationIs right.
2. Non independent variable. A change in a quantity will cause changes in other quantities except the dependent variable.It is a big taboo to regard dependent variables as independent variables to determine the relationship between physical quantities.
Correctly determining whether the physical quantity in the physical expression is a constant or a variable, an independent variable or a dependent variable, is not only the prerequisite and guarantee for correctly solving relevant problems, but also can simplify the solution process.
Methods On demand: When a problem is related to multiple factors, the control variable method is usually used to explore the relationship between the problem and one of the factors.
statistics
Variables are characteristics of objects in statistical research.It can be qualitative or quantitative. A quantitative variable is either discrete or continuous.In social sciencesResearch variableA variable is usually calledindependent variable(independent variable), and the other variable is called dependent variable (dependent variable)
Discrete variable can also be calledDiscrete indexIt refers to an indicator that can only be displayed as an overall value.
2. Continuous variable
Continuous variables can also be called continuous indicators, which refer to indicators that can have decimals.
application
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Explore the factors that affect the speed of evaporation, and explore the loudness andtoneIdeal inclined plane experiment, relationship between inquiry force and movement, inquiry influencesliding friction Factors of size, exploration influence pressureEffect of forceThe factors ofLiquid pressureFactors of size, factors affecting buoyancy, factors affecting mechanical efficiency of pulley block, and influenceskinetic energyFactors of size and exploration influenceGravitational potential energyFactors of size, verificationOhm's law. Explore the relationship between the current of the resistance and the voltage at both ends, and explore the impactWork done by currentHow many factors, explore the impactThermal effect of currentThe factors ofelectromagnetThe strength of magnetism.And tests are needed.[1]
Experimental examples
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In 1583, GalileoPisa Cathedral Notice the swing of a hanging lamp, and then simulate it with a wire hanging copper ball（Simple pendulum）Experiments confirmed thatswingOfIsochronityAnd pendulum length pairscycleFrom which a pulse meter was created tomeasureshorttime interval。The method used is the control variable method.
Explore the relationship between resistance and current
We can first control the voltage artificially (i.e. unchanged), change the resistance, and then measure the current corresponding to each resistance value, so that we can know that when the voltage is constant, the current passing through the conductor is inversely proportional to the resistance.The control variable method is to studyphysical quantityRelationship between。
Explore the relationship between displacement, speed and time
S=vt, that is, displacement=speed * time. This formula can be studied by using the control variable method, that is, know "speed", "displacement" and "time", but in order to study“Displacement=speed × time”For this formula, we will use the control variable method.
The research method is as follows: we let a small car run at a constant speed for a period of time, and then watch its displacement.In order to study the relationship between displacement and "speed" and "time", we first let the trolley compare the displacement under two conditions at the same time in different situations.
For example, first drive at the speed of 3m/s for 5 seconds and record the displacement of 15m;Then drive at the speed of 9m/s for 5 seconds and record the displacement of 45m. In this way, we can see that the speed has increased several times and the displacement has also increased several times in the same time, that isDisplacement is proportional to speed。Note that in this example, we purposely keep the time of two trips of the car the same (both are 5 seconds), so that we can find the relationship between "displacement and speed are proportional". Because the variable "time" is controlled to keep it unchanged, so that we can study problems, this method is called "control variable method".Similarly, if we control the variable "speed", we can also find that“Displacement is proportional to time”This relationship.(The way is to let the car run at the same speed for different times, and compare the displacement under the two conditions.) You can also use the DIS experimental system for experiments (usually in high schools).
