F Value of Two Samples given Sample Standard Deviations Calculator

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✖Standard Deviation of Sample X is the square root of expectation of the squared deviation of the random variable associated with the given sample X from a population from its sample mean.ⓘ Standard Deviation of Sample X [σ_X]			+10% -10%
✖Standard Deviation of Sample Y is the square root of expectation of the squared deviation of the random variable associated with the given sample Y from a population from its sample mean.ⓘ Standard Deviation of Sample Y [σ_Y]			+10% -10%

✖F Value of Two Samples is a parameter connecting two different samples that gives the ratio of the variances of those samples.ⓘ F Value of Two Samples given Sample Standard Deviations [F_(X/Y)]

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F Value of Two Samples given Sample Standard Deviations

Formula

`"F"_{"(X/Y)"} = ("σ"_{"X"}/"σ"_{"Y"})^2`

Example

`"3.104308"=("7.4"/"4.2")^2`

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F Value of Two Samples given Sample Standard Deviations Solution

STEP 0: Pre-Calculation Summary

Formula Used

F Value of Two Samples = (Standard Deviation of Sample X/Standard Deviation of Sample Y)^2
F_(X/Y) = (σ_X/σ_Y)^2
This formula uses 3 Variables

Variables Used

F Value of Two Samples - F Value of Two Samples is a parameter connecting two different samples that gives the ratio of the variances of those samples.
Standard Deviation of Sample X - Standard Deviation of Sample X is the square root of expectation of the squared deviation of the random variable associated with the given sample X from a population from its sample mean.
Standard Deviation of Sample Y - Standard Deviation of Sample Y is the square root of expectation of the squared deviation of the random variable associated with the given sample Y from a population from its sample mean.

STEP 1: Convert Input(s) to Base Unit

Standard Deviation of Sample X: 7.4 --> No Conversion Required
Standard Deviation of Sample Y: 4.2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

F_(X/Y) = (σ_X/σ_Y)^2 --> (7.4/4.2)^2

Evaluating ... ...

F_(X/Y) = 3.10430839002268

STEP 3: Convert Result to Output's Unit

3.10430839002268 --> No Conversion Required

FINAL ANSWER

3.10430839002268 ≈ 3.104308 <-- F Value of Two Samples

(Calculation completed in 00.001 seconds)

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National Institute of Technology (NIT), Jamshedpur

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< 16 Basic Formulas in Statistics Calculators

P Value of Sample

Go P Value of Sample = (Sample Proportion-Assumed Population Proportion)/sqrt((Assumed Population Proportion*(1-Assumed Population Proportion))/Sample Size)

Sample Size given P Value

Go Sample Size = ((P Value of Sample^2)*Assumed Population Proportion*(1-Assumed Population Proportion))/((Sample Proportion-Assumed Population Proportion)^2)

t Statistic of Normal Distribution

Go t Statistic of Normal Distribution = (Sample Mean-Population Mean)/(Sample Standard Deviation/sqrt(Sample Size))

t Statistic

Go t Statistic = (Observed Mean of Sample-Theoretical Mean of Sample)/(Sample Standard Deviation/sqrt(Sample Size))

Chi Square Statistic

Go Chi Square Statistic = ((Sample Size-1)*Sample Standard Deviation^2)/(Population Standard Deviation^2)

Number of Classes given Class Width

Go Number of Classes = (Largest Item in Data-Smallest Item in Data)/Class Width of Data

Class Width of Data

Go Class Width of Data = (Largest Item in Data-Smallest Item in Data)/Number of Classes

Expectation of Difference of Random Variables

Go Expectation of Difference of Random Variables = Expectation of Random Variable X-Expectation of Random Variable Y

Chi Square Statistic given Sample and Population Variances

Go Chi Square Statistic = ((Sample Size-1)*Sample Variance)/Population Variance

Expectation of Sum of Random Variables

Go Expectation of Sum of Random Variables = Expectation of Random Variable X+Expectation of Random Variable Y

Number of Individual Values given Residual Standard Error

Go Number of Individual Values = (Residual Sum of Squares/(Residual Standard Error of Data^2))+1

F Value of Two Samples given Sample Standard Deviations

Go F Value of Two Samples = (Standard Deviation of Sample X/Standard Deviation of Sample Y)^2

F Value of Two Samples

Go F Value of Two Samples = Variance of Sample X/Variance of Sample Y

Range of Data given Largest and Smallest Items

Go Range of Data = Largest Item in Data-Smallest Item in Data

Smallest Item in Data given Range

Go Smallest Item in Data = Largest Item in Data-Range of Data

Largest Item in Data given Range

Go Largest Item in Data = Range of Data+Smallest Item in Data

F Value of Two Samples given Sample Standard Deviations Formula

F Value of Two Samples = (Standard Deviation of Sample X/Standard Deviation of Sample Y)^2
F_(X/Y) = (σ_X/σ_Y)^2

What is F-test in Statistics?

An F-test is any statistical test in which the test statistic has an F-distribution under the null hypothesis. It is most often used when comparing statistical models that have been fitted to a data set, in order to identify the model that best fits the population from which the data were sampled. Exact "F-tests" mainly arise when the models have been fitted to the data using least squares.
Common examples of the use of F-tests include the study of the following cases:
(i) The hypothesis that the means of a given set of normally distributed populations, all having the same standard deviation, are equal. This is perhaps the best-known F-test, and plays an important role in the analysis of variance (ANOVA).
(ii) The hypothesis that a proposed regression model fits the data well. See Lack-of-fit sum of squares.
(iii) The hypothesis that a data set in a regression analysis follows the simpler of two proposed linear models that are nested within each other.

How to Calculate F Value of Two Samples given Sample Standard Deviations?

F Value of Two Samples given Sample Standard Deviations calculator uses F Value of Two Samples = (Standard Deviation of Sample X/Standard Deviation of Sample Y)^2 to calculate the F Value of Two Samples, F Value of Two Samples given Sample Standard Deviations formula is defined as a parameter connecting two different samples that gives the ratio of the variances of those samples, and calculated using the standard deviations of both samples in the given information. F Value of Two Samples is denoted by F_(X/Y) symbol.

How to calculate F Value of Two Samples given Sample Standard Deviations using this online calculator? To use this online calculator for F Value of Two Samples given Sample Standard Deviations, enter Standard Deviation of Sample X (σ_X) & Standard Deviation of Sample Y (σ_Y) and hit the calculate button. Here is how the F Value of Two Samples given Sample Standard Deviations calculation can be explained with given input values -> 3.104308 = (7.4/4.2)^2.

FAQ

What is F Value of Two Samples given Sample Standard Deviations?

F Value of Two Samples given Sample Standard Deviations formula is defined as a parameter connecting two different samples that gives the ratio of the variances of those samples, and calculated using the standard deviations of both samples in the given information and is represented as F_(X/Y) = (σ_X/σ_Y)^2 or F Value of Two Samples = (Standard Deviation of Sample X/Standard Deviation of Sample Y)^2. Standard Deviation of Sample X is the square root of expectation of the squared deviation of the random variable associated with the given sample X from a population from its sample mean & Standard Deviation of Sample Y is the square root of expectation of the squared deviation of the random variable associated with the given sample Y from a population from its sample mean.

How to calculate F Value of Two Samples given Sample Standard Deviations?

F Value of Two Samples given Sample Standard Deviations formula is defined as a parameter connecting two different samples that gives the ratio of the variances of those samples, and calculated using the standard deviations of both samples in the given information is calculated using F Value of Two Samples = (Standard Deviation of Sample X/Standard Deviation of Sample Y)^2. To calculate F Value of Two Samples given Sample Standard Deviations, you need Standard Deviation of Sample X (σ_X) & Standard Deviation of Sample Y (σ_Y). With our tool, you need to enter the respective value for Standard Deviation of Sample X & Standard Deviation of Sample Y and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate F Value of Two Samples?

In this formula, F Value of Two Samples uses Standard Deviation of Sample X & Standard Deviation of Sample Y. We can use 1 other way(s) to calculate the same, which is/are as follows -

F Value of Two Samples = Variance of Sample X/Variance of Sample Y

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