Standard Error of Difference of Means Calculator

✖Standard Deviation of Sample X is the measure of how much the values in Sample X vary. It quantifies the dispersion of data points in Sample X around the mean of Sample X.ⓘ Standard Deviation of Sample X [σ_X]			+10% -10%
✖Size of Sample X in Standard Error is the number of individuals or items in Sample X.ⓘ Size of Sample X in Standard Error [N_X(Error)]			+10% -10%
✖Standard Deviation of Sample Y is the measure of how much the values in Sample Y vary. It quantifies the dispersion of data points in Sample Y around the mean of Sample Y.ⓘ Standard Deviation of Sample Y [σ_Y]			+10% -10%
✖Size of Sample Y in Standard Error is the number of individuals or items in Sample Y.ⓘ Size of Sample Y in Standard Error [N_Y(Error)]			+10% -10%

✖Standard Error of Difference of Means is the standard deviation of the difference between sample means in two independent samples.ⓘ Standard Error of Difference of Means [SE_μ1-μ2]

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Formula

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Standard Error of Difference of Means

Formula

`"SE"_{"μ1-μ2"} = sqrt((("σ"_{"X"}^2)/"N"_{"X(Error)"})+(("σ"_{"Y"}^2)/"N"_{"Y(Error)"}))`

Example

`"1.549193"=sqrt(((("4")^2)/"20")+((("8")^2)/"40"))`

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Standard Error of Difference of Means Solution

STEP 0: Pre-Calculation Summary

Formula Used

Standard Error of Difference of Means = sqrt(((Standard Deviation of Sample X^2)/Size of Sample X in Standard Error)+((Standard Deviation of Sample Y^2)/Size of Sample Y in Standard Error))
SE_μ1-μ2 = sqrt(((σ_X^2)/N_X(Error))+((σ_Y^2)/N_Y(Error)))
This formula uses 1 Functions, 5 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Standard Error of Difference of Means - Standard Error of Difference of Means is the standard deviation of the difference between sample means in two independent samples.
Standard Deviation of Sample X - Standard Deviation of Sample X is the measure of how much the values in Sample X vary. It quantifies the dispersion of data points in Sample X around the mean of Sample X.
Size of Sample X in Standard Error - Size of Sample X in Standard Error is the number of individuals or items in Sample X.
Standard Deviation of Sample Y - Standard Deviation of Sample Y is the measure of how much the values in Sample Y vary. It quantifies the dispersion of data points in Sample Y around the mean of Sample Y.
Size of Sample Y in Standard Error - Size of Sample Y in Standard Error is the number of individuals or items in Sample Y.

STEP 1: Convert Input(s) to Base Unit

Standard Deviation of Sample X: 4 --> No Conversion Required
Size of Sample X in Standard Error: 20 --> No Conversion Required
Standard Deviation of Sample Y: 8 --> No Conversion Required
Size of Sample Y in Standard Error: 40 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

SE_μ1-μ2 = sqrt(((σ_X^2)/N_X(Error))+((σ_Y^2)/N_Y(Error))) --> sqrt(((4^2)/20)+((8^2)/40))

Evaluating ... ...

SE_μ1-μ2 = 1.54919333848297

STEP 3: Convert Result to Output's Unit

1.54919333848297 --> No Conversion Required

FINAL ANSWER

1.54919333848297 ≈ 1.549193 <-- Standard Error of Difference of Means

(Calculation completed in 00.004 seconds)

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< 7 Errors Calculators

Standard Error of Difference of Means

Go Standard Error of Difference of Means = sqrt(((Standard Deviation of Sample X^2)/Size of Sample X in Standard Error)+((Standard Deviation of Sample Y^2)/Size of Sample Y in Standard Error))

Standard Error of Data given Mean

Go Standard Error of Data = sqrt((Sum of Squares of Individual Values/(Sample Size in Standard Error^2))-((Mean of Data^2)/Sample Size in Standard Error))

Standard Error of Proportion

Go Standard Error of Proportion = sqrt((Sample Proportion*(1-Sample Proportion))/Sample Size in Standard Error)

Residual Standard Error of Data given Degrees of Freedom

Go Residual Standard Error of Data = sqrt(Residual Sum of Squares in Standard Error/Degrees of Freedom in Standard Error)

Residual Standard Error of Data

Go Residual Standard Error of Data = sqrt(Residual Sum of Squares in Standard Error/(Sample Size in Standard Error-1))

Standard Error of Data given Variance

Go Standard Error of Data = sqrt(Variance of Data in Standard Error/Sample Size in Standard Error)

Standard Error of Data

Go Standard Error of Data = Standard Deviation of Data/sqrt(Sample Size in Standard Error)

Standard Error of Difference of Means Formula

What is Standard Error and it's importance?

In Statistics and data analysis standard error has great importance. The term "standard error" is used to refer to the standard deviation of various sample statistics, such as the mean or median. For example, the "standard error of the mean" refers to the standard deviation of the distribution of sample means taken from a population. The smaller the standard error, the more representative the sample will be of the overall population.
The relationship between the standard error and the standard deviation is such that, for a given sample size, the standard error equals the standard deviation divided by the square root of the sample size. The standard error is also inversely proportional to the sample size; the larger the sample size, the smaller the standard error because the statistic will approach the actual value.

How to Calculate Standard Error of Difference of Means?

Standard Error of Difference of Means calculator uses Standard Error of Difference of Means = sqrt(((Standard Deviation of Sample X^2)/Size of Sample X in Standard Error)+((Standard Deviation of Sample Y^2)/Size of Sample Y in Standard Error)) to calculate the Standard Error of Difference of Means, Standard Error of Difference of Means formula is defined as the standard deviation of the difference between sample means in two independent samples. Standard Error of Difference of Means is denoted by SE_μ1-μ2 symbol.

How to calculate Standard Error of Difference of Means using this online calculator? To use this online calculator for Standard Error of Difference of Means, enter Standard Deviation of Sample X (σ_X), Size of Sample X in Standard Error (N_X(Error)), Standard Deviation of Sample Y (σ_Y) & Size of Sample Y in Standard Error (N_Y(Error)) and hit the calculate button. Here is how the Standard Error of Difference of Means calculation can be explained with given input values -> 1.549193 = sqrt(((4^2)/20)+((8^2)/40)).

FAQ

What is Standard Error of Difference of Means?

Standard Error of Difference of Means formula is defined as the standard deviation of the difference between sample means in two independent samples and is represented as SE_μ1-μ2 = sqrt(((σ_X^2)/N_X(Error))+((σ_Y^2)/N_Y(Error))) or Standard Error of Difference of Means = sqrt(((Standard Deviation of Sample X^2)/Size of Sample X in Standard Error)+((Standard Deviation of Sample Y^2)/Size of Sample Y in Standard Error)). Standard Deviation of Sample X is the measure of how much the values in Sample X vary. It quantifies the dispersion of data points in Sample X around the mean of Sample X, Size of Sample X in Standard Error is the number of individuals or items in Sample X, Standard Deviation of Sample Y is the measure of how much the values in Sample Y vary. It quantifies the dispersion of data points in Sample Y around the mean of Sample Y & Size of Sample Y in Standard Error is the number of individuals or items in Sample Y.

How to calculate Standard Error of Difference of Means?

Standard Error of Difference of Means formula is defined as the standard deviation of the difference between sample means in two independent samples is calculated using Standard Error of Difference of Means = sqrt(((Standard Deviation of Sample X^2)/Size of Sample X in Standard Error)+((Standard Deviation of Sample Y^2)/Size of Sample Y in Standard Error)). To calculate Standard Error of Difference of Means, you need Standard Deviation of Sample X (σ_X), Size of Sample X in Standard Error (N_X(Error)), Standard Deviation of Sample Y (σ_Y) & Size of Sample Y in Standard Error (N_Y(Error)). With our tool, you need to enter the respective value for Standard Deviation of Sample X, Size of Sample X in Standard Error, Standard Deviation of Sample Y & Size of Sample Y in Standard Error and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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