t Statistic Calculator

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✖Observed Mean of Sample is the average of the individual values in the given sample statistical data, and obtained by experimental or practical observation.ⓘ Observed Mean of Sample [μ_Observed]			+10% -10%
✖Theoretical Mean of Sample is the average of the individual values in the given sample statistical data, and obtained by theoretical methods of calculation.ⓘ Theoretical Mean of Sample [μ_Theoretical]			+10% -10%
✖Sample Standard Deviation is the square root of expectation of the squared deviation of the random variable associated with the given sample from a population from its sample mean.ⓘ Sample Standard Deviation [s]			+10% -10%
✖Sample Size is the total number of individuals present in the given sample in a population under investigation.ⓘ Sample Size [N]			+10% -10%

✖t Statistic is the standard parameter that characterize a sample from population using the observed mean and theoretical mean of the sample with respect to the sample standard deviation.ⓘ t Statistic [t]

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t Statistic

Formula

`"t" = ("μ"_{"Observed"}-"μ"_{"Theoretical"})/("s"/sqrt("N"))`

Example

`"2.555506"=("16"-"14")/("3.5"/sqrt("20"))`

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t Statistic Solution

STEP 0: Pre-Calculation Summary

Formula Used

t Statistic = (Observed Mean of Sample-Theoretical Mean of Sample)/(Sample Standard Deviation/sqrt(Sample Size))
t = (μ_Observed-μ_Theoretical)/(s/sqrt(N))
This formula uses 1 Functions, 5 Variables

Functions Used

sqrt - Square root function, sqrt(Number)

Variables Used

t Statistic - t Statistic is the standard parameter that characterize a sample from population using the observed mean and theoretical mean of the sample with respect to the sample standard deviation.
Observed Mean of Sample - Observed Mean of Sample is the average of the individual values in the given sample statistical data, and obtained by experimental or practical observation.
Theoretical Mean of Sample - Theoretical Mean of Sample is the average of the individual values in the given sample statistical data, and obtained by theoretical methods of calculation.
Sample Standard Deviation - Sample Standard Deviation is the square root of expectation of the squared deviation of the random variable associated with the given sample from a population from its sample mean.
Sample Size - Sample Size is the total number of individuals present in the given sample in a population under investigation.

STEP 1: Convert Input(s) to Base Unit

Observed Mean of Sample: 16 --> No Conversion Required
Theoretical Mean of Sample: 14 --> No Conversion Required
Sample Standard Deviation: 3.5 --> No Conversion Required
Sample Size: 20 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t = (μ_Observed-μ_Theoretical)/(s/sqrt(N)) --> (16-14)/(3.5/sqrt(20))

Evaluating ... ...

t = 2.55550625999976

STEP 3: Convert Result to Output's Unit

2.55550625999976 --> No Conversion Required

FINAL ANSWER

2.55550625999976 ≈ 2.555506 <-- t Statistic

(Calculation completed in 00.001 seconds)

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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

t Statistic Formula

t Statistic = (Observed Mean of Sample-Theoretical Mean of Sample)/(Sample Standard Deviation/sqrt(Sample Size))
t = (μ_Observed-μ_Theoretical)/(s/sqrt(N))

What is the t test in Statistics?

A t test is a statistical test that is used to compare the means of two groups. It is often used in hypothesis testing to determine whether a process or treatment actually has an effect on the population of interest, or whether two groups are different from one another. There are three t tests to compare means: a one-sample t test, a two-sample t test and a paired t test.

How to Calculate t Statistic?

t Statistic calculator uses t Statistic = (Observed Mean of Sample-Theoretical Mean of Sample)/(Sample Standard Deviation/sqrt(Sample Size)) to calculate the t Statistic, t Statistic formula is defined as the standard parameter that characterize a sample from population using the observed mean and theoretical mean of the sample with respect to the sample standard deviation. t Statistic is denoted by t symbol.

How to calculate t Statistic using this online calculator? To use this online calculator for t Statistic, enter Observed Mean of Sample (μ_Observed), Theoretical Mean of Sample (μ_Theoretical), Sample Standard Deviation (s) & Sample Size (N) and hit the calculate button. Here is how the t Statistic calculation can be explained with given input values -> 2.555506 = (16-14)/(3.5/sqrt(20)).

FAQ

What is t Statistic?

t Statistic formula is defined as the standard parameter that characterize a sample from population using the observed mean and theoretical mean of the sample with respect to the sample standard deviation and is represented as t = (μ_Observed-μ_Theoretical)/(s/sqrt(N)) or t Statistic = (Observed Mean of Sample-Theoretical Mean of Sample)/(Sample Standard Deviation/sqrt(Sample Size)). Observed Mean of Sample is the average of the individual values in the given sample statistical data, and obtained by experimental or practical observation, Theoretical Mean of Sample is the average of the individual values in the given sample statistical data, and obtained by theoretical methods of calculation, Sample Standard Deviation is the square root of expectation of the squared deviation of the random variable associated with the given sample from a population from its sample mean & Sample Size is the total number of individuals present in the given sample in a population under investigation.

How to calculate t Statistic?

t Statistic formula is defined as the standard parameter that characterize a sample from population using the observed mean and theoretical mean of the sample with respect to the sample standard deviation is calculated using t Statistic = (Observed Mean of Sample-Theoretical Mean of Sample)/(Sample Standard Deviation/sqrt(Sample Size)). To calculate t Statistic, you need Observed Mean of Sample (μ_Observed), Theoretical Mean of Sample (μ_Theoretical), Sample Standard Deviation (s) & Sample Size (N). With our tool, you need to enter the respective value for Observed Mean of Sample, Theoretical Mean of Sample, Sample Standard Deviation & Sample Size 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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