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T-Statistic Calculator

T-Statistic Calculator

The calculator calculates the t-value of the dataset with sample mean, population mean, standard deviation, and sample size.

Sample mean (x̄)

Population mean (μ)

Sample size

Sample standard deviation (s)

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For a given set of values, the t statistic calculator calculates the T statistic and the corresponding p-value, allowing you to determine the statistical significance of the results. In this way, you can determine the difference between the mean of the two groups.

What Is T-Statistics?

T-Test Statistics is the metric that is used to quantify the relation between a sample and its population. This t-test statistics assesses the hypotheses regarding the population mean.

The t-statistics determines that the results rejected or support the null hypothesis and it takes into account the probability of results occurring by chance. The t-statistic is a key part of the Student’s t-test, which compares the average of a sample with the average of the whole population.

Formula:

\( t=\frac{\bar{x}-\mu}{s \sqrt{n}}\)

Where:

X̄ = sample mean
μ = population mean
n = sample size
s = standard deviation

In the case of small sample sizes or uncertain population standard deviation, the t statistics is commonly used in place of the z-statistics.

How To Calculate T Statistic?

The t statistic is evaluated by comparing the difference between the sample means to the variability within the samples, and the t statistics calculator automates this calculation for ease and accuracy.

Example:

If a sample of learners has different average heights from the known population average height is 65 inches. How to calculate T value for one sample in which the mean height is 67 inches and the sample standard deviation is 3 inches?

Given Values:

  • Population Mean (μ) = 65 inches
  • Sample Mean x̄ = 67 inches
  • Sample Size (n) = 25
  • Sample Standard Deviation (s) = 3 inches

Solution:

\(=\dfrac{\bar{x} – μ}{s \sqrt{n}}\)

\(=\dfrac{67 – 65}{3 \sqrt{25}}\)

\(=\dfrac{2}{3 * 5}\)

\(=\dfrac{2}{15}\)

\(=0.13\)

Steps To Use T Value Calculator:

It is a simple process to use the t score calculator to interpret the statistical significance of your data. So have a look at the points below:

Inputs:

  • (x̄) Sample mean
  • (μ) Population mean
  • Sample size
  • (s) Sample standard deviation

Outputs:

  • T statistics
  • Complete solution with steps

Relation Of T-Score With Data Values:

In hypothesis testing, t-score is used to compare various sets of data or multiple values within the same set. It measures how similar the data is in terms of standard deviations. So;

  • A low t-score shows that the groups have similarities between the two sample sets.
  • A large t-score shows that the groups are different between the two sample sets.