T Test Calculator Mean Sd N

A t-test is a statistical test used to determine whether there is a significant difference between the means of two groups. This calculator helps you compute t-test statistics when you know the mean, standard deviation, and sample size for each group.

What is a T-Test?

A t-test is a type of inferential statistic used to determine if there is a significant difference between the means of two groups. It's commonly used in research to compare sample means to assess whether an effect is statistically significant.

There are several types of t-tests, including:

One-sample t-test: Compares a sample mean to a known population mean
Independent samples t-test: Compares means of two independent groups
Paired samples t-test: Compares means of the same group at different times

This calculator focuses on the independent samples t-test, which compares means of two separate groups.

How to Use This Calculator

Enter the mean value for Group 1
Enter the standard deviation for Group 1
Enter the sample size for Group 1
Enter the mean value for Group 2
Enter the standard deviation for Group 2
Enter the sample size for Group 2
Click "Calculate" to compute the t-test statistics

The calculator will display the t-value, degrees of freedom, and p-value, along with a visualization of the distribution.

Formula Explained

T-Test Formula

The t-value for an independent samples t-test is calculated as:

t = (x̄₁ - x̄₂) / √(s₁²/n₁ + s₂²/n₂)

Where:

x̄₁, x̄₂ = sample means for Group 1 and Group 2
s₁, s₂ = sample standard deviations for Group 1 and Group 2
n₁, n₂ = sample sizes for Group 1 and Group 2

The degrees of freedom (df) for the t-test is calculated as:

df = n₁ + n₂ - 2

The p-value is determined from the t-distribution table using the calculated t-value and degrees of freedom.

Interpreting Results

The t-value indicates the size of the difference relative to the variation in your sample data. The p-value helps you determine the significance of your results.

If p ≤ 0.05, you can reject the null hypothesis and conclude there is a statistically significant difference between the groups
If p > 0.05, you fail to reject the null hypothesis and conclude there is no statistically significant difference

Note

A significant result indicates that the difference between the groups is unlikely to have occurred by chance. However, it does not prove causation.

Worked Example

Suppose you want to compare the test scores of two groups:

Group	Mean	Standard Deviation	Sample Size
Group 1	75	10	30
Group 2	80	8	30

Using the calculator:

Enter Group 1 mean: 75
Enter Group 1 SD: 10
Enter Group 1 n: 30
Enter Group 2 mean: 80
Enter Group 2 SD: 8
Enter Group 2 n: 30
Click Calculate

The calculator will show:

T-value: -2.58
Degrees of Freedom: 58
P-value: 0.012

Since the p-value (0.012) is less than 0.05, we can conclude there is a statistically significant difference between the two groups.

FAQ

What is the difference between a t-test and a z-test?

A t-test is used when the population standard deviation is unknown and must be estimated from the sample data. A z-test is used when the population standard deviation is known.

What assumptions does a t-test require?

The t-test assumes that the data is normally distributed, that the samples are independent, and that the variances of the two groups are equal (homoscedasticity).

What does a significant p-value mean?

A significant p-value (typically ≤ 0.05) indicates that the observed difference between groups is unlikely to have occurred by random chance, suggesting a true difference exists.