Independent T-Test Calculator

Independent T-Test Formula:

\[ t = \frac{m_1 - m_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \]

Mean of Group 1 (m₁):

Standard Deviation of Group 1 (s₁):

Sample Size of Group 1 (n₁):

Mean of Group 2 (m₂):

Standard Deviation of Group 2 (s₂):

Sample Size of Group 2 (n₂):

T-Statistic:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Independent T-Test?

The independent t-test (also called Student's t-test) compares the means of two independent groups to determine if there is statistical evidence that the associated population means are significantly different. It assumes that the two populations have normal distributions and equal variances.

2. How Does the Calculator Work?

The calculator uses the independent t-test formula:

\[ t = \frac{m_1 - m_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \]

Where:

\( m_1 \) — Mean of group 1
\( m_2 \) — Mean of group 2
\( s_1 \) — Standard deviation of group 1
\( s_2 \) — Standard deviation of group 2
\( n_1 \) — Sample size of group 1
\( n_2 \) — Sample size of group 2

Explanation: The numerator measures the difference between group means, while the denominator estimates the standard error of this difference.

3. Importance of T-Test Calculation

Details: The t-test is fundamental in hypothesis testing, allowing researchers to determine if observed differences between groups are statistically significant or likely due to chance.

4. Using the Calculator

Tips: Enter the means, standard deviations, and sample sizes for both groups. All values must be valid (sample sizes > 0, standard deviations ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: When should I use an independent t-test?
A: Use it when comparing means from two independent groups with continuous, normally distributed data.

Q2: What's the difference between one-tailed and two-tailed tests?
A: One-tailed tests check for a difference in one direction only, while two-tailed tests check for any difference (more conservative).

Q3: What if my variances are unequal?
A: Consider using Welch's t-test, which doesn't assume equal variances.

Q4: How do I interpret the t-statistic?
A: Compare it to critical values from the t-distribution based on your degrees of freedom and significance level.

Q5: What are the assumptions of the t-test?
A: Independence of observations, normality, and (for standard t-test) homogeneity of variance.