2 Sample T Test Calculator

2 Sample T Test Formula:

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

Mean of Sample 1 (m₁):

Standard Deviation of Sample 1 (s₁):

Sample Size 1 (n₁):

Mean of Sample 2 (m₂):

Standard Deviation of Sample 2 (s₂):

Sample Size 2 (n₂):

T Value:

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1. What is the 2 Sample T Test?

The 2 sample t-test (independent samples t-test) determines whether there is a statistically significant difference between the means of two independent groups. It's commonly used in research to compare experimental and control groups.

2. How Does the Calculator Work?

The calculator uses the 2 sample 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 sample 1
\( m_2 \) — Mean of sample 2
\( s_1 \) — Standard deviation of sample 1
\( s_2 \) — Standard deviation of sample 2
\( n_1 \) — Size of sample 1
\( n_2 \) — Size of sample 2

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

3. Interpretation of Results

Details: The calculated t-value needs to be compared with critical values from the t-distribution table. A larger absolute t-value suggests stronger evidence against the null hypothesis of equal means.

4. Using the Calculator

Tips: Enter all required parameters. Sample sizes should be positive integers, standard deviations non-negative numbers. The calculator assumes independent samples and approximately normal distributions.

5. Frequently Asked Questions (FAQ)

Q1: When should I use a 2 sample t-test?
A: When comparing means from two independent groups with continuous data that is approximately normally distributed.

Q2: What's the difference between paired and unpaired t-tests?
A: Paired tests compare measurements from the same subjects at different times, while unpaired tests compare different groups.

Q3: What if my data isn't normally distributed?
A: Consider non-parametric alternatives like the Mann-Whitney U test.

Q4: How do I determine statistical significance?
A: Compare your t-value to critical values at your chosen significance level (typically 0.05) with appropriate degrees of freedom.

Q5: What assumptions does this test make?
A: Independence of observations, approximately normal distributions, and homogeneity of variance (though Welch's correction can handle unequal variances).