2 Sample T-Test P Value Calculator

2 Sample T-Test:

\[ t = \frac{\bar{X}_1 - \bar{X}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \] \[ df \approx n_1 + n_2 - 2 \]

Sample 1 Mean (X̄₁):

Sample 1 Standard Deviation (s₁):

Sample 1 Size (n₁):

Sample 2 Mean (X̄₂):

Sample 2 Standard Deviation (s₂):

Sample 2 Size (n₂):

Test Type:

T-Statistic (t):

Degrees of Freedom (df):

P-Value:

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1. What is a 2 Sample T-Test?

The two-sample t-test (also known as the independent samples t-test) is a statistical method used to determine whether the means of two independent groups are significantly different from each other. It compares the means of two groups while accounting for variability and sample size.

2. How Does the Calculator Work?

The calculator uses the following formulas:

\[ t = \frac{\bar{X}_1 - \bar{X}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \] \[ df \approx \frac{\left(\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}\right)^2}{\frac{(s_1^2/n_1)^2}{n_1-1} + \frac{(s_2^2/n_2)^2}{n_2-1}} \]

Where:

\( \bar{X}_1, \bar{X}_2 \) — Sample means
\( s_1, s_2 \) — Sample standard deviations
\( n_1, n_2 \) — Sample sizes
\( df \) — Degrees of freedom (Welch-Satterthwaite equation)
\( t \) — Calculated t-statistic

Explanation: The t-statistic measures how many standard errors the difference between means represents. The p-value indicates the probability of observing such a difference if the null hypothesis (no difference) were true.

3. Interpretation of Results

Key concepts:

T-statistic: Larger absolute values indicate greater difference between groups relative to variability
Degrees of freedom: Affects the shape of the t-distribution used to calculate the p-value
P-value: Probability of observing the data if the null hypothesis is true (typically compared to α=0.05)

4. Using the Calculator

Tips:

Enter means, standard deviations, and sample sizes for both groups
Select whether you're performing a one-tailed or two-tailed test
Standard deviations must be ≥0
Sample sizes must be ≥2

5. Frequently Asked Questions (FAQ)

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

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

Q4: How large should my sample sizes be?
A: Generally ≥30 per group for reliable results with moderate effect sizes, but depends on expected effect size.

Q5: What's a good p-value?
A: Typically p<0.05 is considered statistically significant, but this threshold depends on your field and study design.