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The t-Test Calculator performs an independent two-sample t-test to determine whether two group means are significantly different. The t-test is one of the most fundamental statistical tests in biology, used to compare treatment vs. control groups, male vs. female measurements, or any two independent samples. It tests the null hypothesis that the two population means are equal.
This calculator uses the Welch-type approximation, which does not assume equal variances, making it robust for most biological data where variance heterogeneity is common.
The t-statistic is calculated as:
t = (Mean₁ - Mean₂) / √(Var₁/n₁ + Var₂/n₂)
The resulting t-value is compared to critical values from the t-distribution. For a two-tailed test at α = 0.05 with large df (>30), the critical value is approximately 2.0. If |t| exceeds the critical value, the means are significantly different.
Inputs
Results
t = 2.92 exceeds the critical value of approximately 2.003 (df=56, α=0.05). The difference is statistically significant.
Inputs
Results
t = 0.66 is below the critical value of 2.048 (df=28, α=0.05). No significant height difference between the two groups.
Use a two-sample t-test when comparing means of exactly two independent groups with continuous data. For more than two groups, use ANOVA. For paired/matched data, use a paired t-test. For non-normal data or small samples, consider non-parametric alternatives like the Mann-Whitney U test. The t-test assumes approximately normal distributions, though it is robust to moderate departures with larger sample sizes.
The critical value depends on degrees of freedom and significance level. Common values at α = 0.05 (two-tailed): df=10 gives 2.228, df=20 gives 2.086, df=30 gives 2.042, df=60 gives 2.000, and df=120 gives 1.980. If your calculated |t| exceeds the critical value, reject the null hypothesis. For precise p-values, consult a t-distribution table or statistical software.
This calculator takes variance (σ²) as input, which is the square of the standard deviation (σ). If you have the standard deviation, square it before entering. For example, if SD = 4, enter variance = 16. Variance is used in the formula because the variances of independent samples are additive, making the calculation cleaner.
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