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math.stats-t-test Calculator
Performs a two-sample t-test from sample means, standard deviations, and sizes, computing the t-statistic and approximate degrees of freedom. The Welch t-test (unequal variances) is the default in R and Python's SciPy — it's more robust than the pooled version.
Inputs
X1
Arithmetic average. Sensitive to outliers — if your data has extreme values, the median may be more representative.
X2
Arithmetic average. Sensitive to outliers — if your data has extreme values, the median may be more representative.
S1
Reference formula or conversion factor shown for context.
N1
Reference formula or conversion factor shown for context.
Results
t statistic
The test statistic for a t-test — the signal-to-noise ratio of the effect. Compare to the critical value for your degrees of freedom and alpha level.
standard error of diff
The difference between the computed result and the exact or true value — a measure of approximation accuracy.
degrees of freedom
The magnitude or severity on the applicable scale.
Cohen d (effect size)
Standardised measure of the magnitude of the difference or relationship, independent of sample size. Cohen's d: 0.2 = small, 0.5 = medium, 0.8 = large.
reject H₀ at 5% (|t|>1.96)?
The value at the specified point or condition.
|t|>2.576 for 1% level
The measured or computed level on the applicable scale.