Why does the two-sample test use Welch's formula instead of the standard t-test?

Welch's t-test doesn't assume both samples have equal variance, which the standard (pooled-variance) two-sample t-test does. Welch's version is considered the safer default in most modern statistical practice since equal variance is often not actually true.

What does a p-value below 0.05 mean?

By the common convention (α = 0.05), it means the observed result would be unlikely to occur by chance alone if there were truly no difference — conventionally interpreted as statistically significant, though this threshold is a convention, not a universal law.

Statistical Significance Test Calculator

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Run a one-sample t-test, two-sample (Welch's) t-test, or chi-square test and get the test statistic and p-value.

Neural Network Parameter & FLOPs Calculator

Estimates total trainable parameters and forward-pass FLOPs for a fully-connected (dense) network from its layer sizes.

Layer sizes (comma-separated, input → output)

Batch size

Total parameters

235.15K (235,146)

FLOPs per sample (forward pass)

469.90K

Total FLOPs (batch of 1)

469.90K

Layer	Shape	Parameters	FLOPs (per sample)
1	784 → 256	200,960	401,664
2	256 → 128	32,896	65,664
3	128 → 10	1,290	2,570

FLOPs counted as 2 per multiply-add (industry convention). Only covers fully-connected layers — convolutional/attention layers have different FLOP formulas not modeled here.

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How to use Statistical Significance Test Calculator

1Choose one-sample t-test, two-sample t-test, or chi-square test.
2Enter your sample data (or observed/expected frequencies for chi-square).
3Review the test statistic, degrees of freedom, and two-tailed p-value.

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About Statistical Significance Test Calculator

Statistical Significance Test Calculator

Runs three commonly needed hypothesis tests:

One-sample t-test: does a sample's mean differ significantly from a hypothesized value?
Two-sample t-test (Welch's): do two independent samples have significantly different means? Uses Welch's formulation, which doesn't assume equal variances between groups — a safer default than the pooled-variance Student's t-test.
Chi-square test: do observed category frequencies differ significantly from expected frequencies?

All p-values are computed from first principles (regularized incomplete beta and gamma functions), verified against standard statistical tables.

Educational Guides & Tutorials

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What a p-value Actually Means (and What It Doesn't)

The precise definition of a p-value, why 0.05 is a convention rather than a law of nature, and the specific misinterpretation that trips up almost everyone.

Read guide →

Frequently Asked Questions

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