Hypothesis Tests

How to use this category

A hypothesis test is a ruled argument. This category keeps each argument on its own page so the null, the standard error, and the degrees of freedom stay visible. Z tests require a known sigma or a proportion model. T tests estimate sigma. Welch does not pool. Paired tests use differences. ANOVA compares means through sums of squares. Chi-square and Fisher's exact test stay with counts. Sample-size formulas sit here too, and they are not interchangeable: Slovin, Cochran, and Yamane ask for different extra information and return different planning numbers.

Read the design before you read the p-value. One sample, two samples, paired differences, and more than two groups are not flavours of the same button. If the population standard deviation is a number you were given, a z test can use it. If you calculated the spread from the same rows you are testing, you want a t test and you want the degrees of freedom written down. Unequal spreads are Welch's problem. A 2 by 2 table of small counts is Fisher's problem even though chi-square is more famous. Sample-size planning is in this category because it is part of the same argument: what would count as evidence, and how many observations that standard requires. Do not plan with Slovin and then test with a procedure that needed Cochran's inputs. The pages exist so that mix-up is visible.

The cards above are the whole category, with one sentence on the job each page actually does. Open a page when that sentence matches the decision in front of you. If the sentence is close but the assumption is wrong, read the comparison section on the page before you copy a number into a report, a bid, or a lesson plan.

Worked examples are prefilled so the first result is auditable. Change one input and the ticket updates. The essay under the ticket walks the same arithmetic in sentences, then a second example, then the move that most often breaks the definition. Five questions at the end answer the objections a careful reader raises after seeing the figure. That structure is repeated because the habit of checking is the point, not because the formulas are the same.

Internal links leave this category only when the next formula genuinely lives next door. A standard deviation page may point at variance and at a t test. It should not point at a decking calculator. If you arrived from search on a broad word, use the one-sentence descriptions to discard the near misses. Near misses are how people report a p-value from a test they did not run.

Each worksheet in Hypothesis Tests keeps one H1, a canonical URL that matches the tool name, and meta text sized for search snippets. The steps are part of the page, not a hidden modal. If you teach from these pages, project the ticket and the assumptions together so students see the same definition you graded against.

When two tools in Hypothesis Tests look alike, read the blurb under each name before you commit. The difference is usually a divisor, a critical value, a waste percent, or a caution that belongs on one page and not the other. That difference is why the URLs stay separate.

Reviewed 21-10-2026. Pages in Hypothesis Tests currently include ANOVA Calculator, Chi-Square Critical Value Calculator, Chi-Square Goodness of Fit Test Calculator, Chi-Square Test Calculator, Cochran's Formula Calculator, Degrees of Freedom Calculator, F Critical Value Calculator, F-Test Calculator, Fisher's Exact Test Calculator, One Proportion Z-Test Calculator, One Sample T-Test Calculator, One Sample Z-Test Calculator, P-Value Calculator, P-Value from Chi-Square Calculator, P-Value from F Calculator, P-Value from T Calculator, P-Value from Z Calculator, Paired T-Test Calculator, R Critical Value Calculator, Slovin's Formula Calculator, T Critical Value Calculator, T-Test Calculator, Two Proportion Z-Test Calculator, Two Sample T-Test Calculator, Two Sample Z-Test Calculator, Welch's T-Test Calculator, Yamane's Formula Calculator, Z Critical Value Calculator, Z-Test Calculator.

Every hypothesis tests page

• ANOVA Calculator One-way ANOVA on two or more groups typed as separate lines of data.
• Chi-Square Critical Value Calculator Returns the upper-tail chi-square cutoff for a given df and alpha.
• Chi-Square Goodness of Fit Test Calculator Compares observed category counts with expected counts or expected proportions.
• Chi-Square Test Calculator Pearson chi-square test of independence for a contingency table of counts.
• Cochran's Formula Calculator Sizes a sample from a z cutoff and either a proportion or a known sigma, with an optional finite-population correction on the proportion path.
• Degrees of Freedom Calculator Returns the degrees of freedom for one sample, two samples, Welch, paired data, ANOVA, chi-square, or a regression slope.
• F Critical Value Calculator Returns the upper-tail F cutoff for numerator df, denominator df, and alpha.
• F-Test Calculator Compares two sample variances with an F ratio and an upper-tail or two-sided p-value.
• Fisher's Exact Test Calculator Exact two-sided or one-sided p-value for a 2×2 table of counts via the hypergeometric distribution.
• One Proportion Z-Test Calculator Tests a sample proportion against a hypothesized p0 with a normal z statistic.
• One Sample T-Test Calculator Tests a mean against mu0 from a list of data, or from a sample mean, sample sd, and n.
• One Sample Z-Test Calculator Tests a sample mean against a hypothesized mean when the population sigma is known.
• P-Value Calculator Chooser that converts a z, t, chi-square, or F statistic into a p-value for the matching reference curve.
• P-Value from Chi-Square Calculator Converts a chi-square statistic and degrees of freedom into an upper-tail p-value.
• P-Value from F Calculator Converts an F statistic and its two degrees of freedom into an upper-tail p-value.
• P-Value from T Calculator Converts a t statistic and degrees of freedom into a one-sided or two-sided p-value.
• P-Value from Z Calculator Converts a standard normal z statistic into a one-sided or two-sided p-value.
• Paired T-Test Calculator Tests the mean of paired differences, from two matched columns or from a list of differences.
• R Critical Value Calculator Converts a t cutoff on n minus 2 degrees of freedom into the critical Pearson correlation.
• Slovin's Formula Calculator Turns a population and a proportional margin into a sample size, or inverts the same equation to recover the margin.
• T Critical Value Calculator Finds the Student t cutoff for your degrees of freedom, alpha, and tail.
• T-Test Calculator Chooser for one-sample, two-sample pooled, or paired t tests from summary numbers.
• Two Proportion Z-Test Calculator Compares two independent sample proportions with a pooled or unpooled z statistic.
• Two Sample T-Test Calculator Compares two means with a pooled variance and df equal to n1 plus n2 minus 2.
• Two Sample Z-Test Calculator Compares two means when both population standard deviations are known.
• Welch's T-Test Calculator Compares two means without a pooled variance, using the Welch standard error and Satterthwaite df.
• Yamane's Formula Calculator Builds the half-and-half sample size, then lifts it for nonresponse and multiplies by a design effect.
• Z Critical Value Calculator Returns the standard-normal cutoff for a chosen alpha and tail, and keeps the familiar table entries beside it as references.
• Z-Test Calculator Chooser for a one-mean z test, two-mean z test, or one-proportion z test when sigma or p0 is known.