Parametric Tests Calculators
This page presents tools that summarise group averages and probability values under distributional assumptions, providing numerical outputs for hypothesis comparisons.
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One Sample T-Test Calculator
A single group's average can be compared with a stated reference value by examining how far the sample's average differs from that reference once variation in the data is taken into account.
Example use: checking whether the average number of steps taken in one day differs from a personal target.
Inputs: input type, sample data, sample mean, standard deviation, sample size, hypothesised population mean, alternative hypothesis, significance level
Outputs: t statistic, degrees of freedom, probability value, critical t value, significance level, result
Visual: a smooth curve showing the t distribution with a marker for the observed t value
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One Sample Z-Test Calculator
A sample average can be compared with a stated reference value when the population's spread is known, using the distance between the sample's average and the reference in standardised units.
Example use: checking whether the average time spent on a short walk differs from a familiar expected duration.
Inputs: input type, sample data, hypothesised mean, known population standard deviation, sample mean, sample size, alternative hypothesis, significance level
Outputs: decision, z statistic, probability value, critical z value, sample mean, standard error, confidence interval
Visual: a smooth normal curve with acceptance and rejection regions and a line marking the z statistic
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One-Way ANOVA Test Calculator
Differences among several group averages can be assessed by comparing variation between the groups with variation within the groups.
Example use: comparing the time three groups take to complete a simple household chore.
Inputs: group data, significance level
Outputs: significance level, critical f value, f statistic, probability value, decision, group summaries, overall average, sum of squares between groups, sum of squares within groups, mean squares, f statistic
Visual: a curve showing the f distribution with acceptance and rejection regions and a marker for the f statistic
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Paired Sample t-Test Calculator
Two related measurements can be compared by analysing the differences within each pair and assessing whether the average difference departs from zero.
Example use: comparing the time taken to complete a short puzzle before and after a brief rest.
Inputs: sample 1 data, sample 2 data, alternative hypothesis, significance level
Outputs: decision, t statistic, degrees of freedom, critical value, probability value, mean difference, standard deviation of differences, standard error, sample size
Visual: a t distribution curve with a highlighted rejection region and a marker for the observed t value
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Two Sample T-Test (Pooled Variance) Calculator
Two independent groups can be compared by combining their variation into a single pooled estimate and assessing whether their averages differ more than expected by chance.
Example use: comparing how long two unrelated groups spend preparing a simple meal.
Inputs: input type, group 1 data, group 2 data, mean, standard deviation, sample size, tail type, significance level
Outputs: t statistic, degrees of freedom, probability value, critical value, significance level, pooled variance, standard error, result, hypotheses, group 1 statistics, group 2 statistics, sum of squares, conclusion
Visual: a t distribution curve with a rejection region and a marker for the calculated t value
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Welch's Two Sample t-Test Calculator for Independent Means
Two independent groups with different levels of variation can be compared by using a separate estimate of spread for each group and adjusting the degrees of freedom accordingly.
Example use: comparing the number of minutes two unrelated groups spend on a short daily activity.
Inputs: calculator type, group 1 data, group 2 data, mean, standard deviation, size, tail type, significance level
Outputs: t statistic, degrees of freedom, probability value, critical t value, result, group means, sample variances, sum of squared deviations, standard error of difference, computed t statistic, welch-satterthwaite degrees of freedom
Visual: a t distribution curve with a rejection region and a marker for the t statistic
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Two Sample Z-Test Calculator
Two independent group averages can be compared using known population spreads to determine whether their difference is larger than expected by chance.
Example use: comparing the average number of pages read per day by two unrelated groups.
Inputs: input method, sample 1 data, sample 2 data, population standard deviation 1, population standard deviation 2, mean 1, mean 2, standard deviation 1, standard deviation 2, size 1, size 2, hypothesis type, significance level
Outputs: z statistic, probability value, critical value, difference in means, standard error, confidence interval, result
Visual: a normal curve with a rejection region and a marker for the observed z value
Parametric Tests FAQs
Parametric tests summarise data using distributional assumptions, generating statistics based on averages, spread and sample size.
They are applied when numerical data meets distribution requirements, including symmetry, consistent variance and interval-based measurement.
Common options include t-tests for one or two groups, z-tests for known variances and ANOVA for comparing several group averages.
A t-test uses estimated variance for smaller samples, whereas a z-test applies fixed variance values for larger sample sizes.
A normal distribution reflects values clustering around a central average with symmetric spread across both sides of the centre.