Research Statistics Toolkit
Free calculators for your research
Sample size, descriptive statistics, hypothesis testing and regression — with full step-by-step working for every result.
Taro Yamane Sample Size Calculator
Find the required sample size when your total population is known.
About this formula
Yamane’s formula (1967) estimates the minimum sample size needed to represent a known population at a chosen margin of error:
n = N1 + Ne²
n = N1 + Ne²
- N — total population size
- e — acceptable margin of error (commonly 0.05 for 95% confidence)
Common values: 0.05 (95% confidence) or 0.10 (90% confidence).
Result
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Cochran Sample Size Calculator
Calculate sample size for large or unknown populations.
About this formula
Cochran’s formula estimates sample size using a target confidence level and expected proportion:
n₀ = Z²pqe²
n₀ = Z²pqe²
- Z — Z-score for your confidence level
- p — estimated proportion (use 0.5 if unknown, this is the most conservative estimate)
- q — 1 − p
- e — margin of error
Result
Show step-by-step working
Descriptive Statistics Calculator
Mean, median, mode, range and standard deviation — in one pass.
About this calculator
Enter a list of numbers to get a quick full descriptive summary. Choose Sample if your data is a subset of a larger population (uses n−1 in the variance divisor), or Population if it is the entire population (uses n).
Result
Standard Deviation & Variance Calculator
Full working for mean, variance and standard deviation.
About this calculator
Standard deviation measures how spread out your data is from the mean. Choose Sample when your data is drawn from a larger population (divides by n−1), or Population when it represents the entire group (divides by n).
Result
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Confidence Interval Calculator
Estimate the range your true population mean likely falls within.
About this calculator
A confidence interval gives a range around your sample mean that is likely to contain the true population mean.
CI = x̄ ± Z × SD√n
This calculator uses the Z-distribution, which is most accurate for sample sizes of 30 or more. For smaller samples, a t-distribution interval is more precise.
CI = x̄ ± Z × SD√n
This calculator uses the Z-distribution, which is most accurate for sample sizes of 30 or more. For smaller samples, a t-distribution interval is more precise.
Result
Show step-by-step working
Two-Sample t-Test Calculator
Compare the means of two independent groups.
About this test
The independent two-sample t-test checks whether the means of two groups are significantly different, assuming both groups have similar variances (a pooled-variance t-test). It reports:
- t statistic and degrees of freedom
- Two-tailed p-value, computed from the exact Student’s t-distribution
- Cohen’s d, an effect-size measure independent of sample size
Group 1
Group 2
Result
Chi-Square Test Calculator (2×2)
Test for association between two categorical variables.
About this test
The chi-square test of independence checks whether two categorical variables are related, by comparing observed counts in a 2×2 contingency table to what would be expected if there were no association. Degrees of freedom for a 2×2 table is always 1.
Yates’ continuity correction is recommended for 2×2 tables, especially with small expected counts — it slightly reduces the chi-square value to avoid overstating significance.
Yates’ continuity correction is recommended for 2×2 tables, especially with small expected counts — it slightly reduces the chi-square value to avoid overstating significance.
Outcome 1
Outcome 2
Group 1
Group 2
Result
Simple Linear Regression Calculator
Fit a line to paired data and predict new values.
About this calculator
Enter paired x, y data points, one pair per line, e.g.:
The calculator fits the line y = mx + b, and reports the correlation coefficient (r) and R² — how much of the variation in y is explained by x.
1,22,43,5
The calculator fits the line y = mx + b, and reports the correlation coefficient (r) and R² — how much of the variation in y is explained by x.
Result
Likert Scale Mean Score Calculator
Calculate mean score and interpretation for questionnaire responses.
How to use this calculator
Enter the number of respondents who selected each option on your scale. The calculator computes the weighted mean score and applies the standard decision rule:
- Mean at or above the scale midpoint → Accepted
- Mean below the scale midpoint → Rejected
Result
Unlock 99Scholar Pro Calculators (100% Free)
Get full access to advanced calculators with data visualization and in-depth statistical analysis.
- Multiple Linear Regression Calculator 3D visualization, regression equation, R² analysis
- ANOVA Calculator ANOVA table, F-test, boxplot visualization
- Bayesian Statistics Calculator Posterior calculation, priors visualization
- Chi-Square Test Calculator χ² test, p-value, observed vs expected