StatCalc

📊 Descriptive Statistics

Try:

Enter your data (comma-separated or one per line):

Formulas Used

Mean: x̄ = Σxᵢ / n
Variance: s² = Σ(xᵢ − x̄)² / (n − 1)
Std Dev: s = √s²
Skewness: g₁ = [n/((n−1)(n−2))] · Σ[(xᵢ−x̄)/s]³
IQR: Q3 − Q1 (linear interpolation)

Sample Size (n)-

Mean (x̄)-

Median-

Standard Deviation (s)-

Variance (s²)-

Min / Max-

IQR (Q1 – Q3)-

Skewness-

📏 Confidence Intervals

Try:

Sample Mean (x̄):

Sample Standard Deviation (s):

Sample Size (n):

Confidence Level:

Formulas Used

Standard Error: SE = s / √n
t-critical: t* from Student's t-distribution at df = n−1
Margin of Error: E = t* × SE
Confidence Interval: x̄ ± E = [x̄ − E, x̄ + E]

Standard Error-

t-critical value-

Margin of Error-

Lower Bound-

Upper Bound-

Confidence Interval-

🎯 One-Sample t-Test

Try:

Sample Mean (x̄):

Sample Std Dev (s):

Sample Size (n):

Null Hypothesis Mean (μ₀):

Test Type:

Formulas Used

t-statistic: t = (x̄ − μ₀) / (s / √n)
Degrees of freedom: df = n − 1
Cohen's d: d = |x̄ − μ₀| / s
p-value from Student's t-distribution

t-statistic-

Degrees of Freedom-

p-value-

Result (α = 0.05)-

Effect Size (Cohen's d)-

⚖️ Two-Sample t-Test

Try:

Compare means of two independent groups (Welch's t-test, unequal variances).

Group 1 data (comma-separated or one per line):

Group 2 data:

Test Type:

Formulas Used (Welch's t-test)

t = (x̄₁ − x̄₂) / √(s₁²/n₁ + s₂²/n₂)
df ≈ (s₁²/n₁ + s₂²/n₂)² / [(s₁²/n₁)²/(n₁−1) + (s₂²/n₂)²/(n₂−1)]
Cohen's d = |x̄₁ − x̄₂| / sₚ where sₚ = √[((n₁−1)s₁² + (n₂−1)s₂²) / (n₁+n₂−2)]

Group 1: n, x̄, s-

Group 2: n, x̄, s-

Mean Difference-

t-statistic-

Degrees of Freedom-

p-value-

Result (α = 0.05)-

Effect Size (Cohen's d)-

95% CI for Difference-

🔗 Paired t-Test

Try:

Compare two related measurements (before/after, matched pairs). Enter paired data — each line has two values separated by comma or tab.

Paired data (value1, value2 per line):

Test Type:

Formulas Used (Paired t-test)

Differences: dᵢ = x₁ᵢ − x₂ᵢ
Mean difference: d̄ = Σdᵢ / n
SD of differences: s_d = √[Σ(dᵢ − d̄)² / (n−1)]
t = d̄ / (s_d / √n), df = n − 1
Cohen's d = |d̄| / s_d

Number of Pairs (n)-

Mean Difference (d̄)-

SD of Differences (s_d)-

t-statistic-

Degrees of Freedom-

p-value-

Result (α = 0.05)-

Effect Size (Cohen's d)-

95% CI for Mean Difference-

📊 Test of Independence

Try:

Enter a contingency table. Each row on a new line, values separated by commas. Rows = categories of variable 1, columns = categories of variable 2.

Contingency table (observed frequencies):

Row labels (optional, comma-separated):

Column labels (optional, comma-separated):

Formulas Used

Expected: Eᵢⱼ = (Row Total × Col Total) / Grand Total
χ² = Σ (Oᵢⱼ − Eᵢⱼ)² / Eᵢⱼ
df = (rows − 1)(cols − 1)
Cramér's V = √(χ² / (n × min(rows−1, cols−1)))

Chi-Square Statistic (χ²)-

Degrees of Freedom-

p-value-

Result (α = 0.05)-

Effect Size (Cramér's V)-

🎯 Goodness of Fit

Try:

Compare observed frequencies against expected frequencies (or a uniform distribution).

Observed frequencies (comma-separated):

Expected frequencies or proportions (leave blank for uniform):

Enter expected counts, or leave blank to assume equal frequencies across categories.

Category labels (optional, comma-separated):

Formulas Used

χ² = Σ (Oᵢ − Eᵢ)² / Eᵢ
df = k − 1 (k = number of categories)
p-value from χ² distribution

Number of Categories (k)-

Chi-Square Statistic (χ²)-

Degrees of Freedom-

p-value-

Result (α = 0.05)-

🔬 One-Way ANOVA

Try:

Enter group data. Each line: GroupName: value1, value2, ...
At least 2 groups required.

Group Data:

Formulas Used

SS_between = Σ nⱼ(x̄ⱼ − x̄)² — variation between group means
SS_within = ΣΣ (xᵢⱼ − x̄ⱼ)² — variation within groups
MS = SS / df, F = MS_between / MS_within
η² = SS_between / SS_total (effect size)
Post-hoc: Bonferroni-corrected pairwise t-tests (α / number of comparisons)

Number of Groups (k)-

Total N-

F-Statistic-

p-value-

Effect Size (η²)-

Conclusion-

📈 Linear Regression & Correlation

Try:

Enter paired (x, y) data. One pair per line, separated by comma or tab.

Data (x, y pairs):

Formulas Used

Slope: b₁ = Σ(xᵢ−x̄)(yᵢ−ȳ) / Σ(xᵢ−x̄)²
Intercept: b₀ = ȳ − b₁x̄
Correlation: r = Σ(xᵢ−x̄)(yᵢ−ȳ) / √[Σ(xᵢ−x̄)² · Σ(yᵢ−ȳ)²]
R² = r² (proportion of variance explained)
Sₑ = √[Σ(yᵢ−ŷᵢ)² / (n−2)]

Sample Size (n)-

Correlation (r)-

R² (coefficient of determination)-

Regression Equation-

Slope (b₁)-

Intercept (b₀)-

Std Error of Estimate (Sₑ)-

Slope t-test (H₀: β₁=0)-

📐 Sample Size & Power

Try:

Effect Size (Cohen's d):

Small: 0.2 · Medium: 0.5 · Large: 0.8

Statistical Power:

Significance Level (α):

Formulas Used

n = ⌈((z_α/2 + z_β) / d)²⌉
where z_α/2 = inverse normal CDF at 1−α/2
z_β = inverse normal CDF at power
d = Cohen's d (effect size in std dev units)

Required Sample Size (n)-

Effect Size Interpretation-

Minimum Detectable Difference-

📊 Descriptive Statistics

📏 Confidence Intervals

🎯 One-Sample t-Test

⚖️ Two-Sample t-Test

🔗 Paired t-Test

📊 Test of Independence

🎯 Goodness of Fit

🔬 One-Way ANOVA

📈 Linear Regression & Correlation

🔮 Prediction

📐 Sample Size & Power

How's StatCalc working for you?