Inference & Regression
Once you're drawing conclusions from a sample rather than just describing it, this is where the math lives: z-scores, p-values, margin of error, and linear regression.
Calculators & Tools
Margin of Error Calculator
The Margin of Error Calculator determines the confidence interval around a survey result using sample size, population proportion, and confidence level (90%, 95%, or 99%). It applies the standard formula: z-score multiplied by the square root of p times (1 minus p) divided by n. At 95% confidence with 1,000 respondents and a 50% response split, the margin of error is approximately plus or minus 3.1 percentage points.
Linear Regression Calculator
The Linear Regression Calculator computes the best-fit line through a set of data points using the ordinary least squares (OLS) method, producing the slope, intercept, correlation coefficient (r), and coefficient of determination (R squared). It accepts up to 50 data pairs and renders the regression equation in the form y = mx + b alongside a scatter plot. Use it to quantify linear relationships and make predictions within the observed data range.
P-Hat Calculator
The p-hat Calculator computes the sample proportion (p-hat) from the number of successes and total sample size, and constructs the confidence interval for the true population proportion. It uses the normal approximation to the binomial distribution for large samples. Use it in hypothesis testing, survey analysis, and quality control to estimate what fraction of a population exhibits a particular characteristic.
Z-Score Calculator
The Z-Score Calculator computes z = (x - mean) / standard deviation and converts the result to a percentile rank using the standard normal distribution. Also performs reverse lookup from z-score to original value and cumulative probability.
P-Value Calculator
The P-Value Calculator computes p-values for z-tests, t-tests, chi-squared tests, and F-tests for both one-tailed and two-tailed hypotheses. Enter the test statistic and degrees of freedom to evaluate statistical significance.