Standard Normal Distribution CDF Calculator Compute the cumulative probability for a standard normal variable: $$ \Phi(x)=\frac{1}{2}\Bigl[1+\operatorname{erf}\Bigl(\frac{x}{\sqrt{2}}\Bigr)\Bigr]. $$ * Enter the value of \( x \). Step 1: Enter \( x \) Value \( x \): e.g., 0 Calculate CDF Calculated CDF \( \Phi(x) \): Recalculate Formula: $$ \Phi(x)=\frac{1}{2}\Bigl[1+\operatorname{erf}\Bigl(\frac{x}{\sqrt{2}}\Bigr)\Bigr]. $$ Standard Normal Distribution CDF Calculator (In-Depth […]

Hierarchical Regression F‑Value Calculator Compute the F‑statistic for the incremental change in \( R^2 \) between two nested regression models: $$ F=\frac{(R^2_{\text{full}}-R^2_{\text{base}})/(k_{\text{full}}-k_{\text{base}})}{(1-R^2_{\text{full}})/(n-k_{\text{full}}-1)}. $$ * Enter the sample size \( n \), baseline model \( R^2 \) and number of predictors \( k_{\text{base}} \), and full model \( R^2 \) and number of predictors \( k_{\text{full}} […]

Enter a chi-square value (x) and the degrees of freedom (df) to find the cumulative probability. This calculator provides an approximate CDF of the Chi-Square distribution. For critical or professional analyses, use specialized statistical software.

t-Distribution CDF Calculator t‑Distribution CDF Calculator Calculate the cumulative probability for a t‑distributed variable: $$ F(t;\nu)= \begin{cases} 1-\frac{1}{2}I_{\frac{\nu}{t^2+\nu}}\Bigl(\frac{\nu}{2},\frac{1}{2}\Bigr) & t\ge0,\\[1ex] \frac{1}{2}I_{\frac{\nu}{t^2+\nu}}\Bigl(\frac{\nu}{2},\frac{1}{2}\Bigr) & t

This calculator computes the p-value given an F-statistic and its corresponding degrees of freedom (df₁ and df₂). Use this for hypothesis testing in ANOVA or regression analyses. For high-stakes decisions, verify results with professional statistical software. F-Test p-Value Calculator F-Test p‑Value Calculator Enter the F‑statistic along with the numerator (\(d_1\)) and denominator (\(d_2\)) degrees of […]

Cumulative Binomial Probability Calculator Cumulative Binomial Probability Calculator Use this calculator to determine the cumulative probability of obtaining up to a certain number of successes in a fixed number of trials. Input the number of trials, probability of success, and number of successes to compute the cumulative binomial probability. Number of Trials (( n )): […]

Enter the chi-square statistic (x) and degrees of freedom (df) to find the p-value (upper-tail probability). This tool uses approximations. For critical analyses, please use professional statistical software. Chi-Square p-Value Calculator | Compute Upper-Tail Probability Chi-Square p-Value Calculator Input Data Chi-Square Value (x): Degrees of Freedom (df): Calculate p-Value Results p-value: 0.0000 *This calculation is […]

Uniform Distribution CDF Calculator Uniform Distribution CDF Calculator Calculate the CDF for a Uniform Distribution over the interval \([a,b]\): $$ F(x)= \begin{cases} 0, & x < a,\\[1ex] \frac{x-a}{b-a}, & a \le x \le b,\\[1ex] 1, & x > b. \end{cases} $$ * Enter the lower bound \(a\), upper bound \(b\) (with \(b > a\)), and […]

F-Distribution PDF Calculator F‑Distribution PDF Calculator Calculate the PDF for an F‑distribution with degrees of freedom \( d_1 \) and \( d_2 \): $$ f(x; d_1, d_2) = \frac{\Gamma\left(\frac{d_1+d_2}{2}\right)}{\Gamma\left(\frac{d_1}{2}\right)\Gamma\left(\frac{d_2}{2}\right)}\left(\frac{d_1}{d_2}\right)^{\frac{d_1}{2}} \frac{x^{\frac{d_1}{2}-1}}{\Bigl(1+\frac{d_1}{d_2}x\Bigr)^{\frac{d_1+d_2}{2}}}. $$ * Enter the F‑value (x), numerator degrees of freedom (\(d_1\)), and denominator degrees of freedom (\(d_2\)). Step 1: Enter Parameters F‑value, \( x \): […]

Binomial PMF Calculator Binomial PMF Calculator Use this calculator to determine the probability ( P(X = k) ) for the Binomial distribution. Input your number of trials ( n ), probability of success ( p ), and the number of successes ( k ) to compute the Binomial PMF. Number of Trials (( n )): […]