📊 统计学工具

🔬 F 方差检验计算器F Test Variance F 方差检验计算器：输入两组样本方差与自由度，计算 F 统计量与临界值，检验两总体方差是否相等，用于方差齐性判定。F Test Variance - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📐 V 计算器Cramers V Cramér&#x27;s V 计算器Cramers V - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📏 Z 分数计算器Z Fraction Calculator 输入原始分数、总体均值与总体标准差，将分数标准化为 Z 分数 (x−μ)/σ，并给出对应的百分位排名，Z>0 表示高于均值、Z<0 表示低于均值，便于横向比较不同分布的数据。Z Fraction Calculator - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📏 d 效应量计算器Cohens D Cohen&#x27;s d 效应量计算器Cohens D - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 🧪 t 检验统计量T 输入样本均值、假设总体均值、样本标准差与样本量，计算单样本 t 统计量 t=(x̄−μ)/(s/√n)，并给出自由度，|t| 越大表示样本均值偏离假设值的证据越强，用于均值假设检验的第一步。T - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📊 二项分布概率计算器Binomial Pmf 输入试验次数 n 与成功次数 k、成功概率 p，计算 n 次独立伯努利试验恰好 k 次成功的概率，用于离散分布与风险建模。Binomial Pmf - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 🎰 假设检验 p 值近似P 输入 Z 统计量，用正态分布近似快速估算双尾 Z 检验的 p 值，并提示 p<0.05 时通常在 5% 水平下拒绝原假设，适用于大样本假设检验时快速判断显著性。P - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 🏔️ 偏度与峰度Statistics 7 输入一组数据，计算偏度Skewness与峰度Kurtosis，判断分布是否左偏或右偏、是否比正态分布更尖或平缓，辅助识别数据分布形态与异常尾部特征。Statistics 7 - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📊 几何平均数计算器Geometric Mean 几何平均数计算器：输入数值集合，按乘积的 n 次根计算几何平均数，适合增长率、比率等相乘型数据的集中趋势度量。Geometric Mean - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 🏋️ 加权平均数Statistics 11 加权平均数计算器：输入数值与对应权重，按权重自动归一化计算加权平均数，用于成绩、指标等加权汇总。Statistics 11 - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📊 单因素 ANOVA 计算器One Way Anova 单因素方差分析（One-way ANOVA）在线计算器，输入多组样本自动计算组间/组内平方和、F 值与 p 值，判断均值差异显著性，纯前端运行。One Way Anova - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📏 单样本 Z 检验计算器One Sample Z Test 输入样本均值、样本量与已知的总体标准差，检验样本均值是否偏离给定的假设值，输出 Z 统计量及双侧与单侧 p 值，适用于总体标准差已知时的均值显著性检验。One Sample Z Test - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📐 单样本 t 检验计算器One Sample T Test 输入样本数据（或样本均值、标准差与样本量），在总体标准差未知时，用样本 t 分布检验样本均值与假设总体均值是否存在显著差异，输出 t 统计量、自由度和 p 值，适用于小样本均值假设检验。One Sample T Test - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📊 卡方检验计算器Chi Square Test 卡方检验计算器：输入观测值与期望值频数，计算 χ² 统计量并判断分布偏离显著性，用于拟合优度与独立性检验。Chi Square Test - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📊 变异系数比较Statistics 10 变异系数比较工具：输入两组数据的均值与标准差，计算变异系数 CV 消除量纲后比较离散程度，用于不同单位数据的波动性对比。Statistics 10 - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📦 四分位距 IQRIqr 输入数据集，计算 Q1、Q2、Q3 与四分位距 IQR，并据 1.5×IQR 规则标出异常值边界，用于箱线图与离群点检测。Iqr - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📈 均值中位数众数Statistics 12 输入最多 7 个数值，快速计算这组数据的算术均值、中位数、众数与极差，并给出数据总和，适合在课堂上或日常中快速描述一组数据的集中趋势与离散程度。Statistics 12 - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📊 均值标准误计算器Standard Error 均值标准误计算器：输入样本标准差与样本量，求样本均值分布的标准误 SE = s/√n，用于置信区间与显著性检验。Standard Error - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📐 均值样本量计算器Sample Size Mean 均值样本量计算器：给定置信水平、容许误差与总体标准差，估计总体均值所需的最小样本量，用于实验设计。Sample Size Mean - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📊 均值置信区间计算器Confidence Interval 均值置信区间计算器：已知总体标准差时输入样本均值与样本量，求给定置信水平下均值的置信区间，用于统计推断。Confidence Interval - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📊 总体方差计算器Population Variance 总体方差在线计算器，输入完整数据集自动求均值与离差平方平均，衡量数据离散程度，支持批量粘贴、结果实时显示，数据本地处理。Population Variance - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📊 最小二乘回归计算器Linear Regression y = a + b·x（最小二乘）Linear Regression - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📊 标准分 Z 值计算器Z Score Calc 标准分 Z 值计算器：输入原始值、均值与标准差，求标准分 Z = (x−μ)/σ，用于数据标准化与离群判断。Z Score Calc - calculate online, free and accurate. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics to... 📉 标准差与方差Standard Deviation and Variance 输入一组数值并选择类型（1 为样本、2 为总体），计算样本或总体标准差、方差以及变异系数 CV，用于衡量数据的离散程度与相对波动水平，便于不同量纲数据的比较。Standard Deviation and Variance - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics to... 📊 样本方差计算器Sample Variance - : s ² = Σ( x ᵢ− x ̄)²/( n − 1 ) 样本方差计算器：输入数据集，按 n−1 自由度计算样本方差，衡量数据离散程度，用于推断统计与假设检验。Sample Variance - : s ² = Σ( x ᵢ− x ̄)²/( n − 1 ) - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of... 🧮 样本量估算Sample Size Estimate 输入可接受的误差幅度、置信水平与总体标准差，估算估计总体均值所需的最小样本量 n，帮助在调查或实验中以足够精度规划抽样数量，避免样本不足导致误差过大。Sample Size Estimate - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📊 正态分布 CDF 计算器Normal Cdf 正态分布 CDF 计算器：输入均值、标准差与取值 x，计算标准正态分布累积概率 P(X ≤ x)，用于概率与分位评估。Normal Cdf - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 🔔 正态分布概率Statistics 输入均值、标准差以及区间上下界，计算正态分布下该区间的概率（即曲线下面积），下界可填很大的负数近似负无穷，用于求某取值范围内的累积概率或分位数区间。Statistics - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 🎯 比例样本量计算器Sample Size ( Ratio ) 比例样本量计算器：给定置信水平、误差界与预期比例，估计总体比例所需样本量，用于抽样调查设计。Sample Size ( Ratio ) - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📊 比例置信区间计算器Confidence Proportion 比例置信区间计算器：输入样本成功数与样本量（或样本比例），按正态近似求总体比例在给定置信水平下的置信区间，用于调查与医学估计。Confidence Proportion - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 🔢 比值比计算器Odds Ratio 输入 2×2 列联表的四项频数，计算比值比 OR 及其置信区间，衡量暴露与结局的关联强度，用于流行病学与医学统计分析。Odds Ratio - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📊 泊松分布概率计算器Poisson Pmf 输入单位时间（或空间）内事件的平均发生率 λ 和目标发生次数 k，计算泊松分布的概率质量函数 P(X=k)，即恰好发生 k 次事件的概率，常用于客服来电、故障次数等稀有事件的建模。Poisson Pmf - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. ⚖️ 独立双样本 t 检验计算器Independent T Test 独立双样本 t 检验计算器：输入两组独立样本数据，计算 t 值与 p 值，判断两总体均值是否存在显著差异，用于实验与对比研究。Independent T Test - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 🥞 由两组样本量方差求合并方差Merge Variance Calculator - Merge Variance : Input n1 , s1 , n2 , s2 , Output s_p ² 输入两组样本量n₁、n₂及其方差s₁²、s₂²，按加权平均求合并方差s_p²，用于两独立样本t检验前的方差齐性处理，适用于实验数据的统计推断。Merge Variance Calculator - Merge Variance : Input n1 , s1 , n2 , s2 , Output s_p ² - free online tool. ↔️ 由临界值与标准误求误差幅度Margin of Error 输入临界值 z 与标准误 SE，按 ME = z×SE 计算置信区间的误差幅度，用于抽样调查、问卷与实验结果的不确定性估计。Margin of Error - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. ➖ 由事件概率求其补事件概率Probability Complement 对立事件概率计算器：输入事件概率 p，按 P(Aᶜ) = 1 − P(A) 求对立（补）事件概率，用于概率基本运算。Probability Complement - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 💯 由均值与标准差求变异系数Coefficient of Variation 输入均值 μ 与标准差 σ，按 CV = σ/μ × 100% 计算变异系数，用于比较不同量纲数据的离散程度与相对波动水平。Coefficient of Variation - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📊 由数值序列求平均绝对偏差Mean Absolute Deviation 输入一组数值，按 MAD = Σ|xᵢ − x̄|/n 计算平均绝对偏差，衡量数据平均离散程度，用于预测误差与稳健性评估。Mean Absolute Deviation - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. ↔️ 由数值序列求极差Range Calculator 极差计算器：输入数值序列，按 R = max − min 求极差，快速衡量数据离散跨度，用于描述统计初筛。Range Calculator - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📈 由数值序列求样本偏度Skewness Sample 样本偏度计算器：输入数值序列，按三阶中心矩公式求样本偏度 g₁，判断分布左偏/右偏及对称程度。Skewness Sample - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📊 由数值序列求样本方差Sample Variance Calculator 输入以逗号或空格分隔的一组数值，计算样本方差 s²=Σ(xᵢ−x̄)²/(n−1)，作为标准差的平方衡量数据离散程度，常用于统计描述与后续检验的方差分析。Sample Variance Calculator - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📊 由数值序列求样本标准差Sample Standard Deviation Calculator 输入以逗号或空格分隔的一组数值，计算样本标准差 s，反映数据相对均值的平均离散程度，按 n−1 作分母的无偏估计，适合评估一组观测值的波动大小。Sample Standard Deviation Calculator - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statisti... #️⃣ 由样本均值、假设均值与标准差求 t 值T Score 输入样本均值 x̄、假设均值 μ、标准差 s 与样本量 n，求 t 统计量。T Score - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 💯 由样本比例与样本量求标准误Standard Error Proportion 输入样本比例 p 与样本量 n，按公式 SE=√[p(1−p)/n] 计算样本比例的标准误，衡量样本比例估计总体比例的抽样波动，用于比例置信区间与假设检验。Standard Error Proportion - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. ⬜ 由相关系数求决定系数Correlation R Squared 决定系数计算器：输入相关系数 r，按 R² = r² 求决定系数，表示回归模型对因变量变异的解释比例，用于回归拟合优度评估。Correlation R Squared - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. ∑ 由试验数、成功概率与上限求累积概率Binomial Cdf 输入试验数 n、成功概率 p 与上限 x，按累积分布求 P(X≤x)，用于质量抽检、可靠性与二项分布下累计概率的统计分析。Binomial Cdf - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 🔀 由赔率求对应概率Odds to Probability 赔率转概率计算器：输入赔率 o，按 p = o/(1+o) 换算对应概率，用于博彩、医学风险与流行病学表达转换。Odds to Probability - convert values online, free and instant. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the St... 📊 百分等级计算器Percentile Rank 百分等级计算器：输入数值与数据集，计算该值低于总体中多少比例的数据（百分等级），用于成绩与排名评估。Percentile Rank - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📊 皮尔逊相关系数计算器Correlation Coefficient 皮尔逊相关系数计算器：输入两变量成对数据，计算 Pearson 相关系数 r 衡量线性相关强度与方向，并给出显著性判断，用于相关分析。Correlation Coefficient - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📈 相对风险计算器Relative Risk ( RR ) 相对风险计算器：输入暴露组与非暴露组的结局发生率，计算相对风险 RR 衡量暴露与结局的关联强度，用于流行病学队列研究。Relative Risk ( RR ) - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📏 线性回归拟合Statistics 16 输入成对(x,y)样本数据，用最小二乘法拟合直线y=ax+b，输出斜率a、截距b、相关系数及拟合优度，并可代入任意x预测y值，用于趋势分析与数据建模。Statistics 16 - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 🎯 置信区间估算Statistics 4 输入样本均值、总体或样本标准差与样本量，并指定置信水平（如 95%），用 Z 分布估算总体均值的置信区间，给出上下限，适用于大样本或已知总体标准差时的区间估计。Statistics 4 - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 📊 调和平均数计算器Harmonic Mean 调和平均数计算器：输入数值集合，按倒数的算术平均之倒数计算调和平均数，适合速率、单价等倒数型数据的平均。Harmonic Mean - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 🧠 贝叶斯定理计算器Bayes Theorem 贝叶斯定理计算器：输入先验概率与似然，按贝叶斯公式更新后验概率，用于医学诊断与统计推断。Bayes Theorem - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools. 🔗 配对 t 检验计算器Paired T Test 输入同一组对象的配对测量值（如服药前后），计算每对差值及其均值与标准差，用配对 t 检验判断差值是否显著不为零，输出 t 统计量、自由度与 p 值，用于前后对照实验的差异检验。Paired T Test - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Statistics tools.