Symbols
- Page ID
- 34988
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)| \(n\) | Sample Size | \(z_{\alpha / 2}\) | Critical Value for Standard Normal Distribution | |
| \(N\) | Population Size | \(z\) | \(z\)-Test Statistic | |
| \(\sum\) | Sum | \(df\) | Degrees of Freedom | |
| \(\bar{x}\) | Sample Mean | \(t_{\alpha / 2}\) | Critical Value for t-Distribution | |
| \(mu\) | Population Mean | t | t Test Statistic | |
| \(s\) | Sample Standard Deviation | \(\text{D}\) | Difference | |
| \(\sigma\) | Population Standard Deviation | \(\bar{D}\) | Mean of the Differences | |
| \(s^{2}\) | Sample Variance | \(s_{D}\) | Standard Deviation of the Differences | |
| \(\sigma^{2}\) | Population Variance | \(\text{F}\) | F Test Statistic | |
| \(\text{CV}\) | Coefficient of Variation | \(\text{F}_{\alpha}\) | F Critical Value | |
| \(z\) | Z-score | \(\chi^{2}\) | Chi-Square Test Statistic | |
| IQR | Interquartile Range | \(\chi_{\alpha}^{2}\) | Chi-Square Critical Value | |
| \(P_{i}\) | Percentile | E | Expected Value | |
| \(Q_{i}\) | Quartile | O | Observed Value | |
| \(\text{P}(x)\) | Probability of \(X = x\) | k | Number of Groups | |
| \(\text{A}^{C}\) | Complement Rule | SS | Sum of Squares | |
| \(\text{A} \cap \text{B}\) | Intersection | MS | Mean Square | |
| \(\text{A} \cup \text{B}\) | Union | \(r\) | Sample Correlation Coefficient | |
| \(\text{A} | \text{B}\) | Conditional Probability | \(\rho\) | Population Correlation Coefficient | |
| \(n!\) | Factorial Rule | \(R\) | Multiple Correlation Coefficient | |
| \({}_{n} C_{r}\) | Combination Rule | \(R^{2}\) | Coefficient of Determination | |
| \({}_{n} P_{r}\) | Permutation Rule | \(1 - R^{2}\) | Coefficient of Nondetermination | |
| \(p\) | Probability of a Success | \(\hat{y}\) | Predicted Value of the Regression Equation | |
| \(q\) | Probability of a Failure | \(b_{0}\) | Sample Y-Intercept Coefficient | |
| \(p\) | Population Proportion | \(b_{1}\) | Population Slope Coefficient | |
| p | P-value | \(e_{i}\) | Residual | |
| \(\alpha\) | Significance Level = \(\text{P(Type I Error)}\) = False Positive Rate | \(s_{\text{est}} = s\) | Standard Error of Estimate = Standard Deviation of the Residuals | |
| \(1 - \alpha\) | \(\text{P(True Negative)}\) | p | Number of predictors in regression | |
| \(\beta\) | \(\text{P(Type II Error)}\) = False Negative Rate | \(\varepsilon\) | Error term in regression | |
| \(1 - \beta\) | Power = \(\text{P(True Positive)}\) | \(\text{R}\) | Sum of the Ranks | |
| \(H_{0}\) | Null Hypothesis | \(w_{s}\) | Wilcoxon Signed-Rank Test Statistic | |
| \(H_{1} = H_{a}\) | Alternative Hypothesis | \(\text{U}\) | Mann-Whitney U Test Statistic |