Statistics Dictionary
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Select Term Absolute Value Accuracy Addition Rule Alpha Alternative Hypothesis ANOVA Back-to-Back Stemplots Balanced Design Bar Chart Bartletts Test Bayes Rule Bayes Theorem Bias Biased Estimate Bimodal Distribution Binomial Distribution Binomial Experiment Binomial Formula Binomial Probability Binomial Random Variable Bivariate Data Blinding Blocking Blocking Variable Bonferroni Correction Boxplot Cartesian Plane Categorical Variable Census Central Limit Theorem Chi-Square Distribution Chi-Square Goodness of Fit Test Chi-Square Statistic Chi-Square Test for Homogeneity Chi-Square Test for Independence Cluster Cluster Sampling Coefficient of Determination Coefficient of Multiple Determination Column Vector Combination Comparisons Complement Completely Randomized Design Conditional Distribution Conditional Frequency Conditional Probability Confidence Interval Confidence Level Confounding Contingency Table Continuous Probability Distribution Continuous Variable Control Group Convenience Sample Correlation Covariance Critical Parameter Value Critical Value Cumulative Frequency Cumulative Frequency Plot Cumulative Probability Decile Decision Rule Degrees of Freedom Dependent Variable Determinant Deviation Score Diagonal Matrix Discrete Probability Distribution Discrete Variable Discriminant Analysis Disjoint Disproportionate Stratification Dotplot Double Bar Chart Double Blinding Dummy Variable E Notation Echelon Matrix Effect Size Element Elementary Matrix Operations Elementary Operators Empirical Rule Empty Set Epsilon Error Rate Familywise Error Rate per Comparison Estimation Estimator Event Event Multiple Expected Value Experiment Experimental Design Extraneous Variable F Distribution F Statistic Factor Factorial Factorial Experiment Finite Population Correction Fixed Effects Model Fixed Factor Frequency Count Frequency Table Full Rank Gaps in Graphs Geometric Distribution Geometric Probability Hartleys Fmax Test Heterogeneous Histogram Homogeneous Hypergeometric Distribution Hypergeometric Experiment Hypergeometric Probability Hypergeometric Random Variable Hypothesis Test Identity Matrix Independent Independent Event Independent Groups Design Independent Variable Influential Point Inner Product Interaction Plot Interactions Interquartile Range Intersection Interval Estimate Interval Scale Inverse IQR Joint Frequency Joint Probability Distribution Law of Large Numbers Level Line Linear Combination of Vectors Linear Dependence of Vectors Linear Regression t-Test Linear Transformation Logarithm Lurking Variable Margin of Error Marginal Distribution Marginal Frequency Marginal Mean Matched Pairs Design Matched-Pairs t-Test Matrix Matrix Dimension Matrix Inverse Matrix Order Matrix Rank Matrix Transpose Mauchly Sphericity Test Mean Mean Square Measurement Scales Median Mixed Model Mode Multicollinearity Multinomial Distribution Multinomial Experiment Multiple Regression Multiplication Rule Multistage Sampling Mutually Exclusive Natural Logarithm Negative Binomial Distribution Negative Binomial Experiment Negative Binomial Formula Negative Binomial Probability Negative Binomial Random Variable Neyman Allocation Nominal Scale Non-Probability Sampling Nonlinear Transformation Nonresponse Bias Normal Approximation to the Binomial Normal Curve Normal Distribution Normal Equation Normal Probability Plot Normal Random Variable Null Hypothesis Null Set Observational Study One-Sample t-Test One-Sample z-Test One-stage Sampling One-Tailed Test One-Way ANOVA One-Way Table Optimum Allocation Ordinal Scale Orthogonal Comparisons Outer Product Outlier P-Value Paired Data Parallel Boxplots Parameter Pearson Product-Moment Correlation Percentage Percentile Permutation Placebo Planned Comparisons Point Estimate Poisson Distribution Poisson Experiment Poisson Probability Poisson Random Variable Population Population Distribution Post Hoc Comparisons Power Precision Probability Probability Density Function Probability Distribution Probability Sampling Proportion Proportionate Stratification Qualitative Variable Quantile Quantitative Variable Quartile Random Effects Model Random Factor Random Number Table Random Numbers Random Sampling Random Variable Randomization Randomized Block Design Randomized Block Experiment Range Ratio Scale Reduced Row Echelon Form Region of Acceptance Region of Rejection Regression Relative Frequency Relative Frequency Table Repeated Measures Design Replication Representative Residual Residual Plot Response Bias Row Echelon Form Row Vector Sample Sample Design Sample Point Sample Space Sample Survey Sampling Sampling Distribution Sampling Error Sampling Fraction Sampling Method Sampling Plan Sampling With Replacement Sampling Without Replacement Scalar Matrix Scalar Multiple Scatterplot Scheffe Test Selection Bias Set Significance Level Simple Random Sampling Simple Regression Simulation Singular Matrix Skewness Slope Sphericity Standard Deviation Standard Error Standard Normal Distribution Standard Normal Distribution Table Standard Score Statistic Statistical Experiment Statistical Hypothesis Statistics Stemplot Strata Stratified Sampling Subset Subtraction Rule Sum Vector Sums of Squares Symmetric Matrix Symmetry Systematic Sampling T Distribution T Score T Statistic t-Test Test Statistic Transpose Treatment Two-Proportion z-Test Two-Sample t-Test Two-Sample z-Test Two-stage Sampling Two-Tailed Test Two-Way Table Type I Error Type II Error Unbiased Estimate Undercoverage Uniform Distribution Unimodal Distribution Union Univariate Data Variable Variance Variance Inflation Factor Vector Inner Product Vector Outer Product Vectors Venn Diagram Voluntary Response Bias Voluntary Sample Welch t-Test Welch-Satterthwaite Approximation Y Intercept z-score
Linear Dependence of Vectors
A set of
vectors
is linearly independent if no vector in
the set is (a) a scalar multiple of another vector in the set or (b)
a
linear combination
of other vectors in the set; conversely,
a set of vectors is linearly dependent if any vector in
the set is (a) a scalar multiple of another vector in the set or (b)
a linear combination of other vectors in the set.
Consider the row vectors below.
Note the following:
Vectors a and b are linearly
independent, because neither vector is a scalar multiple of the
other.
Vectors a and d are linearly
dependent, because d is a scalar multiple of
a ; i.e.,
d = 2a .
Vector c is a linear combination of vectors a
and b , because c =
a + b . Therefore, the set of vectors
a , b , and c
is linearly dependent.
Vectors d , e , and
f are linearly independent, since no vector in the
set can be derived as a scalar multiple or a linear combination of any other
vectors in the set.