Statistics and Probability Dictionary
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Statistics Dictionary
Absolute Value
Accuracy
Addition Rule
Alpha
Alternative Hypothesis
Back-to-Back Stemplots
Bar Chart
Bayes Rule
Bayes Theorem
Bernoulli Distribution
Bernoulli Trial
Bias
Biased Estimator
Bimodal Distribution
Binomial Distribution
Binomial Experiment
Binomial Probability
Binomial Random Variable
Bivariate Data
Blinding
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
Column Vector
Combination
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
Critical Parameter Value
Critical Value
Cumulative Frequency
Cumulative Frequency Plot
Cumulative Probability
Decision Rule
Degrees of Freedom
Dependent Variable
Determinant
Deviation Score
Diagonal Matrix
Discrete Probability Distribution
Discrete Variable
Disjoint
Disproportionate Stratification
Dotplot
Double Bar Chart
Double Blinding
E Notation
Echelon Matrix
Effect Size
Element
Elementary Matrix Operations
Elementary Operators
Empty Set
Estimation
Estimator
Event
Event Multiple
Expected Value
Experiment
Experimental Design
F Distribution
F Statistic
Factor
Factorial
Frequency Count
Frequency Table
Full Rank
Gaps in Graphs
Geometric Distribution
Geometric Probability
Heterogeneous
Histogram
Homogeneous
Hypergeometric Distribution
Hypergeometric Experiment
Hypergeometric Probability
Hypergeometric Random Variable
Hypothesis Test
Identity Matrix
Independent
Independent Variable
Influential Point
Inner Product
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 Transformation
Logarithm
Lurking Variable
Margin of Error
Marginal Distribution
Marginal Frequency
Matched Pairs Design
Matched-Pairs t-Test
Matrix
Matrix Dimension
Matrix Inverse
Matrix Order
Matrix Rank
Matrix Transpose
Mean
Measurement Scales
Median
Mode
Multinomial Distribution
Multinomial Experiment
Multiplication Rule
Multistage Sampling
Mutually Exclusive
Natural Logarithm
Negative Binomial Distribution
Negative Binomial Experiment
Negative Binomial Probability
Negative Binomial Random Variable
Neyman Allocation
Nominal Scale
Nonlinear Transformation
Non-Probability Sampling
Nonresponse Bias
Normal Distribution
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 Table
Optimum Allocation
Ordinal Scale
Outer Product
Outlier
Paired Data
Parallel Boxplots
Parameter
Pearson Product-Moment Correlation
Percentage
Percentile
Permutation
Placebo
Point Estimate
Poisson Distribution
Poisson Experiment
Poisson Probability
Poisson Random Variable
Population
Power
Precision
Probability
Probability Density Function
Probability Distribution
Probability Sampling
Proportion
Proportionate Stratification
P-Value
Qualitative Variable
Quantitative Variable
Quartile
Random Number Table
Random Numbers
Random Sampling
Random Variable
Randomization
Randomized Block Design
Range
Ratio Scale
Reduced Row Echelon Form
Region of Acceptance
Region of Rejection
Regression
Relative Frequency
Relative Frequency Table
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 With Replacement
Sampling Without Replacement
Scalar Matrix
Scalar Multiple
Scatterplot
Selection Bias
Set
Significance Level
Simple Random Sampling
Singular Matrix
Skewness
Slope
Standard Deviation
Standard Error
Standard Normal Distribution
Standard Score
Statistic
Statistical Experiment
Statistical Hypothesis
Statistics
Stemplot
Strata
Stratified Sampling
Subset
Subtraction Rule
Sum Vector
Symmetric Matrix
Symmetry
Systematic Sampling
T Distribution
T Score
T Statistic
Test Statistic
Transpose
Treatment
t-Test
Two-Sample t-Test
Two-stage Sampling
Two-Tailed Test
Two-Way Table
Type I Error
Type II Error
Unbiased Estimator
Undercoverage
Uniform Distribution
Unimodal Distribution
Union
Univariate Data
Variable
Variance
Vector Inner Product
Vector Outer Product
Vectors
Voluntary Response Bias
Voluntary Sample
Y Intercept
z Score

Randomized Block Design
With a randomized block design, the experimenter
divides subjects into subgroups called blocks,
such that the variability within blocks is less than the
variability between blocks. Then, subjects within each block are
randomly assigned to treatment conditions. Compared to a
completely randomized design ,
this design
reduces variability within treatment conditions and potential confounding,
producing a better estimate of treatment effects.

The table below shows a randomized block design for a hypothetical
medical experiment.

Gender
Treatment
Placebo
Vaccine
Male
250
250
Female
250
250

Subjects are assigned to blocks, based on
gender. Then, within each block, subjects are randomly assigned
to treatments (either a
placebo
or a cold vaccine). For this design,
250 men get the placebo, 250 men
get the vaccine, 250 women get the placebo, and 250 women
get the vaccine.

It is known that men and women are physiologically different
and react differently to medication. This design ensures that
each treatment condition has an equal proportion of men and women.
As a result, differences between treatment conditions cannot
be attributed to gender. This randomized block design removes
gender as a potential source of variability and as a
potential confounding variable.