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
Bias
Biased Estimate
Bimodal Distribution
Binomial Distribution
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Binomial Probability
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Bivariate Data
Blinding
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Cartesian Plane
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Central Limit Theorem
Chi-Square Distribution
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Chi-Square Statistic
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Cluster
Cluster Sampling
Coefficient of Determination
Column Vector
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Complement
Completely Randomized Design
Conditional Distribution
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Contingency Table
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Correlation
Critical Parameter Value
Critical Value
Cumulative Frequency
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Decision Rule
Degrees of Freedom
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Deviation Score
Diagonal Matrix
Discrete Probability Distribution
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Dotplot
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E Notation
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Empty Set
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Factor
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Gaps in Graphs
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Identity Matrix
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Interval Estimate
Interval Scale
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Joint Probability Distribution
Law of Large Numbers
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Linear Combination of Vectors
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Margin of Error
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Matched-Pairs t-Test
Matrix
Matrix Dimension
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Matrix Transpose
Mean
Measurement Scales
Median
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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
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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
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Permutation
Placebo
Point Estimate
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P-Value
Qualitative Variable
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Quartile
Random Number Table
Random Numbers
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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
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Scalar Matrix
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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
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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 Estimate
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

Critical Value
The critical value is a factor used to compute
the margin of error, as shown in the equations below.

Margin of error = Critical value x Standard deviation of the statistic
Margin of error = Critical value x Standard error of the statistic

When the
sampling distribution
of the statistic is
normal
or nearly normal, the critical value
can be expressed as a
t score
or as a
z score .
To find the critical value, follow these steps.

Compute alpha (α): α = 1 - (confidence level / 100)
Find the critical probability (p*): p* = 1 - α/2
To express the critical value as a z score, find the z score
having a
cumulative probability
equal to the critical probability (p*).
To express the critical value as a t score, follow these steps.
Find the
degrees of freedom
(df). Often, df is equal to the sample
size minus one.
The critical t score (t*) is
the t score having degrees of freedom equal to df and a
cumulative probability
equal to the critical probability (p*).
Should you express the critical value as a t score or as a z score?
There are several ways to answer this question. As a practical matter,
when the sample size is large (greater than 40), it doesn't make much
difference. Both approaches yield similar results. Strictly speaking,
when the population standard deviation is unknown or when the
sample size is small, the t score is preferred. Nevertheless, many
introductory texts and the Advanced Placement Statistics Exam use the
z score exclusively. On this web site, we provide sample problems that
illustrate both approaches.

You can use the
Normal Distribution Calculator
to find the critical z score, and the
t Distribution Calculator to find
the critical t score. You can also use a
graphing calculator or
standard statistical tables (found in the appendix of
most introductory statistics texts).