How do you use the Grubbs' test table?

To use the Grubbs' test table: (1) Identify the most extreme observation in your data set (the value farthest from the mean). (2) Calculate G = |x_suspect − x̄| / s using your sample mean and standard deviation. (3) Record your sample size n. (4) Choose a significance level α (typically 0.05). (5) Find the row for your n in the table. (6) Read the critical value G_crit. (7) If G ≥ G_crit, the suspect value is an outlier at significance level α. If G < G_crit, there is insufficient evidence to declare it an outlier.

What is the formula for the Grubbs test statistic?

The Grubbs test statistic is G = |x_i − x̄| / s, where x_i is the suspected outlier (the observation with the maximum absolute deviation from the mean), x̄ is the arithmetic mean of all n observations, and s is the sample standard deviation computed using n−1 in the denominator. G measures how many standard deviations the suspect observation lies from the sample mean. A larger G indicates a more extreme departure from the rest of the data.

What are the assumptions of Grubbs' test?

Grubbs' test requires three conditions: (1) The data must come from a normal (Gaussian) distribution — the test is not valid for skewed or heavily tailed distributions. (2) Only one outlier is tested at a time (the single most extreme value). Testing multiple outliers sequentially using Grubbs' test without correction inflates the Type I error rate. (3) Observations must be independent of one another. If the data are correlated or the normality assumption is violated, non-parametric alternatives such as the IQR method should be considered instead.

What is the difference between Grubbs' test and Dixon's Q test?

Both tests identify a single outlier in a small sample, but they differ in calculation and scope. Grubbs' test uses G = |x_i − x̄| / s and works well for n = 3 to 100+. Dixon's Q test uses Q = |x_suspect − x_neighbor| / range and is typically restricted to n = 3 to 30. For small samples (n ≤ 10), Dixon's Q test is sometimes preferred because it does not require computing the mean and standard deviation, which are themselves influenced by the outlier. For larger samples, Grubbs' test is generally more powerful and widely used in standards such as ASTM E178 and ISO 5725-2.

Can Grubbs' test detect multiple outliers?

The standard Grubbs' test detects only one outlier at a time. If you apply it repeatedly (removing the detected outlier and retesting), you inflate the overall Type I error rate — this sequential approach is statistically improper. For data with potentially more than one outlier, the Generalized Extreme Studentized Deviate (GESD) test, developed by Rosner (1983), is the correct procedure. GESD tests up to r suspected outliers simultaneously while controlling the overall error rate. GESD is also described in NIST/SEMATECH Engineering Statistics Handbook section 8.1.3.1.

What significance level should I use for Grubbs' test?

α = 0.05 is the standard choice in most scientific and engineering applications and is required by ASTM E178. Use α = 0.10 when false negatives (failing to catch real outliers) carry a higher cost than false positives — exploratory laboratory work or environmental monitoring sometimes justifies this. Use α = 0.01 when falsely removing a valid observation would be costly, such as in pharmaceutical manufacturing or final product acceptance testing. Always select α before collecting or analyzing the data; choosing α after seeing the results invalidates the test.

What is the null hypothesis in Grubbs' test?

The null hypothesis in Grubbs' test is H₀: There are no outliers in the data set. The alternative hypothesis is H₁: The most extreme observation (the one with the largest |x_i − x̄| / s) is an outlier from the normal population from which the other observations came. Rejecting H₀ means the probability of observing a G value that large by chance alone — assuming all n values came from the same normal distribution — is less than α.

Is Grubbs' test valid for non-normal data?

No. Grubbs' test is designed specifically for normally distributed data. Applying it to skewed, heavy-tailed, or multimodal data produces unreliable results — the critical values in the table are derived from the assumption of normality. Before running Grubbs' test, check normality using a Shapiro-Wilk test, a Q-Q plot, or a histogram. If the data are not normally distributed, consider a log transformation (for right-skewed data) or a non-parametric outlier detection method such as the Tukey IQR fence (Q1 − 1.5×IQR, Q3 + 1.5×IQR).

When should I use a two-sided vs one-sided Grubbs' test?

A one-sided Grubbs' test is appropriate when you already know which end of the distribution the potential outlier is on — for example, testing only the maximum value. A two-sided test checks whether either the maximum or minimum is an outlier without pre-specifying the direction. For a two-sided test at overall α = 0.05, use the critical values in the α = 0.025 column. This Bonferroni correction accounts for the fact that you are performing two comparisons. In most quality control and laboratory settings, the one-sided test at the stated α is standard practice.

How do I report the result of a Grubbs' test?

A complete Grubbs' test report includes: the sample size n, the suspected outlier value, the calculated G statistic, the critical value G_crit at the chosen α and n, and the decision. Example: 'The maximum observation (x = 42.7) was tested for outlyingness using Grubbs' test. G = 2.84, G_crit(n=15, α=0.05) = 2.409. Since G > G_crit, the observation is identified as a statistically significant outlier at α = 0.05.' Always report what was done with the outlier (retained, removed, or flagged for further investigation) and the justification.

What sample sizes does Grubbs' test support?

Grubbs' test is valid for n ≥ 3. The minimum of three observations is needed because with only two data points, the standard deviation is always exactly half the range, making any G value mechanically equal to 1/√2 regardless of how extreme one value is. Practical use of Grubbs' test is most common for n = 3 to n = 100; for larger samples, outliers are often better handled with robust statistical methods or process control charts. This table provides critical values through n = 100.

What is the Extreme Studentized Deviate (ESD) test?

The Extreme Studentized Deviate (ESD) test is another name for Grubbs' test when applied to a single outlier. The term comes from the fact that the test statistic G = |x_i − x̄| / s is the standardized (studentized) maximum absolute deviation from the mean — making G the most extreme possible standardized residual. The Generalized ESD test (GESD) extends this to test r ≥ 1 potential outliers simultaneously, which avoids the masking problem that can occur when two or more outliers are present.

What alternatives exist to Grubbs' test?

Several alternatives address different scenarios: Dixon's Q test works for n ≤ 30 and uses the range rather than standard deviation. The Tukey IQR fence (non-parametric, no normality assumption) flags values outside Q1 − 1.5×IQR and Q3 + 1.5×IQR. Z-scores identify values more than 2 or 3 standard deviations from the mean, but are sensitive to masking by multiple outliers. The Generalized ESD test handles multiple outliers in normal data. Chauvenet's Criterion is a simpler variant sometimes used in experimental physics. The right choice depends on data distribution, sample size, and whether one or multiple outliers are expected.

How does sample size affect the Grubbs' test critical value?

The critical value G_crit increases as n increases. With small samples (n = 5), G_crit at α = 0.05 is 1.672 — an observation only 1.67 standard deviations from the mean can be declared an outlier. With n = 50, G_crit = 2.956. This makes intuitive sense: in a large sample from a normal distribution, you expect to see observations several standard deviations from the mean by chance, so the threshold for declaring a value an outlier must be higher. Conversely, in a very small sample, any extreme deviation is unusual relative to what chance variation can produce.

What is the Grubbs test critical value at α = 0.05 for n = 10?

The Grubbs test critical value at α = 0.05 for n = 10 is G_crit = 2.176. This means that for a sample of 10 observations, a suspected outlier must be at least 2.176 standard deviations from the sample mean to be declared statistically significant at the 5% level. If your calculated G = |x_suspect − x̄| / s ≥ 2.176, you reject H₀ and conclude the observation is an outlier.

Grubbs' Test Table: Complete G Critical Values (n = 3

Grubbs' Test Critical Value Calculator

Sample Size (n)

Significance Level (α)

Your G statistic (optional)

G critical =

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What Is Grubbs' Test?

Grubbs' test checks whether the most extreme observation in a normally distributed data set is a statistical outlier. It was developed by Frank E. Grubbs and published in The Annals of Mathematical Statistics (1950) with refinements appearing in Technometrics (1969). The test is also known as the Extreme Studentized Deviate (ESD) test because the test statistic G is the maximum absolute studentized residual.

You compute G for the single most suspicious observation (the value farthest from the mean), then compare it against the critical value from this table. If G meets or exceeds G_crit, the observation is flagged as an outlier at significance level α. The test does not identify what caused the extreme value — only that it is statistically inconsistent with the rest of the data under the assumption of normality.

Grubbs' test in practice: it is the required outlier test in ASTM E178 (Standard Practice for Dealing With Outlying Observations) and is specified by ISO 5725-2 for evaluating interlaboratory reproducibility data. Quality engineers, laboratory scientists, and environmental analysts use it to decide whether an extreme measurement warrants removal before further analysis.

The Grubbs Test Statistic Formula

The test statistic G measures how many sample standard deviations the suspect observation lies from the sample mean:

G = |x_suspect − x̄| / s

Where x_suspect is the observation being tested (the maximum or minimum of the data), x̄ is the arithmetic mean of all n observations, and s is the sample standard deviation using n − 1 in the denominator.

Testing the Maximum

G = (x_max − x̄) / s

Use when the largest observation looks suspiciously high.

Testing the Minimum

G = (x̄ − x_min) / s

Use when the smallest observation looks suspiciously low.

G ranges from 0 to its mathematical maximum of (n−1)/√n. For a sample of n = 10, the theoretical maximum G is 9/√10 ≈ 2.846, which is why the critical values in the table cannot exceed this bound.

Grubbs' Test Critical Value Table

Select the tab for your significance level. Each cell shows the G_crit value — the minimum G required to declare an outlier. Click any cell to highlight it and load it into the calculator above.

Reject H₀ (declare an outlier) if G ≥ G_crit. Source: Grubbs, F.E. (1969). Procedures for detecting outlying observations in samples. Technometrics, 11(1), 1–21; ASTM E178-16a. For a two-sided test at overall α = 0.05, use the α = 0.025 column.

Complete Grubbs' Test Reference Table — All Significance Levels

The table below shows all four significance levels side by side. The α = 0.05 column is the standard choice for most scientific and engineering applications.

n	α = 0.10	α = 0.05	α = 0.025	α = 0.01

One-sided Grubbs test. For two-sided testing at α = 0.05, use the α = 0.025 column. All values sourced from Grubbs (1969) and ASTM E178.

How to Use the Grubbs' Test Table: Step by Step

Follow these six steps every time you test for an outlier using Grubbs' test.

Step 1 — State the Hypotheses

H₀: No outliers exist. H₁: The most extreme observation is an outlier. Set α before examining the data — using 0.05 is standard in most laboratory and quality control work. The test is one-sided by default (you pre-identify which end to test: the maximum or the minimum).

Step 2 — Verify Normality

Grubbs' test is only valid for normally distributed data. Examine a Q-Q plot or run a Shapiro-Wilk test on your data before proceeding. If the distribution is clearly skewed or non-normal, consider a log transformation or a non-parametric alternative such as the Tukey IQR fence.

Step 3 — Calculate the Sample Mean and Standard Deviation

Compute x̄ = (Σx_i) / n from all n observations — including the suspect value. Compute s = √[Σ(x_i − x̄)² / (n − 1)], the sample standard deviation with n − 1 in the denominator. Both statistics must be computed including the suspect point, not after removing it.

Step 4 — Compute G

G = |x_suspect − x̄| / s. Identify the observation with the largest absolute deviation from the mean (either the maximum or minimum of your data set). Subtract the mean, take the absolute value, and divide by the standard deviation.

G = |x_suspect − x̄| / s

Step 5 — Look Up G Critical and Compare

Find the row for your n in the table above, or use the calculator to retrieve G_crit instantly. Then apply the decision rule:

If G ≥ G_crit → Reject H₀ → Observation is a statistically significant outlier at α
If G < G_crit → Fail to reject H₀ → No statistical evidence of outlyingness at α

Step 6 — Report and Take Action

A complete result report states: n, the suspect value, G, G_crit, α, and the decision. Example: "G(n = 15) = 2.61 > G_crit(α = 0.05) = 2.409. The maximum observation of 47.3 is identified as an outlier." Then investigate the cause — transcription error, equipment failure, or genuine process variation — before deciding whether to remove or retain the value.

Worked Example: Laboratory Titration Data

Scenario: A chemist records the following seven titration volumes (mL): 23.1, 23.4, 23.3, 23.5, 23.2, 23.4, 28.6. The value 28.6 mL looks suspicious. Is it an outlier at α = 0.05?

Solution — Step by Step

Step	Calculation	Result
1	State hypotheses, set α	H₀: no outliers; H₁: max is outlier; α = 0.05
2	Compute sample mean x̄	x̄ = (23.1+23.4+23.3+23.5+23.2+23.4+28.6)/7 = 24.071
3	Compute sample std dev s	s = 2.033 (using n−1 = 6 in denominator)
4	Compute G	G = \|28.6 − 24.071\| / 2.033 = 4.529 / 2.033 = 2.228
5	Look up G_crit	n=7, α=0.05 → G_crit = 1.938
6	Compare G vs G_crit	2.228 > 1.938 → Reject H₀ → Outlier detected

Interpretation

The value 28.6 mL is a statistically significant outlier at α = 0.05. The chemist should investigate its origin before running further calculations. Possible explanations include a pipetting error, a contaminated standard solution, or a transcription error. The decision to remove the value from the analysis requires a substantive justification, not just the statistical test result.

Worked Example 2: Manufacturing Quality Control

Scenario: A production engineer measures the tensile strength (MPa) of 12 steel samples: 415, 418, 421, 416, 420, 419, 417, 422, 415, 418, 420, 395. Is 395 MPa an outlier at α = 0.05?

x̄ = (sum of all 12 values) / 12 = 4996 / 12 = 416.33 MPa. s = 7.21 MPa (computed with n−1 = 11). G = |395 − 416.33| / 7.21 = 21.33 / 7.21 = 2.959. At n = 12, α = 0.05: G_crit = 2.285. Since 2.959 > 2.285, the value of 395 MPa is a statistically significant outlier at the 5% level.

One-Sided vs Two-Sided Grubbs' Test

The test direction determines which end of the data you are testing and affects the correct column to use in the table.

One-Sided Test (Standard)

You already know which end to test — either the maximum (high outlier) or the minimum (low outlier) — based on the physical context of the experiment. Use the column matching your stated α directly. Example: α = 0.05 → use the α = 0.05 column.

n=10, α=0.05 → G_crit = 2.176

Two-Sided Test (Bonferroni Adjusted)

You don't know in advance whether the outlier is high or low — you're checking whichever extreme turns out to be larger. For an overall α = 0.05, use the α = 0.025 column. This Bonferroni correction accounts for testing both tails simultaneously.

n=10, overall α=0.05 → use α=0.025 → G_crit = 2.410

Assumptions of Grubbs' Test

Grubbs' test gives valid results only when these conditions are met. Violating them can lead to either too many or too few outliers being detected.

Normal distribution: The data must come from a normal (Gaussian) distribution. This is the most critical assumption. Use a Q-Q plot, a Shapiro-Wilk test, or the standard normality tests to check this before running Grubbs' test on your data.

Single outlier: The test checks for exactly one outlier at a time — the most extreme observation. If two or more outliers are present, masking can occur: the first outlier inflates s (pulling the second extreme value closer to G_crit), making both harder to detect. Use the Generalized ESD test for multiple-outlier scenarios.

Independent observations: All measurements must be statistically independent of one another. Grubbs' test is not appropriate for autocorrelated time-series data or for replicate measurements that share a systematic source of variation.

Sample size n ≥ 3: With n = 2, the test statistic is mechanically fixed and the test is undefined. The table starts at n = 3. For n > 100, the large-sample approximation is reliable, but consider robust methods (e.g., median absolute deviation) for very large datasets with potential contamination.

Grubbs' Test vs Other Outlier Detection Methods

Choosing the right outlier test depends on your data distribution, sample size, and the number of suspected outliers. The table below compares the most widely used methods.

Method	Normality Required	Sample Size	Outliers Detected	Best Use Case
Grubbs' Test	Yes	n ≥ 3	1	Laboratory, QC (ASTM E178, ISO 5725-2)
Dixon's Q Test	Yes	3–30	1	Very small samples; avoids s inflation issue
Generalized ESD	Yes	n ≥ 15	Up to r	Multiple outliers; controls family-wise error
Tukey IQR Fence	No	Any	Multiple	Skewed data, exploratory analysis, box plots
Z-Score Method	Yes	n > 30	Multiple	Large samples; subject to masking by outliers
Chauvenet's Criterion	Yes	Any	1	Experimental physics; less rigorous than Grubbs

Limitations of Grubbs' Test

Masking Problem

When two or more outliers exist, each one inflates the sample standard deviation s, which shrinks the G statistic for the other outliers. This can cause all of them to appear non-significant — even though they are. Sequential application of Grubbs' test does not solve this; use the Generalized ESD procedure instead.

Normality Dependence

The critical values in this table assume normality. If the underlying distribution has heavier tails than the normal — for example, a t-distribution or a lognormal distribution — Grubbs' test will flag too many observations as outliers. Verify the distribution before applying the test.

One at a Time

Grubbs' test tests a single observation. Running the test, removing the detected outlier, and then rerunning it on the remaining data is sometimes done in practice but inflates the overall Type I error rate. Each iteration changes the distribution of the test statistic in ways the original critical values do not account for.

Symbol and Concept Glossary

The table below defines every symbol in the Grubbs test procedure and notes the single most common source of confusion for each.

Symbol	Name	Definition	Common Error
G	Grubbs statistic	\|x_i − x̄\| / s — the number of sample SDs the suspect value lies from the mean	Computing G without the suspect value in the mean and SD
G_crit	Critical value	Threshold from this table; G ≥ G_crit means outlier declared at α	Using the wrong α column or a one-sided value for a two-sided test
x̄	Sample mean	Σx_i / n — arithmetic average of all n observations including the suspect value	Excluding the suspect point when computing the mean
s	Sample standard deviation	√[Σ(x_i−x̄)² / (n−1)] — must include the suspect value in the calculation	Using population SD (dividing by n instead of n−1)
n	Sample size	Total number of observations in the data set	Using the wrong n row when the suspect value has already been removed
α	Significance level	Probability of falsely declaring an outlier when none exists (Type I error rate)	Selecting α after examining the data to "make" an observation significant
H₀	Null hypothesis	All observations come from the same normal distribution — no outliers exist	Rejecting H₀ and automatically removing the value without further investigation
ESD	Extreme Studentized Deviate	Another name for the Grubbs test statistic G — refers to the maximum absolute standardized residual	Confusing the single-outlier ESD (G) with the Generalized ESD test for multiple outliers

Grubbs' test uses the sample mean and standard deviation (G = |x_i − x̄| / s), making it more powerful for larger samples. Dixon's Q test uses only the range (Q = gap / range), so it is less affected by the suspected outlier itself. For sample sizes of 7 or fewer, Dixon's Q test is often preferred because the mean and standard deviation are less stable. For samples between 8 and 30, either test is appropriate, while Grubbs' test is generally preferred for sample sizes greater than 30.

Applying Grubbs' test repeatedly after removing detected outliers is common but statistically inappropriate because the original critical values no longer control the overall Type I error rate. If you expect multiple outliers, the recommended approach is the Generalized ESD (Rosner) test, which tests for several outliers simultaneously while maintaining the correct significance level.

Grubbs' test assumes normally distributed data. If your data is right-skewed, a log transformation may restore normality before applying the test. Otherwise, consider robust alternatives such as Tukey's IQR rule, which identifies observations outside Q1 − 1.5 × IQR or Q3 + 1.5 × IQR, or use the Median Absolute Deviation (MAD) method for non-normal or ordinal data.

A significant Grubbs' test indicates that an observation is statistically unusual, but it does not prove the value is incorrect. Before removing it, investigate possible causes such as recording errors, instrument failure, contamination, or other identifiable problems. If no clear cause exists, it is generally best to keep the observation and compare analyses with and without the outlier while documenting your decision.

A significant Grubbs' test only indicates that the most extreme observation is unlikely to belong to the same normal distribution as the remaining data. It does not explain why the value is unusual, whether it is a measurement error, or whether it should be removed. Likewise, a non-significant result does not prove the observation is correct. It simply means there is insufficient evidence to classify it as an outlier at the chosen significance level.

Related Statistics Resources

Outliers in Statistics

A full guide to what outliers are, why they matter, and the range of methods for detecting and handling them.

Standard Deviation

The denominator of the Grubbs statistic. Understand how s is calculated and what it measures.

Significance Level (α)

Why you set α before testing and what it means to control the Type I error rate.

Null vs Alternative Hypothesis

How to frame H₀ and H₁ correctly before running any hypothesis test, including Grubbs' test.

Normality Tests

Check whether your data meet the normality assumption that Grubbs' test requires.

P-Values Explained

What a p-value means, how it relates to the significance level, and the common misinterpretations.

What Is Grubbs' Test?

Grubbs' test identifies whether the most extreme observation in a normally distributed sample is a statistical outlier. Compute G = |x_i − x̄| / s. If G ≥ G_crit from this table, declare the observation an outlier at significance level α. The test requires normality and tests one observation at a time.

Quick Reference (α = 0.05, One-Sided)

n = 5 1.672

n = 7 1.938

n = 10 2.176

n = 15 2.409

n = 20 2.557

n = 25 2.663

n = 30 2.745

n = 50 2.956

Formula & Decision Rule

G = |x_i − x̄| / s
G_crit from table
G ≥ G_crit → Outlier
G < G_crit → Not outlier

Assumptions Checklist

Data normally distributed

Only one outlier suspected

Observations independent

n ≥ 3

α set before testing

Statistics Fundamentals

Tables, calculators & complete guides

More Outlier & Reference Tables

→ Dixon's Q Test Table → Z-Table (Standard Normal) → T-Distribution Table → Chi-Square Table → F-Table (ANOVA) → Pearson Correlation Table

Related Calculators

→ Descriptive Statistics Calculator → Z-Score Calculator → Standard Deviation Calculator → Outlier Detector (Visual)

Understanding Why G_crit Increases with Sample Size

Why G_crit Rises as n Grows

In a large sample from a normal distribution, the most extreme observation is expected to be further from the mean — not because it is an error, but because with more data, you are more likely to see rare events by chance. A G value of 2.5 in a sample of 5 is remarkable; the same G value in a sample of 50 is entirely plausible. The table encodes this relationship precisely, so the threshold adjusts appropriately rather than using a fixed cutoff.

The Role of the t-Distribution

The Grubbs critical values are derived from the t-distribution. For a sample of n observations, the test uses a t-distribution with n−2 degrees of freedom at an internal significance level of α / n (the Bonferroni correction for the n possible extreme values). This is why the formula G_crit = [(n−1)/√n] × t_p,n−2 / √(n−2+t²_p,n−2) is equivalent to the table lookup — both approaches yield exactly the same critical value.

Grubbs' Test and NIST Standards

The NIST/SEMATECH Engineering Statistics Handbook covers Grubbs' test (section 8.1.3.1) and the Generalized ESD variant. The handbook presents a slightly different form of the critical value table, computed with an internal α/(2n) correction rather than α/n. The values shown in this table follow the original Grubbs (1969) paper and ASTM E178, which use α/n internally — the standard used in most engineering and chemistry laboratories worldwide.

Grubbs' Test — Quick Definition

Grubbs' test (Extreme Studentized Deviate test) detects whether the most extreme value in a normally distributed sample is an outlier. The test statistic is G = |x_i − x̄| / s, where x_i is the suspect observation, x̄ is the sample mean, and s is the sample standard deviation. If G exceeds the critical value G_crit from the Grubbs table at the chosen significance level α and sample size n, the observation is declared a statistically significant outlier. The test assumes normality, tests one outlier at a time, and requires n ≥ 3. It is specified in ASTM E178 and ISO 5725-2 for laboratory and interlaboratory data analysis.

Grubbs' Test Critical Value Calculator

What Is Grubbs' Test?

The Grubbs Test Statistic Formula

Testing the Maximum

Testing the Minimum

Grubbs' Test Critical Value Table

Complete Grubbs' Test Reference Table — All Significance Levels

How to Use the Grubbs' Test Table: Step by Step

Step 1 — State the Hypotheses

Step 2 — Verify Normality

Step 3 — Calculate the Sample Mean and Standard Deviation

Step 4 — Compute G

Step 5 — Look Up G Critical and Compare

Step 6 — Report and Take Action

Worked Example: Laboratory Titration Data

Solution — Step by Step

Interpretation

Worked Example 2: Manufacturing Quality Control

One-Sided vs Two-Sided Grubbs' Test

One-Sided Test (Standard)

Two-Sided Test (Bonferroni Adjusted)

Assumptions of Grubbs' Test

Grubbs' Test vs Other Outlier Detection Methods

Limitations of Grubbs' Test

Masking Problem

Normality Dependence

One at a Time

Symbol and Concept Glossary

Related Statistics Resources

Outliers in Statistics

Standard Deviation

Significance Level (α)

Null vs Alternative Hypothesis

Normality Tests

P-Values Explained

Understanding Why Gcrit Increases with Sample Size

Why Gcrit Rises as n Grows

The Role of the t-Distribution

Grubbs' Test and NIST Standards

Grubbs' Test — Quick Definition

Understanding Why G_crit Increases with Sample Size

Why G_crit Rises as n Grows