Add introduction

Author: kgryte

lib/node_modules/@stdlib/stats/incr/grubbs/README.md

@@ -24,6 +24,72 @@ limitations under the License.
 
 <section class="intro">
 
+[Grubbs' test][grubbs-test] (also known as the **maximum normalized residual test** or **extreme studentized deviate test**) is a statistical test used to detect outliers in a univariate dataset assumed to come from a normally distributed population. [Grubbs' test][grubbs-test] is defined for the hypothesis:
+
+-   **H_0**: the dataset does **not** contain outliers.
+-   **H_1**: the dataset contains **exactly** one outlier.
+
+The [Grubbs' test][grubbs-test] statistic for a two-sided alternative hypothesis is defined as
+
+<!-- <equation class="equation" label="eq:grubbs_test_statistic" align="center" raw="G = \frac{\operatorname{max}_{i=0,1,ldots,N-1} |Y_i - \bar{Y}|}{s}" alt="Grubbs' test statistic."> -->
+
+<div class="equation" align="center" data-raw-text="G = \frac{\operatorname{max}_{i=0,1,ldots,N-1} |Y_i - \bar{Y}|}{s}" data-equation="eq:grubbs_test_statistic">
+    <img src="" alt="Grubbs' test statistic.">
+    <br>
+</div>
+
+<!-- </equation> -->
+
+where `s` is the sample standard deviation. The [Grubbs test][grubbs-test] statistic is thus the largest absolute deviation from the sample mean in units of the sample standard deviation.
+
+The [Grubbs' test][grubbs-test] statistic for the alternative hypothesis that the minimum value is an outlier is defined as
+
+<!-- <equation class="equation" label="eq:grubbs_test_statistic_min" align="center" raw="G = \frac{\bar{Y} - Y_{\textrm{min}}}{s}" alt="Grubbs' test statistic for testing whether the minimum value is an outlier."> -->
+
+<div class="equation" align="center" data-raw-text="G = \frac{\bar{Y} - Y_{\textrm{min}}}{s}" data-equation="eq:grubbs_test_statistic_min">
+    <img src="" alt="Grubbs' test statistic for testing whether the minimum value is an outlier.">
+    <br>
+</div>
+
+<!-- </equation> -->
+
+The [Grubbs' test][grubbs-test] statistic for the alternative hypothesis that the maximum value is an outlier is defined as
+
+<!-- <equation class="equation" label="eq:grubbs_test_statistic_max" align="center" raw="G = \frac{Y_{\textrm{max}} - \bar{Y}}{s}" alt="Grubbs' test statistic for testing whether the maximum value is an outlier."> -->
+
+<div class="equation" align="center" data-raw-text="G = \frac{Y_{\textrm{max}} - \bar{Y}}{s}" data-equation="eq:grubbs_test_statistic_max">
+    <img src="" alt="Grubbs' test statistic for testing whether the maximum value is an outlier.">
+    <br>
+</div>
+
+<!-- </equation> -->
+
+For a two-sided test, the hypothesis that a dataset does **not** contain an outlier is rejected at significance level α if
+
+<!-- <equation class="equation" label="eq:grubbs_test_two_sided" align="center" raw="G > \frac{N}{N-1} \sqrt{\frac{t^2_{\alpha/(2N),N-2}}{N - 2 + t^2_{\alpha/(2N),N-2}}}" alt="Two-sided Grubbs' test."> -->
+
+<div class="equation" align="center" data-raw-text="G > \frac{N}{N-1} \sqrt{\frac{t^2_{\alpha/(2N),N-2}}{N - 2 + t^2_{\alpha/(2N),N-2}}}" data-equation="eq:grubbs_test_two_sided">
+    <img src="" alt="Two-sided Grubbs' test.">
+    <br>
+</div>
+
+<!-- </equation> -->
+
+where `t` denotes the upper critical value of the _t_-distribution with `N-2` degrees of freedom and a significance level of `α/(2N)`.
+
+For a one-sided test, the hypothesis that a dataset does **not** contain an outlier is rejected at significance level α if
+
+<!-- <equation class="equation" label="eq:grubbs_test_one_sided" align="center" raw="G > \frac{N}{N-1} \sqrt{\frac{t^2_{\alpha/N,N-2}}{N - 2 + t^2_{\alpha/N,N-2}}}" alt="One-sided Grubbs' test."> -->
+
+<div class="equation" align="center" data-raw-text="G > \frac{N}{N-1} \sqrt{\frac{t^2_{\alpha/N,N-2}}{N - 2 + t^2_{\alpha/N,N-2}}}" data-equation="eq:grubbs_test_one_sided">
+    <img src="" alt="One-sided Grubbs' test.">
+    <br>
+</div>
+
+<!-- </equation> -->
+
+where `t` denotes the upper critical value of the _t_-distribution with `N-2` degrees of freedom and a significance level of `α/N`.
+
 </section>
 
 <!-- /.intro -->