Chapter 5, Problem 9Q

Interpretation Introduction

Interpretation:

The measurement that can be discarded in problem 8 needs to be determined using the Grubbs test.

Concept Introduction:

The method to detect a single outlier in the data following an approximately normal distribution is known as Grubb's test. This is also known as the maximum normed residual test. It is defined for the following hypothesis:

  $H_o$ -In the data set, there are no outliers.

  $H_a$ -In the data set, there is exactly one outlier.

Here, an outlier is a data point that is significantly different from the other observations. It may occur due to the variable measurements. It may result in an experimental error and can be excluded from the set of data. In the statistical analysis, an outlier can cause serious problems.

The statistic of Grubb's test can be defined as follows:

  $G_{\text{calculated}}=\frac{\max \left|X_i-\overline{X}\right|}{s}$

Here, $X_i$ is the discordant value, $\overline{X}$ is the sample mean and s is the standard deviation.

The G critical values corresponding to the number of observations are as follows:

Number of observations	G critical value
3	1.15
4	1.46
5	1.67
6	1.82
7	1.94
8	2.03
9	2.11
10	2.18
11	2.23
12	2.29
13	2.33
14	2.37
15	2.41

If the above value of $G_{\text{calculated}}$ for any value from data is more than $G_{\text{critical}}$ value from the table thus, the value can be discarded.