4.166 - Elementary Statistics

Question

In the article "Comparison of Fiber Counting by TV Screen and Eyepieces of Phase Contrast Microscopy" (Amer. icon Industrial Hyeiene Asseciution Journal, Vol. 63, Pp. 756-761), 1. Moa et al. reported on determining fiber density by two different methods. Twenty samples of varying fiber density were each counted by 10 viewers by means of an eyepiece method and a television screen method to determine the relationship between the counts done by each method. The results, in fibers per square millimeter, are presented on the Weiss Stats site.

(a). Decide whether use of the linear correlation coefficient as a descriptive measure for the data is

appropriate, If so, then also parts $\left(b\right)$and$\left(c\right)$. 

Step-by-Step Solution

Answer

(a) The linear correlation coefficient is not an adequate descriptive metric for the data.

Step 1: Given Information

Whether the use of linear correlation coefficient is appropriate or not.

Step 2: Explanation

Using an ocular approach and a television screen method, ten observers tallied the data of twenty samples of variable fibre density.

$\begin{array}{|ll|}\hline \text{ EYE PIECE }& \text{ TV }\\ 3.5& 1.8\\ 4.5& 7.4\\ 6.8& 3.2\\ 7.9& 8.8\\ 9.3& 11.5\\ 13.8& 5.6\\ 18.3& 23.9\\ \hline\end{array}$

$\begin{array}{|ll|}\hline 20.8& 46.6\\ 23.1& 21.7\\ 49.5& 84.6\\ 56.3& 55.4\\ 89.2& 115.8\\ 105.1& 92.4\\ \hline\end{array}$

$\begin{array}{|ll|}\hline 116.1& 182.4\\ 145.2& 135.7\\ 201.5& 261.4\\ 224.8& 89.6\\ 250.5& 194.7\\ 265& 314.9\\ 307.9& 300.4\\ \hline\end{array}$

Step 3: Explanation

The scatterplot for the given data can be drawn by using the MINITAB:

Because the observations on the Eye Piece technique and the TV screen methods create a quadratic pattern, it is not realistic to draw a regression line for the data from the preceding scatterplot. As a result, there is no linear trend in the data. As a result, portions (b) through (c) will be omitted.