Q. 6.133 - Elementary Statistics

Question

In the article "Distribution of Oxygen in Surface Sediments from Central Sagami Bay, Japan: In Situ Measurements by Microelectrodes and Planar Optodes", R. Glud et al. explored the distributions of oxygen in surface sediments from central Sagami Bay. The oxygen distribution gives important information on the general biogeochemistry of marine sediments. Measurements were performed at$16$ sites. A sample of $22$ depths yielded the following data, in millimoles per square meter per day, on diffusive oxygen uptake (DOU).

Part (a):Obtain a normal probability plot of the given data.

Part (b): Use part (a) to identify any outliers.

Part (c): Use part (a) to assess the normality of the variable under consideration.

Step-by-Step Solution

Answer

Part (a): The required normal probability plot is given below,

Part (b): On identifying the outliers, we get $6.7,7.6$.

Part (c): Diffusive oxygen uptakes in surface sediments from central Sagami Bay do not appear to be normally distributed.

Part (a) Step 1. Given information.

Consider the given question,

Part (a) Step 2. Construct a normal probability plot.

The variable is diffusive oxygen uptake (DOU). To construct a normal probability plot, we first arrange the data in increasing order and obtain the normal scores from normal scores table.

The ordered data are shown in the first column of the below table; the normal scores form $n=22$column of normal scores table, are shown in the second column of the below table.

Part (a) Step 3. Plot the points.

Use the z-scores to construct normal probability plot for the given data,

Part (b) Step 1. Identify any outliers.

Consider the normal probability plot from part (a),

From the above probability plot, we can observe that the diffusive oxygen uptakes, $6.7,7.6$ are outliers. These two observations fall outside the overall pattern of the data.

Part (c) Step 1. Access the normality of the variable under consideration.

Consider the normal probability plot from part (a),

The above normal probability plot is not roughly linear. So, we can assume that diffusive oxygen uptakes are not approximately normally distributed.