Question

Replicate measurements of the sodium concentration (in ppm) yielded the following: 85.10, 84.62, 84.65, 84.70. Apply the Q test to the data and determine whether or not a data point should be rejected at the 95% confidence level. (9)

Answer 1

Given data: 85.10, 84.62, 84.65, 84.70

Let us solve it for data point 85.10 because it seems to be little bit out of range

Step 1: Arrange the data into increasing order (smallest to largest).
84.62, 84.65, 84.70, 85.10

Step 2 : Find the Q statistic using the following formula:

Where:· x2 suspected outlier, x1 next nearest data value, and xn is the largest value.

lexp X2 – X1 Xn - X

Inserting the values into the formula, we get:
Qexp = (85.10 – 84.70) / 85.10 – 84.62 = 0.4/0.48 = 0.833

Step 3: Find Q critical value for n = 4 for a confidence level 95% in the Q-table = 0.829

Step4: Compare the calculated to the tabulated critical Q-value

Q exp is greater than the Q critical (0.833 > 0.829)

Since Qexp > Qcrit, the point can be rejected at confidence level 95%