Question

During a fluorescence measurement, 10 replicate measurements of the same calibration standard give the following values. Use the Q-test (95% confidence interval) to determine if any of the following measurements should be removed from the data set as an outlier

Signal (counts/sec)
1044
1099
1104
1066
1024
1069
1033
1077
1200
1012

Answer 1

Ans: In a Q-test outlier detection, first we need to arrange the data in increasing order.

1012, 1024, 1033, 1044, 1066, 1069, 1077, 1099, 1104, 1200

Now look for potential outlier. it will be either lowest value or highest value.

Q_ts > Q_table its indeed outlier. and if  Q_ts < Q_table the value is not an outlier.

Qtable is a referance value and from a reference table it can be found as 0.466 for 95% confidence level with a table size 10.

Qts = gap/range; gap = difference between adjuscent values. and range is difference between first and last values

For value 1012, Gap = 1024 - 1012 = 12 and range = 1200 - 1012 = 188  

So Qts = 12/188 = 0.0638

Qts = 0.0638 << Qtable = 0.466.

so 1012 is not an outlier.

Let us look For value 1200, Gap = 1200 - 1104 = 96 and range = 1200 - 1012 = 188  

So Qts = 96/188 = 0.51

Qts = 0.51 > Qtable = 0.466.

So, 1200 is an outlier.