Question

2. Consider five results 3.65, 3.70, 3.52, 3.91, and 3.58.

(a). Using Q-test to justify whether 3.91 should be rejected?

(b). Using G-test to justify whether 3.91 should be rejected?

Answer 1

2. (a) 3.65 , 3.70, 3.52, 3.91, 3.58
Q = gap / range
   gap = 3.91 - 3.58 (nearest value to 3.91) = 0.33
   range = 3.91 - 3.52 (min in data) = 0.39
Q = 0.33 / 0.39 = 0.8461
Now look into Dixon Q table for Q_critical ; at N = 5 and at 95% confidence level
Therefore Q_critical = 0.710
if Q > Q_critical then you can consider the suspected value as outlier and reject it
Since, 0.84661 > 0.710 you can reject 3.91

(b) G = |x - x_mean | / s.d
   x_mean = (3.65+3.70+3.52+3.91.3.58)/5 = 3.672
s.d² = [(3.65-3.672)²+(3.70-3.672)²+(3.52-3.672)²+(3.91-3.672)²+(3.58-3.672)²] / 5-1
s.d = 0.14956
G = 3.91 - 3.672 / 0.14956 = 1.5912
From G table at N=5 and at 95% confidence level, G_critical = 1.672
If G > G_critical then that data point can be rejected
since, 1.5912 < 1.672 you should not reject 3.91