3.2.4. Number of bees to be examined to detect the presence of HBTM
About 3050 bees are examined per colony in most studies. Because the tracheal networks on the two sides of the bees do not interconnect, this represents independent samples of 60100 tracheae. There are different ways of determining the sample size needed to accurately detect tracheal mite infestation of a colony. Frazier et al. (2000) developed a sequential sampling technique which they validated twice by using two levels of significance (α = 0.10 and 0.20), and a precision level of β = 0.05 and 0.10 (Table 2). This technique allows one to classify lowinfested (<10%) and highly infested (>10%) colonies. Such information is needed before deciding when to treat or not to treat a colony, and also if further sampling is necessary. This improved technique can save time and money since it requires fewer than 50 bees to reach a decision.
For example, when 3 bees are found infested after examining 37 bees, stop sampling and decide to treat the colony because it is highly infested. However, if only 1 or 2 bees are infested with the first 7 examined, continue dissecting samples. If after dissecting 17 bees only 1 bee is found infested, also stop sampling and declare the colony to be lowinfested and therefore, no treatment is required. However, if 5 bees are infested out of 17 bees examined, then the colony is highlyinfested and needs to be treated. If only 2, 3 or 4 bees are infested out of 17 bees, continue sampling (see Table 2).
The following equation developed by Cochran (1963) is another way of finding the number of bees that need to be sampled for each colony in order to get an accurate number of mites per bee and therefore if the colony needs to be treated:
Where:
n_{0} is the sample
size needed,
Z^{2} is the abscissa
of the normal curve that cuts off an area at the tails (1 equals the desired
confidence level). The value for Z is found in statistical tables which contain
the area under the normal curve.
e is the desired
level of precision (for example, setting it at 0.05 means that the sample size
provides 95% certainty of detecting a 5% tracheal mite infestation level),
p is the
estimated proportion of bees infested with tracheal mites,
q is 1p.
Example: A colony has an expected infestation of about 5%. Using this equation to determine a sample size, we will have:
Z = 1.96; α (Alpha) = 0.05 (significance level)
p = 0.05 (5%, estimated proportion of bees that are
infested)
q = 0.95 (10.05)
e (Beta, β) = 0.05 (95% precision level)
Substituting the values:
If,
on the other hand, infestation is estimated to be 10%, about 17 bees should be
examined; an estimated 20% infestation only requires about 4 bees to be
examined, since there is a higher percentage of bees infestated. This method as
well as the sequential sampling technique may be useful for detection purposes
(to determine when to apply treatments or for regulatory purposes) and is not
recommended for scientific reporting. In that case, a full sample should be analysed
(e.g. 50 or 100 bees) to determine mite prevalence (percentage of hosts
infested) and/or mite abundance (number of mites per host bee). In general, tracheal mite infestations lower than
20% do not require treatment, but this depends on the severity and length of
the winter months (when bees are confined in their hives).
Table 2. How to make decisions using the sequential sampling technique (modified from Frazier et al., 2000); Calderone and Shimanuki 1992; see text 3.2.4. for explanation.
No. of bees examined 
Number of infested bees  
Low infestation (stop, don't treat) 
High infestation (stop, treatment) 
Moderate infestation (continue sampling) 

1      0,1 
2      0,1,2 
3    3  0,1,2 
4    3  0,1,2 
5    3  0,1,2 
6    3  0,1,2 
7    3  0,1,2 
8    4  0,1,2,3 
9    4  0,1,2,3 
10    4  0,1,2,3 
11  0  4  0,1,2,3 
12  0  4  1,2,3 
13  0  5  1,2,3,4 
14  0  5  1,2,3,4 
15  0  5  1,2,3,4 
16  1  5  1,2,3,4 
17  1  5  2,3,4 
18  1  6  2,3,4,5 
19  1  6  2,3,4,5 
20  1  6  2,3,4,5 
21  1  6  2,3,4,5 
22  1  6  2,3,4,5 
23  2  6  3,4,5 
24  2  7  3,4,5,6 
25  2  7  3,4,5,6 
26  2  7  3,4,5,6 
27  2  7  3,4,5,6 
28  3  7  4,5,6 
29  3  8  4,5,6,7 
30  3  8  4,5,6,7 
31  3  8  4,5,6,7 
32  3  8  4,5,6,7 
33  4  8  5,6,7 
34  4  8  5,6,7,8 
35  4  9  5,6,7,8 
36  4  9  5,6,7,8 
37  4  9  5,6,7,8 
38  4  9  5,6,7,8 
39  5  9  6,7,8 
40  5  10  6,7,8,9 
41  5  10  6,7,8,9 
42  5  10  6,7,8,9 
43  5  10  6,7,8,9 
44  6  10  7,8,9 
45  6  11  7,8,9,10 
46  6  11  7,8,9,10 
47  6  11  7,8,9,10 
48  6  11  7,8,9,10 
49  6  11  7,8,9,10 
50  7  11  8,9,10 