Question

Question 4 [5] A forensic entomologist rates the incident of damage on clothes from incident sites. The damaged by a beetle was recorded as mild (M) or heavy (H). HMMMHHMMHMHHHMMHHHHMMHHMMMM Is there a pattern to the beetle damage?

Answer 1

ANSWER::

Here , the question basically asks whether the damage by beetle is randomly distributed or they have some pattern.

We may use Runs test for one sample .

Null hypothesis: The damage by beetle is random

Alternative Hypothesis : The damage by beetle is not random i.e. it follows some pattern

Now we calculate number of runs. ( We take successive same occurences to be 1)

H - 1

M,M,M - 2

H,H -3

M,M -4

H-5

M-6

H,H,H -7

M,M-8

H,H,H,H -9

M,M-10

H,H- 11

M,M,M,M -12

So total number of runs =12

Where total recording of damage = 27

No. Of mild recording (m) = 14

No. Of heavy recording (n) = 13

Both m and n are less than 20 , so it is a small sample and we use below table for getting critical values . This table is from non parametric statistics book. You may also find it online.

so we see m and n and find upper and lower limit , if value of R is between it then process is random else not random.

ms APPENDIX I TABLES 331 TANLEG Critical values al values of r in the runs test Given in the tables are va one-sample runs test, an greater than or equal to es are various critical values of for values of m and n less than or equal to 20. For uns test, any observed value of r which is less than or equal to the smaller value, or or equal to the larger value in a pair is significant at the 05 level. 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 2 9 2 10 3 10 3 11 3 11 3 - 3 - 2 - 2 9 3 10 3 11 3 12 3 12 4 13 4 13 4 13 4 13 5 - 6 2 - 2 - 3 11 3 12 3 13 4 13 4 14 5 14 5 14 5 14 5 15 5 15 15 - 3 2 - 3 - 3 11 3 12 4 13 4 14 5 15 6 16 6 16 6 16 6 16 6 17 7 17 7 17 7 17 6 16 6 16 6 17 7 17 7 18 7 18 7 18 8 18 8 18 18 2 - 2 - 3 - 3 - 3 - 3 - 4 4 5 13 14 14 4 5.5 13 14 15 5 15 5 16 16 6 16 6 17 7 17 7 18 7 18 8 19 7 8 8 18 1919 8 8 9 1920 20 2 3 - 4 - 4 13 5 14 5 6 15 16 6 17 7 17 7 18 7 8 1919 20 8 9 9 9 10 5 14 7 18 7 19 8 19 8 20 - - 13 6 16 6 16 6 16 6 17 7 17 7 18 9 10 10 10 3 - 4 - 5 - 5 15 19 19 20 20 8 8 9 9 10 10 3 4 5 - - 15 6 15 9 9 10 6 4 5 3 10 23 22 23 24 - 8 19 8 20 4 6 7 16 17 6 7 16 18 6 7 17 18 7 17 18 7 8 17 18 8 20 9 21 7 18 7 18 8 19 8 19 8 19 10 23 11 23 11 24 11 25 12 25 21 6 - 6 - 6 - 5 - 5 - 5 - * 10 22 10 23 4 9 20 10 11 23 11 24 21 25 26 26 26 99 20 21 22 23 11 24 11 25 12 25 12 26 13 26 27 6 - 6 - 7 17 8 18 8 20 13 26 13 27 13 27 21 22 23 23 24 25 26 5 6 - 6 - 7 17 8 18 9 20 9 21 10 22 10 23 11 24 12 25 12 25 13 26 13 27 13 27 14 28 • Adapted from Swed, and Eisenhar Swed, and Eisenhart, C. (1943). Tables for testing randomness of grouping in a sequence of alte Mathematical Statistics, 28.86 with the indeparmici

So upper limit for runs is 20 and lower is 9. Our no. Of runs is 12. Which is between these two values. So we accept null hypothesis at 5% level of significance i.e. damage by beetle is random , it does not follow any patterns.

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