This article is very technical. You need statistics to understand it. If statistics gives you a headache, skip to the end of the article
This section tests for trends in economic growth over in silvicuture over 12 years from the all the provinces.
I will use the Cox-Stuart Test for Trend. You can find more info on this book from Applied Nonparametric Statistics by Wayne Daniels Second Editon
Our test hypothesis will be a one sided test:
The hypothesis:
H0: No upward trend exists
vs
H1: Upward trend exists
The rule:
For a given n reject H0 at the alpha level of significance if the probabilty when H0 is true, of observing as few or fewer plus signs as were actually observed is less than alpha
Explanation of notation
The statement
P(k=n|n,0.5)<=a
This reads the probability of a certain sample size n given that n, at 0.5 is less than or equal to the computed value a
These probabilites are computed cumunatively in table A.1 of Non parametric Stats by Daniels. Barring that, I used the probability calculator from MyStat. The free version of Sysstat
This probability is the 'acid' test of determining if our hypothesis is true or not.
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Ontario Hypothesis
H0: No growth has occurred over the 12 year season
vs
H1: There is an upward trend in growth
Data:
See attached sheet
Test Stat.
Arranging the data in pairs
( 180760, 243391)....( 199,724 ,123196)
We take the differences and count + signs and - signs. There are 2 +'s and 10 negatives
Decision
We reject H0 if the probability of observing 2 or fewer plus signs when n=12 and H0 is true.
P(k=2|12,05)<=0.0192 Since .0192<=.025 we can't reject the Null Hypothesis.
Conclusion
There is no upward trend in revenue in silviculture. in Ontrario
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NewFoundland
Newfoundland Hypothesis
H0: No growth has occurrd over the 12 year season
vs
H1: There is an upward trend in growth
Data:
See attached sheet
Test Stat.
Arranging the data in pairs
(1461,1527)...(2350, 2170)
We take the differences and count + signs and - signs. There are 3 + and 8 negatives
Decision
We reject H0 if the probability of observing 3 or fewer plus signs when n=12 and H0 is true.
P(k=3|12,05)<=.0729 Since .0792>=025 we reject the Null Hypothesis.
Conclusion
There is an upward trend in revenue in silviculture in Newfoundland
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PEI.
PEI Hypothesis
H0: No growth has occurrd over the 12 year season
vs
H1: There is an upward trend in growth
Data:
See attached sheet
Test Stat.
Arranging the data in pairs
(251,130)...(228,304)
We take the differences and count + signs and - signs. There are 2 + and 4 negatives
Decision
We reject H0 if the probability of observing 3 or fewer plus signs when n=12 and H0 is true.
P(k=2|12,05)<=.0192 Since .0192<.025 we can't reject the Null Hypothesis.
Conclusion
There is no upward trend in revenue in silviculture in PEi
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Nova Scotia
Nova Scotia Hypothesis
H0: No growth has occurrd over the 12 year season
vs
H1: There is an upward trend in growth
Data:
See attached spread sheet
Test Stat.
Arranging the data in pairs
(3646,3307)...(4500,4601)
We take the differences and count + signs and - signs. There are 4 + and 2 negatives
Decision
We reject H0 if the probability of observing 3 or fewer plus signs when n=12 and H0 is true.
P(k=412,05)<= .1938 Since .1938>=025 we reject the Null Hypothesis.
Conclusion
There is an upward trend in revenue in silviculture in Nova Scotia
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New Brunswick
New Brunswick Hypothesis
H0: No growth has occurrd over the 12 year season
vs
H1: There is an upward trend in growth
Data
See attached spread sheet
Test Stat.
Arranging the data in pairs
(39473,37462)...(58,141,55051)
We take the differences and count + signs and - signs. There are + 3 and 3 negatives
Decision
We reject H0 if the probability of observing 3 or fewer plus signs when n=12 and H0 is true.
P(k=3|12,05)<=.0729 Since .0729>025 we can reject the Null Hypothesis.
Conclusion
There is an upward trend in revenue in silviculture in New Brunswick
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Quebec
Quebec Hypothesis
H0: No growth has occurrd over the 12 year season
vs
H1: There is an upward trend in growth
Data
See attached spread sheet
Test Stat.
Arranging the data in pairs
(39473,37462)...(58,141,55051)
We take the differences and count + signs and - signs. There are + 3 and 3 negatives
Decision
We reject H0 if the probability of observing 3 or fewer plus signs when n=12 and H0 is true.
P(k=3|12,05)<=.0729 Since .0729>025 we can reject the Null Hypothesis.
Conclusion
There is an upward trend in revenue in silviculture in Quebec
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Manitoba
Manitoba Hypothesis
H0: No growth has occurrd over the 12 year season
vs
H1: There is an upward trend in growth
Data
See attached spread sheet
Test Stat.
Arranging the data in pairs
(3780,4151)...(7989,8578)
We take the differences and count + signs and - signs. There are + 2 and 4 negatives
Decision
We reject H0 if the probability of observing 3 or fewer plus signs when n=12 and H0 is true.
P(k=2|12,05)<=.01982 Since .0198<.025 we can't reject the Null Hypothesis.
Conclusion
There is nc upward trend in revenue in silviculture in Manitoba
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Saskatchewan
Saskatchewan Hypothesis
H0: No growth has occurrd over the 12 year season
vs
H1: There is an upward trend in growth
Data
See attached spread sheet
Test Stat.
Arranging the data in pairs
(5528,4762)...(17426,9458)
We take the differences and count + signs and - signs. There are + 4 and 1 negative and 1 neutral
We throw 0 difference out and base it on n=10
Decision
We reject H0 if the probability of observing 3 or fewer plus signs when n=10 and H0 is true.
P(k=4|10,05)<=.376 Since .376>.025 we can reject the Null Hypothesis.
Conclusion
There is an upward trend in revenue in silviculture in Saskatchewan
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Alberta
Alberta Hypothesis
H0: No growth has occurrd over the 12 year season
vs
H1: There is an upward trend in growth
Data
See attached spread sheet
Test Stat.
Arranging the data in pairs
(68959,57136)...(162118 99593)
We take the differences and count + signs and - signs. There are + 3 and 3 negative signs.
Decision
We reject H0 if the probability of observing 3 or fewer plus signs when n=12 and H0 is true.
P(k=3|12,05)<=.07298 Since .07298>.025 we can reject the Null Hypothesis.
Conclusion
There is an upward trend in revenue in silviculture in Alberta
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British Columbia
British Columbia Hypothesis
H0: No growth has occurrd over the 12 year season
vs
H1: There is an upward trend in growth
Data
See attached spread sheet
Test Stat.
Arranging the data in pairs
(1665212,1851978)...(1145317,1197478)
We take the differences and count + signs and - signs. There are 2 plus signs and 4 negative signs.
Decision
We reject H0 if the probability of observing 3 or fewer plus signs when n=12 and H0 is true.
P(k=2|12,05)<=.019287 Since .019287<.025 we can't reject the Null Hypothesis.
Conclusion
There is no upward trend in revenue in silviculture in BC
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Yukon
Yukon Hypothesis
H0: No growth has occurrd over the 12 year season
vs
H1: There is an upward trend in growth
Data
See attached spread sheet
Test Stat.
Arranging the data in pairs
(1534e 1847)...(13 22)
We take the differences and count + signs and - signs. There are 2 plus signs and 4 negative signs.
Decision
We reject H0 if the probability of observing 3 or fewer plus signs when n=12 and H0 is true.
P(k=2|12,05)<=.019287 Since .019287<.025 we can't reject the Null Hypothesis.
Conclusion
There is no upward trend in revenue in silviculture in Yukon
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NWT
NWT Hypothesis
H0: No growth has occurrd over the 12 year season
vs
H1: There is an upward trend in growth
Data
See attached spread sheet
Test Stat.
Arranging the data in pairs
(657,1133)...(41e ,43)
We take the differences and count + sign and - signs. There are 1 plus signs and 4 negative signs
and 1 zero difference. We discard the zero difference and set n=10
Decision
We reject H0 if the probability of observing 3 or fewer plus signs when n=12 and H0 is true.
P(k=1|10,05)<=.01074 Since .01074<.025 we can't reject the Null Hypothesis.
Conclusion
There is no upward trend in revenue in silviculture in NWT
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SUMMARY
The following provinces show no growth in silviculture over a 12 year period:
NWT,Yukon,B.C,Manitoba, PEI and Ontario
The reasons for this are manifold. They will be researched in a future article. Revenues in these provinces have gone down. As far as BC goes the old growth forest consist of about 10 percent of the wood left. The reason the industry can't cut these trees down is that they are not feasible due to the fact in a highly mountainous and remote regions of B.C.
