Mannan and Meslow (1984) studied bird foraging behavior in a forest in Oregon. I

Question

Mannan and Meslow (1984) studied bird foraging behavior in a forest in Oregon. In a managed forest, 54% of the canopy volume was Douglas fir, 40% was ponderosa pine, 5% was grand fir, and 1% was western larch. They made 156 observations of foraging by red-breasted nuthatches; 70 observations (45% of the total) in Douglas fir, 79 (51%) in ponderosa pine, 3 (2%) in grand fir, and 4 (3%) in western larch. The biological null hypothesis is that the birds forage randomly, without regard to what species of tree they're in. Test that hypothesis that the proportions of foraging events are equal to the proportions of canopy volume at the 5% significance level. What test should we use?

Explanation / Answer

We use a chi^2 test of fit here.

Doing an observed/expected value table,          
O   E   (O - E)^2/E  
84.24   70   2.896822857  
62.4   79   3.488101266  
7.8   3   7.68  
1.56   4   1.4884  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    15.55332412      
          
As df = a - 1,           
          
a =    4      
df = a - 1 =    3      
          
Then, the critical chi^2 value is          
          
significance level =    0.05      
chi^2(crit) =    7.814727903      
          
Also, the p value is          
          
p =    0.001399956      
          
Thus, as chi^2 > 7.815, and P < 0.05, we   REJECT THE NULL HYPOTHESIS.      
          
Thus, there is significant evidence that the the proportions of foraging events are not equal to the proportions of canopy volume at 0.05 level. [CONCLUSION]

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