statistics

Chapter 10, 11. ANOVA: Parametric and Non-Parametric

1. Deer researchers at a University Wildlife department in some western state were interested in how home range size of wintering mule deer varied with the degree of human development—especially ski lodges, villages, and ski trails- on key winter range. They chose 3 sites with differing degrees of development on critical winter range and fitted 5deer on each site with a GPS satellite collar for tracking data and estimation of home range size. [note: home range is the area in which an organism spends all of its activities in: feeding, mating, resting, denning, etc]. At the end of the study, the data was downloaded remotely, and home range size (ha) determined. The researchers instincts told them home ranges should increase with the amount of development, reflecting the impact on food distribution and the necessity of traveling further to find it (deer don’t eat Walmart french fries). The data are below. Using ANOVA, test the Ho: µ1=µ2=µ3 vs Ha: Not all the means are equal at α = 0.05.If the F test is significant, then use Tukey’s mean separation procedure to determine which mean home ranges differ. This one is by hand, show your work, and attach additional pages if necessary with an identifier of the problem (e.g, prob#1).15 points.

Lake Tahoe, NV (Xi-Grd Mean)2Snowmass, CO(Xi-Grd Mean)2Jackson Hole, WY(Xi-Grd Mean)2

360 243 608

400 250 515

475 272 661

336 313 637

398 212 554 ________________

2. Three different methods were used to test the dissolved oxygen content of lake water. Each method was tested on 3 of the constructed wetlands at the TAMU-C artificial wetland site south of Commerce, TX. Conduct a nonparametric ANOVA (Kruskal-Wallis Test) to test the equality of mean dissolved oxygen produced by each of the three methods. 15 pts

Method 1 R1 Method 2 R2 Method 3 R3

10.96 10.88 10.73

10.77 10.75 10.79

10.9 10.8 10.78

Chapter 19. Correlation. (5points each)

3. John Deere and Joe Buck, whitetail deer biologists, conducted feeding trials on antler growth in white-tail deer. Having taken BSC 412, they knew to randomly and independently allocate each of 12 white-tail bucks to a forage ration containing different levels of calcium (g Ca/100lbs of feed). In the fall, when antlers were full grown and hardened, John and Joe sawed the antlers offand determined the bone density (grams Ca/cm3of antler bone) of the right antler from each deer. The data is below. A) Calculate the correlation coefficient, r. B) Calculate the coefficient of determination, r2. C) Test H0: ρ = 0 vsHa:ρ ≠ 0. Show your work.

Deer ID Calcium level in diet Bone density

Big Tex 59 298

Big Charlie 52 303

Drop tine 1 42 233

Bob 59 287

Simba 24 236

Caesar 24 245

Buckzilla 40 265

Monster 32 233

Superman 63 286

Birdnest 57 290

King 36 264

Mombo 24 239

4. Using the data above, calculate the nonparametric Spearman rank correlation coefficient. Test the H0: ρs = 0 vs Ha:ρs ≠ 0. Show your work.

5. From its inception, the technique of aging deer by tooth wear has been controversial.As to it’s reliability and accuracy.Age structure is an important vital statistic to understandpopn dynamics, and is dependent on accurate age estimates of any popn. Two techniques are generally used to estimate age of deer where true age is not known: tooth wear and cementum annuli. The first estimates age on the basis of overall wear patterns of molar ridges and amount of dentine and enamel on the molars. The cementum annuli method requires pulling a lower incisor, and thinly slicing it in cross section to count the growth rings much as you would to age a tree. A) Using the data below calculate the concordance correlation of estimated deer ages using each technique. What is the concordance or agreement between these two techniques? This part of the problem is to be done by hand . B) Extra credit: using the third column of data…the true known age of the deer, conduct a regression analysis to evaluate which technique is more strongly associated with the true age. Use all your knowledge to this point, provide regression ANOVA tables, a, b, r2, residuals, etc. This part of the problem can be done on Computer.

Age estimate

Deer # Tooth wear Cementum annuli Known Age

1 2.5 4.5 3.5

2 5.5 4.5 4.5

3 3.5 6.5 5.5

4 4.5 6.5 6.5

5 6.5 6.5 7.5

6 6.5 7.5 8.5

7 7.5 8.5 9.5

8 7.5 10.5 10.5

9 8.0 10.5 11.5

10 9.5 11.5 12.5

Chapter 21-22. χ2, and Contingency tables. (5 points each)

6. As part of a larger study evaluating the effect of ‘roundup’ events on rattlesnake populations, you conduct a small pilot study to determine the sex ratio of rattlesnakes exiting 4 known den sites on warm mid-March mornings. Your final count when all snakes have left the dens is as follows: 102 Males and 128 females. Test the hypothesis that sex ratios of denning rattlesnakes are equal.

7. You are working as a moose biologist on Isle Royale, Michigan. You were interested in habitat utilization of wintering moose. You have no funds for radio-telemetry, but you do have money for 1 day aerial helicopter survey. You plot moose location on a map, and record the habitat type where each moose was located in. At the end of the survey of Isle Royale, you have recorded 1000 and 600 cow and bull moose respectively. Using the data below, conduct a Chi-square 2 x 4 contingency table analysis to test the hypotheses that winter habitat use is independent of sex[e.g., bulls and cows select habitats with the same frequency].

Habitat type

Hemlock bottoms Open Deciduous forest Closed evergreen forest Old field

Cows 485 100 300 115

Bulls 150 285 90 75