Interest of Tree Growth along the Tagliamen River - Statistics Project Example

Interest of Tree Growth along the Tagliamen River Introduction The present research investigates the following questions and their accompanying hypotheses: Question 1: Is there significant positive correlation between the depth of water in the river and the rate of discharge reported? Hypothesis: The depth of the river is not significantly, positively correlated to the rate of discharge. Question 2: Is there a difference in the heights, number of annual rings and girth of the trees for the 2005 and 2010 results? Hypothesis 1: There is no significant difference in the height of the trees between 2005 and 2010. Hypothesis 2: There is no significant difference in the girth of the trees between 2005 and 2010. Hypothesis 3: There is no significant difference in the number of annual growth rings for the trees between 2005 and 2010. Methods Three types of statistical tests were used: correlation analysis, independent samples t-test, and analysis of variance (ANOVA). Descriptive and inferential statistics were reported based on the SPSS analysis of the research questions listed above. In order to undertake the ANOVA test, the defining factor, place of the trees along the river’s length was changed from a string to a numerical variable. Results and Discussion Based on the ‘tree growth data’, seven tree sites with a total of 280 were explored. The sites were located along the river’s channel, with each site having an equal number of trees. Site A was the furthest upstream site, with the other sites following in an alphabetical order to the seventh, site G. Measurements were taken in two sessions; the first in 2005 and the second in 2010. 140 measurements were taken in each of the two sessions. The average tree height was 304.75 cm (std. dev. = 28.67), with the tallest being 407cm and the shortest 247 cm. The average trunk diameter for the 180 trees was 2.12 (std. dev. = 0.55), with the thickest being 5.0 cm and the thinnest 1.1 cm. The average number of annual growth rings was 8.38 (std. dev. = 3.38); the maximum being 20 and the minimum 3. Based on the ‘river data’, measurements of the various components of the river’s waters were done between the 65th and 90th years. The 90th year had the most measurements, with 19 (6.8%) occurring in that year. The 71st year had the least number of measurements (1, 0.4) recorded. Through the years, June and November recorded the lowest number of measurements taken (20, comprising 7.2% for each) while July and December recorded the highest number (26, comprising 9.3% for each). Most measurements were taken on the 1st day of any month (96, translating to 34.4%) while none were taken on the 21st and 25th days. The average depth of the water in the river was 0.389m (std. dev. = 0.147), with the deepest measurement taken at 0.782m and the shallowest 0.036m. The average discharge rate was 10.663m3/s (std. dev. = 4.203), with the highest rate reported at 22.653m3/s and the lowest at 3.751 m3/s. The research sought to investigate the research question: is there significant positive correlation between the depth of water in the river and the rate of discharge reported? Correlation analysis was undertaken. The test hypothesis is: H0: The depth of the river is not significantly, positively correlated to the rate of discharge. H1: The depth of the river is significantly, positively correlated to the rate of discharge. The Pearson correlation coefficient was statistically significant (ρ = 0.764, p < 0.001). The null hypothesis was rejected at the 5% level of significance. This indicates that the rate of water discharge is significantly, highly correlated to the depth of water. Simply put, the higher the deeper the water, the higher the rate of discharge. Equally, shallower water levels attract proportionally low rate of discharge. The second hypothesis tested was based on the question: Is there a difference in the heights, number of annual rings and girth of the trees for the 2005 and 2010 results? Three hypotheses were tested concurrently. The independent samples t-test was used. H0: There is no significant difference in the height of the trees between 2005 and 2010. H1: There is significant difference in the height of the trees between 2005 and 2010. H0: There is no significant difference in the girth of the trees between 2005 and 2010. H1: There is significant difference in the girth of the trees between 2005 and 2010. H0: There is no significant difference in the number of annual growth rings for the trees between 2005 and 2010. H1: There is significant difference in the number of annual growth rings for the trees between 2005 and 2010. The heights were not significantly different (t = 0.994, p = 0.321). The null hypothesis was not rejected. There were no significant differences in the heights of the tree between 2005 and 2010 measurement periods. The trunk diameters were significantly different between the two measurement periods (t = 2.305, p = 0.022). The null hypothesis was rejected. The thicknesses of the trees had significant statistical differences between the 2005 and 2010 measurement periods. Similarly, there was significant difference between the numbers of annual growth rings recorded for the two periods (t = 8.514, p < 0.001). Finally, the research question: does the height, trunk diameter, and number of annual growth rings change with the location along the river length? One-way ANOVA was used. The hypotheses corresponding to this question were: H0: There is no significant difference in the height of the trees along the river length. H1: There is significant difference in the height of the trees along the river length. H0: There is no significant difference in the girth of the trees along the river length. H1: There is significant difference in the girth of the trees along the river length. H0: There is no significant difference in the number of annual growth rings for the trees along the river length. H1: There is significant difference in the number of annual growth rings for the trees along the river length. Overall, there were no significant differences in height (F = 1.432, p = 0.202). The differences in height did not change significantly along the length of the river. Significant differences were observed for the tree diameters (F = 15.001, p < 0.001); as well as for the number of annual growth rings (F = 34.616, p < 0.001). Clearly, trunk diameters and the number of annual growth rings changed significantly along the river length. Conclusion and Evaluation There was significant correlation between the depth of the river’s waters and the pressure of discharge. The results showed that the heights of the trees did not change between the two measurement periods; 2005 and 2010. Further, the results showed that the number of annual growth rings and the trunk diameters were significantly different between the two periods. The heights did not change significantly along the river’s length. However, the number of annual growth rings and the trunk diameters changed significantly. Further analysis of the results on the differences between the various measurements of tree growth could have been enhanced by use of post-hoc tests. These tests would allow the researcher to find out which points between the seven recorded along the river length had significant differences, and sizes of the differences (University of Oregon, 1999). References University of Oregon. 1999. Post hoc tests in ANOVA. [Online]. http://pages.uoregon.edu/stevensj/posthoc.pdf. Read More