Question

17. To obtain a preliminary measure of plant species richness in various habitats m2 quadrats were used at three locations on North Stradbroke Island: Brown Lele 18-Mile Swamp, and Pt. Lookout. The number of different species in each quadrat was recorded. (a) Is there a significant difference in plant species richness among these locations? Brown Lake 18-Mile Swamp Pt. Lookout 14 15 18 19 20 23 16 20 12 12 13 14 17 24 29 (b) Carry out a set of paired comparisons at the o 0.05 level or explain wily is inappropriate to do so.

How to solve this problem using R-studio?

Answer 1

To test whether there is a significant difference in three or more group means, we use ONE WAY ANOVA.

(a) ONE WAY ANOVA:

HYPOTHESIS:

The hypothesis is given by:

$H_{0}$: The mean plant species richness for three different locations are the same.

$H_{1}$: The mean plant species richness for at least two different locations differ.

LEVEL OF SIGNIFICANCE:

a-0.05

ONE WAY ANOVA R OUTPUT:

> #ONE WAY ANOVA > one_way-aov (species_richness locations, data-data) >summary (one way) Df Sum Sq Mean Sq F value Pr (>F) locations 2 225.7 112.83 9.266 0.00273 * Residuals 14 170.5 12.18 Signif. codes: 0 、 , 0.001 、**, 0.01 '치 0.05 \., 0.1 、, 1

CONCLUSION:

Since the p-value is
0,00273
which is less than
a-0.05
. Hence we reject null hypothesis at 5% level and conclude that the mean plant species richness for at least two different locations differ.

BOX PLOT:

> #BOX PLOT > boxplot (species_richness-locations, data-data,main + x1ab= "Locations", ylab="Species Richness") "Comparison of Species richness"

Comparison of Species richness 18_mile_swamp brown lake pt_lookout Locations

From the box plot we can conclude that there is a significant difference in the mean species richness for different locations. It can also be observed that the mean species richness for pt lookout is the highest and 18 mile swamp is the lowest.

Since we have found that there is significant difference in species richness among different locations, we use "Tukey Pairwise comparison" to test among which locations does the species richness differs.

PAIRWISE COMPARISON:

> #PAIRWISE COMPARISON > TukeyHSD (one_way) Tukey multiple comparisons of means 95% family-wise confidence level Fit: aov (formulaspecies richnesslocations, data-data) Slocations diff lwr upr p adj brown lake-18 mile swamp 5.000000 -0.2728493 10.272849 0.0641154 pt lookout-18 mile swamp 9.033333 3.5031223 14.563544 0.0020786 pt_lookout-brown_lake 4.033333 -1.49687779.563544 0.1727512

CONCLUSION:

Since the p-value 0.0021 is less than 0.05, there is a statistically significant difference in mean species richness between the locations pt lookout and 18 mile swamp at 5% level of significance.

o The difference in mean species richness between the locations pt lookout and 18 mile swamp is 9.03 ( i.e.) the species richness of pt lookout is 9.03 units higher than 18 mile swamp. The 95% confidence interval is (3.503, 14.564) i.e. the difference in the mean species richness between locations pt lookout and 18 mile swamp may lie between 3.503 and 14.564.