Question

6. Can we analyze the data in that study as paired data? If not, describe a paired design that could be implemented to study the same research question. Categorize the paired design as one of the four types of paired designs given in lecture on paired sampling

4 types given in lecture:

pre-test/post-test samples in which a factor is measured before and after an intervention.

matched samples, in which individuals are matched on personal characteristics such as age and sex.

cross-over trials in which individuals are randomized to two treatments and then the same individuals are crossed-over to the alternative treatment

. duplicate measurements on the same biological samples.

Given data

Freshwater wetlands are important ecosystems for many plants, invertebrates, and vertebrate animals. They can either be permanent or ephemeral (wet for part of the year and dry for other parts of the year). Scientists collected a variety of data for randomly selected wetlands in a preserve in Wisconsin. Determine if plant species richness (number of species) differs between permanent and ephemeral wetlands in this preserve. (Study and data from Amanda Little, University of Wisconsin - Stout)

# Dataset: Plant and macroinvertebrate species richness in ephemeral and permanent wetlands in Wisconsin, 2013

plant_eph = [34,51,20,47,22,19,24,18,33,45,36,42,30,25,44,33,47,35,51,15,24,13,25,32,49,28,37,17,13,32,24,18,22]
plant_perm = [31,40,43,37,23,45,53,46,44,25,47,34,41,31,37,34,42,37,14,29,18,15,14,28]
invert_eph = [33,27,25,32,26,29,24,25,17,21,18,21,21,18,27,20,31,26,27,30,29,16,29,28,32,25,26,28,35,23,31,23,24]
invert_perm = [33,25,19,30,29,33,32,30,30,29,32,34,34,32,36,34,33,34,34,31,34,31,29,35]

Answer 1

Here, we are asked to Determine if plant species richness (number of species) differs between permanent and ephemeral wetlands in this preserve.

Let us denote with subscript 1 as plant ephemeral and 2 as plant permanent. Let be the population mean number of species of both the groups. We calculate the mean and SD for both the data sets as

Level of significance:

Test statistic: We shall be applying a two sample independent t-test to test the significance. The formula for the same is:

will have a t distribution with df.

where

is the pooled variance;

The critical value of t( two sided) =2.004. Since the calculated critical, we fail to reject the null hypothesis. Hence we conclude that there is not enough evidence to claim that plant species richness (number of species) differs between permanent and ephemeral wetlands in this preserve.