Question

Psychologists question the importance of biodiversity on the psychological health of humans in urban areas. Urban residents often visit green spaces such as parks within urban environments. Fuller et al., conducted a study on 15 different green spaces to determine the impacts of green space on people's psychological health.

To assess how much people liked the green space, scientists had participants fill out a survey to determine their attachment to the green space. Scientists then then quantified the biodiversity of birds, plants, and butterflies at the different green spaces.

Here is a link to a dataset relating biodiversity to residents' attachment to a location.

Which biodiversity measurement (butterfly species; bird species; plant species) variable is most strongly correlated with residents' "attachment"?  

Calculate the correlation coefficients using the =correl() function in Excel.

What is the standard error of that correlation?  

Calculate your answer using Excel and report your answer to four decimal places.

Which species exhibited the weakest correlation?  

What is the correlation coefficient of the weakest relationship?  

Calculate your answer using Excel and report your answer to four decimal places.

What is the value of t for the correlation of bird species?

Report your answer to four decimal places

What is the p value associated with the t value calculated in Question 5? Use the excel formula =2*(1-(T.Dist(ABS(t,df,TRUE))))

This is a two-tailed t-test

degrees of freedom (df) = n - 2

We are using a cumulative probability function so we type TRUE

Report your answer to 4 decimal places

Based on this p value, should the authors reject or fail to reject the null hypothesis that bird species abundance is not correlated to attachment?

DATA SET

Site ID	Attachment	Area (ha)	Butterfly Species	Bird Species	Plant Species
A	4.4	23.8	6	12	5.1
B	4.5	16	14	18	5.5
C	4.7	6.9	8	8	6.4
D	4.5	2.3	10	17	4.7
E	4.3	5.7	6	7	5.3
F	3.8	1.2	5	4	4.6
G	4.4	1.4	5	8	4.5
H	4.6	15	7	22	5.5
I	4.1	3.1	9	7	5.2
J	4.2	3.8	5	4	4.6
K	4.6	7.6	10	11	4.5
L	4.2	12.9	9	11	5
M	4.3	4	12	13	5
N	4.4	5.6	11	16	5.6
O	4.2	4.9	7	7	5.4

Answer 1

Correlation co-efficeints

	Correlation Coefficient
Butterfly Species vs Attachment	0.3506
Bird Species vs Attachment	0.6056
Plant Species vs Attachment	0.4136

Bird Species are strongly correlated with the attachment.

Butterfly species exhibit the weakest correlation with the attachment.

The correlation coefficient of the weakest relationship = 0.3506 in thsi question , In general for the weakest correlation the r = 0.

Standard Errors

where r = correlation coefficient

n = number of observations

	Std. Errors
Butterfly Species vs Attachment	0.2597
Bird Species vs attachment	0.2207
Plant Species vs attachment	0.2525

t-value = r/SE_r

value of t for the correlation of bird species = 0.6056/0.2207 = 2.7439

p-value = 0.016732

p-value is less than level of significance 0.05 hence we reject null hypothesis. And we conclude that there exist a correlation between the bird species and the attachment.