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.https://docs.google.com/spreadsheets/u/1/d/1vnoPdn5S0i5LV1OQ19FUyzs2WDdwBwmAgvhuCH5B0KE/copy

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

Calculate your answers using the =correl() function in Excel and report your answer to four decimal places.

2)What is the standard error of that correlation?  

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

3)Which correlation is weakest?  

4)What is the correlation coefficient of the weakest relationship?  

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

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

Report your answer to four decimal places

6)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

7)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?

Answer 1

THe solution

https://docs.google.com/spreadsheets/d/1QOLvYPPU0-dnEoaFs359O03RopdBK53p9JOAeL3ka48/edit?usp=sharing

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
	correlation coefficient between Butterfly Species & Attachment =r1				0.3506203631
	correlation coefficient between Bird Species & Attachment =r2				0.6055798411
	correlation coefficient between Plant Species & Attachment =r3				0.4135939319
	standard error of correlation coefficient between Butterfly Species & Attachment =					(1-r1^2)/sqrt(n)	0.2264573024
	standard error of correlation coefficient between Butterfly Species & Attachment =					(1-r2^2)/sqrt(n)=	0.1635104
	standard error of correlation coefficient between Butterfly Species & Attachment =					(1-r3^2)/sqrt(n)=	0.214031403
	solution(a)
	correlation coefficient between Bird Species & Attachment =r2 =				0.6056
	i.e bird species is most strongly related to attachement sincr r2 is greater than r1 and r3
	solution(b)
	the standard error of the correlation of r2=				0.1635
	solution(c)
	correlation between Butterfly Species & Attachment
	solution(d)
	the correlation coefficient of the weakest relationship is r1=0.3506
	i.e.correlation coefficient between Butterfly Species & Attachment =r1 is weakest relationship
	solution(5)
	let R is the population correlation between birds species and attachment
	then
	Ho; R=0
	H1: R is not equal to zero
	Test statistics	t=(r2-R)/sqrt((1-r^2)/n-2) =		2.743769225
	tabulated t=	2.160368656
	since tabulated t is less than calculated t so we accept hypothesiis that the population correlation between birds species and attachment is zero