Question

What effect do nutrient additions have on plant species diversity? Long-term experiments at the Rothamstead Experimental Station in the U.K. sought to investigate the relationship, with some interesting findings.

Calculate everything in excel

Plot	Nutrients added	# of species
1	0	36
2	0	36
3	0	32
4	1	34
5	2	33
6	3	30
7	1	20
8	3	23
9	4	21
10	4	16

1) Produce a scatter plot of the data (click here for a generic youtube video on creating a scatter plot from excel data - this is for informational purposes only - it's not your data)

Which is the explanatory variable? (nutrients OR species)

Which is the response variable? (nutrients OR species)

Looking at your scatter plot, do you observe a positive or negative relationship?  

2) Add the least-squares regression line to your scatter plot. (click here for a generic youtube video on adding trendlines to scatter plots - this is for informational purposes only - it's not your data)

What fraction of the variation in the number of plant species is "explained" by the number of nutrients added? Answer to two decimal places.

3) Test the hypothesis of no treatment effect on the number of plant species.

What is your t-value?  

Do you accept or reject the null hypothesis?

Also, could you please let me know what type of T test is used? Like equal variance or unequal variance

Answer 1

1)

The explanatory variable: Nutrients added

The response variable: # of species

Following is the scatter plot of the data:

2)

Click on add trendline. Select linear trend line. Select display equation on line and r-square. Following is the scatter plot with line:

The equation of line:

y' = -3.34x + 34.11

The r-square is: 0.54

3)

Following is the output of regression analysis:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.732105551
R Square	0.535978538
Adjusted R Square	0.477975855
Standard Error	5.336058185
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	263.1118644	263.111864	9.240581867	0.016067379
Residual	8	227.7881356	28.4735169
Total	9	490.9
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	34.11016949	2.599312938	13.1227637	1.08142E-06	28.11614311	40.10419587
Nutrients added	-3.338983051	1.098410195	-3.0398325	0.016067379	-5.8719215	-0.806044602

The t test statistics is:

t = -3.04

The p-value is: 0.0161

Since p-value is less than 0.05 so we can conclude that there is a significant relationship between the variables.

Reject the null hypothesis at 5% level of signficance