In: Statistics and Probability
In a study, soil cores were taken from two locations in a forest: 1) under an opening in the forest canopy (the "gap" location); 2) at a nearby area under heavy tree growth (the "growth" location). The amount of carbon dioxide given off by each soil core (respiration rate) was measured in mol CO2/g soil/hr. A scientist is then asked to test whether the gap and growth areas differ with respect to soil respiration. A preliminary descriptive statistics check reveals that the sampling distribution is not normal.
1.1 1 Does the amount of CO2 given off by the soil differ according to the location? What kind of statistical analysis should you use to answer this question? Elaborate.
1.2 Is this a one-tailed or two-tailed test? Why? Elaborate.
1.3 How would you compare the two types of location and explain which type is better for soil respiration? Support this statement with associated statistics.
Using Excel, go to Data, select Data Analysis and choose t-test: Two-Sample Assuming Unequal Variances. Put values of growth in Bariable 1 Range and values of gap in Variable 2 Range as follows:
1. H0: µ1 = µ2, Amount of CO2 given off by the soil does not differ according to the location
H0: µ1 ≠ µ2, Amount of CO2 given off by the soil differs according to the location
Since here only two groups are to be compared, use t-Test: Two-Sample Assuming Unequal Variances.
Growth | Gap | |
Mean | 114 | 16.75 |
Variance | 13087 | 45.07143 |
Observations | 7 | 8 |
Hypothesized Mean Difference | 0 | |
df | 6 | |
t Stat | 2.24577 | |
P(T<=t) one-tail | 0.032911 | |
t Critical one-tail | 1.94318 | |
P(T<=t) two-tail | 0.065823 | |
t Critical two-tail | 2.446912 |
Since p-value (two-tail=0.0658) is more than 0.05, we do not reject the null hypothesis and conclude that µ1 = µ2, Amount of CO2 given off by the soil does not differ according to the location.
2. Since we are testing for two conditions µ1 > µ2 and µ1 < µ2 in the alternate hypothesis, we use a two-tailed test.
3. We can compare the two locations by their variances.
Variance for Growth = 13087
Variance for Gap = 45.07
Since variance for gap is less than that of growth and is also quite low, we can say that gap location is better for soil respiration.