1. Homework #2: Calculating a correlation yearGDP/capitaODA (millions) 2000200173 2001200175 2002220175 2003240176.5 2004300178 2005270179 2006375400 20073501000 2008375400 2009400200 2010450200 NOTE: these have different scale so I wouldn’t graph them together, but you could do two separate graphs. Do they move together?

2. Calculating a correlation in Excel Click on an empty cell and click on Insert function. Choose Correlation (either Correl or Pearson will work) Highlight array #1 (i.e. highlight the entire GNP/capita series) and then choose the second array (i.e. tech, ed., etc). Both arrays should span the same time period and have the same number of observations

3. Interpretation (+) positive relationship between the two variables (1 would be a perfect correlation). They move together. (-) Negative relationship (-1 would be perfectly negative correlation). They move in the opposite direction 0 If it is close to zero, there is no correlation.

4. Testing for statistical signficance of RCTs

5. Are the results reliable? A T-test simply measures whether there is a reliable difference between two means Control group Average collection Treatment group Average collection

6. Calculating a t-test (for unpaired samples, unequal variance) T statistic= difference between groups Variance within groups

8. Excel's TTEST Excel takes the T statistic and the degrees of freedom (based on the sample size (N-2)) to calculate a p-value: a test to see if you results are statistically significant When you do TTEST in Excel, it will return the p-value

9. P values: The smaller, the more significant! Statistical significance Good*: If it is less than 0.1 then the two samples are statistically different There’s a 1/10 chance that the difference is due to chance Better**: If it is less than 0.05 There’s a 1/20 chance that the difference is due to chance Best***: Less than 0.01 There’s a 1/100 chance that the difference is due to chance

10. Using Excel to calculate a t-test Click on empty cell Insert function TTEST Choose first array (control) Choose second array (treatment) Choose 2 tailed distribution Choose 3 sample unequal variance Enter Result shows p value.

11. Excel calculation Calculate the following: 1.Mean of control, Mean of treatment 2.P-value of TTEST Cans of food collected controltreatment 01 01 30 40 02 03 22 11 42 22 02 23 14 10 01 01 00 11 22 02 12 03 21 00 00 02 11 10 02 11 total2942

12. Excel calculation Calculate the following: 1.Mean of control, Mean of treatment 0.966667 and 1.4 2.Pvalue of TTEST 0.143184 > 0.10 so NOT statistically significant at 10% level Cans of food collected controltreatment 01 01 30 40 02 03 22 11 42 22 02 23 14 10 01 01 00 11 22 02 12 03 21 00 00 02 11 10 02 11 totaltotal2942