Metr 485/785 Homework 4 (Used to Be Last Part of Homework 3)

Reproducability of results: an exercise in application of the scientific method: Part 2

The purpose of this exercise is not to encourage carping or unbridled skepticism without purpose. The purpose is to show to the students the degree to which the results summarized in the paper can be reproduced or are statistically valid, either in support or disagreement with the claims of the authors.

Due Monday 23 February (final version of Homework 3....and first pass at 1 and 2) and for Wednesday 25 February everything will be due.

Look through the webpage on background to get more of a feel for what you are doing.

  1. (a) Using the CDC Climate Division Website Websites....correlate PDO on rainfall, SOI on rainfall, Nino3 on rainfall.

    Chart 1

    Chart 2

    Chart 3

    (b) Using your spreadsheet, correlate seasonal PDOs on seasonal rainfall for LA Civic Center.

    Correlation coefficient was 0.262 and corresponds roughly to that seen in Chart 1.
  3. Using the Brown correlation spreadsheet, statistically, evaluate the following questions:
    (a) is there a true correlation between the three time series and rainfall for the south coastal California climate divsion or is it just the luck of the draw?
PDO SOI NINO3
r 0.25 -0.55 0.55
r* significance 0.0739 <0.0001 <0.0001
Critical r* 0.273 -0.273 0.273
r confidence interval -0.25 to 0.49 -0.326 to -0.716 0.326 to 0.716
% of variance explained 6.25% 30% 30%


The correlation of PDO (obtained from Chart 1) on seasonal rainfall was 0.25, and this neither meets the test for statistical significance nor does it account for a large portion of the variance. Hence, there is no meaningful correlation between PDO and southern California precipitation. The correlations of SOI and NINO3 on southern California seasonal rainfall are meaninful because they are greater than 0.5, are statistically significant, and account for more than 25% of the variance (variability) in the record.

(b) What is the minimum correlation coefficient for each three that meets the test of statistical significance?
PDO, .273; SOI, -.273 and NINO3, .273.

(c) Determine the range of correlation coefficients that probably determine the true range of correlations for each of the cases with a 95% confidence.
PDO, -0.25 to 0.49; SOI, -0.326 to -0.716 and NINO3, 0.326 to 0.716.

(d) Do the same as you did for (a), (b) and (c) for your results in 1 (b) above.

The correlation of actual PDO values on seasonal rainfall at LA Civic Center was significant at the 5% level, but still only accounts for 7% of the variance. It has little predicitive value, therefore.

3. Now are your findings similar or different than those that LaDochy et al. make with respect to the relationship of PDO, SOI, Nino3 to Southern California rainfall?

Note: This work will serve as basis for your answers to one of the questions on the CCM Exam that you will be getting from the AMS.