Question 637:

Asked on February 22, 2009

Tags: Confidence Intervals , Adjusted Wald

1

Answer:

No answer provided yet.

Regarding the reflectivity performance of the signs, I agree, you will need data from different time periods—historical data. Ideally you have a few points in time so that I can help you with either a regression equation or some other time-series analysis which shows trends and helps predict future values. At the very least we will need data from 2 points in time to make some rudimentary predictions about future values.

 

Regarding the signs reflectivity and meeting minimum acceptable. I’ve shown the detailed computations in the last questions, so I’ll focus on the results and interpreting them here.  It looks like this specification is requiring all signs to meet the minimum specification, as opposed to the mean being above some point.  In looking at the data there doesn’t appear to be any values for Yellow. For the Class 1 White the specs are the mean values should be above 380, but as you noted, it appears that much of the data-might be confounded by the older signs being mixed in.  So, if you are able to collect data on whether the sign is old or new, this would help the validity of the analysis, as well as provide a better picture of the number of signs out of specification—since there are quite a few below.

 

So, lets assume there is a mix of old and new in this dataset. What I’ve done is flagged the ones which fail to meet both the new and old standards. For example, for white this would be anything below 250. That leaves 5 out of 21 which will fail to meet the standard on both old and new. To estimate the total number of signs that fail to meet the White Standard we’d build a binomial confidence interval around the proportion 5/21 = .2381. The 95% confidence interval is between 10.23% and 45.49% of all White signs fail to meet the old White standard of 250. Using the new standard of 350 increases the proportion out of spec to 12/21 = .5714 and has a 95% confidence interval between 36.52% and 75.56%. So there is a big difference there, so again I recommend trying to identify old vs new signs.

 

For the Red signs we’ll use the same procedure and we get 3 out of 6 (.50) that fail to meet BOTH the old and new standard of 50 and 75 respectively. Given this sample size we can be 95% confident between 18.76% and 81.24% of all Red signs fail to meet the standard.

 

For Class 2 signs there are 2/3 yellow that are below the minimum standard making the actual occurrence for all Class 2 yellow between 20.24% and 94.37%.  For White I counted 25 out of 47 out of spec making the 95% confidence interval between 39.23% and 66.67% for all Class 2 White signs. Finally, there is 1/2 red signs below standard making the 95% confidence interval between 9.45% and 90.55% of all Red signs below standard. This last interval is very large because there are only 2 data-points. This interval will get narrower quickly with just a few more observations.