Robert's Stochastic thoughts: Brad DeLong agrees with Matthew Yglesias: This tends to uhm strongly suggest that they are both right, but I beg to differ. The question is whether the Gallup tracking poll fluctuations which totally control my mood are due to sampling error alone. I say no. Brad writes something along the lines of "yes" or "don't panic"
You can't back out daily polls but you can test the null that true opinion hasn't changed. for non overlapping polls this is easy. variance of Obama - McCain in one poll is around 1/3000 (less than 1/(sample size) because some people are undecided so the correlation of "for Obama" and "for McCain" is not exactly -1). Var of dif of dif is about 1/1500 so se of dif of dif is about 2.7% (just tried to calculate a square root in my head).
With one day overlap you can calculate the change in 2 day averages (3/2)(change in 3 day as one day is the same). So about 10% convention bounce so far. sample sizes only around 1800 so var dif around 1/2000 so var dif of dif around 1/1000 se around 3.2% so change over 3 standard deviations. The evidence of a convention bounce (including Michelle and Hillary but not Bill and Joe) is statistically significant. People do change their minds based on cheering Germans, dumb dumber dumbest negative ads and party conventions. Those people might be so flighty that there is no way to guess what the hell they will do on election day, but they do exist. "Normal fluctuations which you shouldn't have a cow about because they tell you virtually nothing about who will be elected" and "fluctuations due to sampling error" are not synonymous statements.
But when I take the data since July 20 and regress the Obama share on a time trend allowing for the MA(3) character of the residual, I get a t-statistic of -0.97; when I omit the "bounce" day of yesterday from the sample, I get a t-statistic of -1.37; and when I regress the Obama share on a time trend and on a "bounce" dummy variable covering yesterday August 27, I get a t-statistics of +1.37 on the bounce. I don't believe that t-statistics of less than 1.5 in absolute value are causes for mood swings.
What's going on? Why are my regressions different than RJW's first-principles variance calculations? According to Robert's calculations, the standard deviation of the one-day change in the moving average should be 0.78%. But the empirical standard deviation is 1.17%. There's day-to-day noise in the sample that does not come from standard statistical sampling error.