I'm perplexed about how such a large sample size wouldn't make this difference in response rates statistically significant. (GASP! I used those words...) If you split the sample into two groups of 240,000 and have one with a success proportion of 0.515 and the other with 0.52, then using a simple two-proportion test results in an incredibly small p-value. On the face of it, it doesn't seem like you'd really have to use any more complicated of a test than a two-proportion test, since it seems like they are just comparing two success rates.
I'm not a trained statistician, but I've been teaching introductory and upper-level statistics for almost 20 years. So am I missing something here??
I would grant you that this could be a setting where "statistical significance" doesn't necessarily mean "practical significance". But the blog/article is saying that the results were not significant at the 0.10 level, so that is speaking to statistical significance.
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Mark Mills
Professor of Mathematics
Central College
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Original Message:
Sent: 11-11-2019 08:11
From: Dennis Pearl
Subject: Census Bureau says a citizenship question would likely not reduce response rates
Note that according to the footnote following the sentence that Terry Meyer quoted, the words "no difference" should be taken to mean 'no significant difference with a 10% significance level'. The actual difference in response rates was 0.5% (52.0% for the group without the citizenship question and 51.5% for the group with the citizenship question). This experiment was conducted to evaluate how many people the census bureau would need to hire to complete the work needed when people don't respond to their initial automated contact efforts through the mail. Thus, their conclusion was that there would be no difference in required staffing levels - not that the citizenship question would not affect response rates. Indeed the question of response rates to live interviewers was not even examined - since this was completely about response to mailings.
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Dennis Pearl
Professor
Penn State University
Original Message:
Sent: 11-07-2019 11:38
From: Terry Meyer
Subject: Census Bureau says a citizenship question would likely not reduce response rates
The Census Bureau tested the response rate for questionnaires with and without the citizenship question. The result was no significant difference.
"The major finding of the test was that there was no difference in self-response rates between forms with and forms without a citizenship question" from
https://www.census.gov/newsroom/blogs/random-samplings/2019/10/2019_census_testpre.html
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Terry Meyer
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