How These Polls Were Conducted

Here are the key things to know about this set of polls from The New York Times, The Philadelphia Inquirer and Siena College:

• Interviewers spoke with 808 voters in Arizona from Oct. 7 to 10, 656 voters in Montana from Oct. Oct. 5 to 8, and 857 voters in Pennsylvania from Oct. 7 to 10.

• Times/Siena polls are conducted by telephone, using live interviewers, in both English and Spanish. Overall, more than 95 percent of respondents were contacted on a cellphone for these polls.

• Voters are selected for the survey from a list of registered voters. The list contains information on the demographic characteristics of every registered voter, allowing us to make sure we reach the right number of voters of each party, race and region. For these polls, interviewers placed about 235,000 calls to nearly 90,000 voters.

• To further ensure that the results reflect the entire voting population, not just those willing to take a poll, we give more weight to respondents from demographic groups that are underrepresented among survey respondents, like people without a college degree. You can see more information about the characteristics of our respondents and the weighted sample at the bottom of the page, under “Composition of the Sample.”

• The margin of sampling error among likely voters is about plus or minus four percentage points. In theory, this means that the results should reflect the views of the overall population most of the time, though many other challenges create additional sources of error. When the difference between two values is computed — such as a candidate’s lead in a race — the margin of error is twice as large.

If you want to read more about how and why the Times/Siena Poll is conducted, you can see answers to frequently asked questions and submit your own questions here.

Full Methodology

The New York Times/Siena College polls of 656 voters in Montana and 808 voters in Arizona and the New York Times/Philadelphia Inquirer/Siena College poll of 857 voters in Pennsylvania were conducted in English and Spanish on cellular and landline telephones. The Arizona ran from Oct. 7 to 10, the Pennsylvania poll ran from Oct. 7 to 10, 2024, and the Montana poll ran from Oct. 5 to 8.

For each poll, the margin of sampling error among the likely electorate is plus or minus 4.3 percentage points in Montana, plus or minus 3.9 percentage points in Arizona and plus or minus 3.8 percentage points in Pennsylvania.

The Times/Siena polls of Pennsylvania in 2024 were conducted in partnership with the Philadelphia Inquirer and were funded in part by a grant from the Lenfest Institute for Journalism. The poll was designed and conducted independently from the institute.

Sample

The survey is a response-rate-adjusted stratified sample of registered voters taken from the voter file maintained by L2, a nonpartisan voter-file vendor, and supplemented with additional voter-file-matched cellular telephone numbers from Marketing Systems Group. The sample was selected by The New York Times in multiple steps to account for differential telephone coverage, nonresponse and significant variation in the productivity of telephone numbers by state.

To adjust for noncoverage bias, the L2 voter file for each state was stratified by statehouse district, party, race, gender, marital status, household size, turnout history, age and homeownership. The proportion of registrants with a telephone number and the mean expected response rate were calculated for each stratum. The mean expected response rate was based on a model of unit nonresponse in prior Times/Siena surveys. The initial selection weight was equal to the reciprocal of a stratum’s mean telephone coverage and modeled response rate. For respondents with multiple telephone numbers on the L2 file, or with differing numbers from L2 and Marketing Systems Group, the number with the highest modeled response rate was selected.

Fielding

The sample was stratified according to political party, race and region. Marketing Systems Group screened the sample to ensure that the cellular telephone numbers were active, and the Siena College Research Institute fielded the poll, with additional fieldwork by ReconMR, the Public Opinion Research Laboratory at the University of North Florida, the Institute for Policy and Opinion Research at Roanoke College, the Center for Public Opinion and Policy Research at Winthrop University in South Carolina and the Survey Center at University of New Hampshire. Interviewers asked for the person named on the voter file and ended the interview if the intended respondent was not available. Overall, more than 95 percent of respondents were reached on a cellular telephone.

In Arizona and Pennsylvania, the questions were translated into Spanish by ReconMR. Bilingual interviewers began the interview in English and were instructed to follow the lead of the respondent in determining whether to conduct the survey in English or Spanish. Monolingual Spanish-speaking respondents who were initially contacted by English-speaking interviewers were recontacted by Spanish-speaking interviewers. Overall, 6 percent of interviews (9 percent of the weighted sample) among self-reported Hispanics were conducted in Spanish, including 2 percent of the interviews (3 percent of the weighted sample) among self-reported Hispanics in Arizona and 26 percent of the interviews (34 percent of the weighted sample) among self-reported Hispanics in Pennsylvania.

An interview was determined to be complete for the purposes of inclusion in the questions about whom the respondent would vote for if the respondent did not drop out of the survey after being asked the two self-reported variables used in weighting — age and education — and answered at least one of the questions about age, education or presidential-election candidate preference.

Weighting (registered voters)

The survey was weighted by The Times using the survey package in R in multiple steps.

First, the sample was adjusted for unequal probability of selection by stratum.

Second, each poll was weighted to match voter file-based parameters for the characteristics of registered voters.

The following targets were used:

• Party registration (L2 data) by whether the respondent has requested an absentee ballot for the 2024 general election (L2 data), in Pennsylvania

• Party registration (L2 data) by race (L2 model), in Arizona

• Six categories of partisanship (Classification based on an NYT model of vote choice in prior Times/Siena polls), in Montana

• Partisanship (L2 model based on commercial data and partisan political contributions), in Montana

• Race or ethnicity (L2 model)

• Age (self-reported age, or voter-file age if the respondent refused) by gender (L2 data)

• Education (four categories of self-reported education level, weighted to match NYT-based targets derived from Times/Siena polls, census data and the L2 voter file)

• White/nonwhite race by college or noncollege educational attainment (L2 model of race weighted to match NYT-based targets for self-reported education in Pennsylvania; L2 model of race weighted to match NYT-based targets derived from census data in Arizona)

• Marital status (L2 model)

• Homeownership (L2 model)

• Turnout history (NYT classifications based on L2 data)

• Method of voting in the 2020 elections (NYT classifications based on L2 data), in Montana and Arizona

• State region (NYT classifications)

• Census block group density (A.C.S. 5-Year Census Block Group data), in Montana

• History of voting in the 2020 presidential primary (L2 data), in Pennsylvania

• Census tract educational attainment, in Arizona

Finally, the sample of respondents who completed all questions in the survey was weighted identically as well as to the result for the general-election horse-race question (including voters leaning a certain way) on the full sample.

Weighting (likely electorate)

The survey was weighted by The Times using the R survey package in multiple steps.

First, the samples were adjusted for unequal probability of selection by stratum.

Second, the first-stage weight was adjusted to account for the probability that a registrant would vote in the 2024 election, based on a model of turnout in the 2020 election.

Third, the sample was weighted to match targets for the composition of the likely electorate. The targets for the composition of the likely electorate were derived by aggregating the individual-level turnout estimates described in the previous step for registrants on the L2 voter file. The categories used in weighting were the same as those previously mentioned for registered voters.

Fourth, the initial likely electorate weight was adjusted to incorporate self-reported intention to vote. Four-fifths of the final probability that a registrant would vote in the 2024 election was based on the registrant’s ex ante modeled turnout score, and one-fifth was based on self-reported intentions, based on prior Times/Siena polls, including a penalty to account for the tendency of survey respondents to turn out at higher rates than nonrespondents. The final likely electorate weight was equal to the modeled electorate rake weight, multiplied by the final turnout probability and divided by the ex ante modeled turnout probability.

Finally, the sample of respondents who completed all questions in the survey was weighted identically as well as to the result for the general election horse-race question (including leaners) on the full sample.

The margin of error accounts for the survey’s design effect, a measure of the loss of statistical power due to survey design and weighting.

The design effect for the full sample is 1.24 for the likely electorate in Montana, 1.29 for the likely electorate in Pennsylvania and 1.30 for the likely electorate in Arizona.

Among registered voters, the margin of sampling error is plus or minus 4.3 points in Montana, including a design effect of 1.26; plus or minus 3.8 points in Arizona, including a design effect of 1.20; and plus or minus 3.7 points in Pennsylvania, including a design effect of 1.23.

For the sample of completed interviews, among the likely electorate, the margin of sampling error is plus or minus 4.5 points in Montana, including a design effect of 1.29; plus or minus 4 points in Pennsylvania, including a design effect of 1.35; and plus or minus 4.1 points in Arizona, including a design effect of 1.30.

Historically, The Times/Siena Poll’s error at the 95th percentile has been plus or minus 5.1 percentage points in surveys taken over the final three weeks before an election. Real-world error includes sources of error beyond sampling error, such as nonresponse bias, coverage error, late shifts among undecided voters and error in estimating the composition of the electorate.