# Estimation of Voter Turnout by Age Group and Gender at the 2015 General Election

## Appendix: Methodology

The purpose of this study is to estimate voter turnout rates for several different demographic groups of interest defined by age and gender at the national, provincial and territorial levels.

### Definition of turnout

The official turnout results published by Canada's Chief Electoral Officer are calculated using the number of registered electors in the denominator instead of the size of the electoral population. This introduces distortion into the turnout results, especially when broken down by age or when making comparisons over time.

The coverage of the electoral list (that is, the percentage of eligible electors listed) changes over time, depending among other things on many factors related to list maintenance activities. If turnout is calculated relative to the number of electors on the list, then measures of change in turnout over time will be confounded by these other factors. This problem is exacerbated when turnout is broken down by age, since the changes in coverage over time may be quite different for different age groups. For example, an apparent decrease in youth turnout may be partly due to Elections Canada's efforts to increase coverage of youth on the list.

For this study, turnout is defined as the number of ballots cast divided by the number of eligible electors. This denominator is calculated by adjusting population estimates obtained from Statistics Canada to include only citizens 18 years of age or over as of polling day (October 19, 2015). In order to get the numerator, we need to know how many people cast a ballot and what group they fall into. A random sample of electors was used to produce an estimate of the numerator for each demographic group of interest. Ultimately, the numerator is obtained by adding this estimate to the known numbers of ballots cast by members of the different groups, whether at advance polls, by special ballot or by persons registering when they voted on polling day.

### Electoral population

The size of the electoral population within a demographic group of interest is required for the denominator of the turnout estimates. This was based on Statistics Canada's 2011 Census, with adjustments made to remove non-citizens and those under 18 years of age, who are not eligible to vote, and to take into account population growth during the time elapsed between census day and polling day, using demographic information provided by Statistics Canada and Immigration, Refugees and Citizenship Canada. The electoral population estimates used for this study can be found on Elections Canada's website at www.elections.ca/res/rec/part/estim/42nd_GE_turnout_e.xlsx.

### Definition of age groups

For the purposes of this study, age as of polling day was divided into eight groups, consistent with previous studies. These groups were defined as follows:

Age group | Date of birth From |
Date of birth To |
---|---|---|

1st time | May 3, 1993 | October 19, 1997 |

not 1st time | October 20, 1990 | May 2, 1993 |

25–34 | October 20, 1980 | October 19, 1990 |

35–44 | October 20, 1970 | October 19, 1980 |

45–54 | October 20, 1960 | October 19, 1970 |

55–64 | October 20, 1950 | October 19, 1960 |

65–74 | October 20, 1940 | October 19, 1950 |

75+ | – | October 19, 1940 |

Youth aged 18–24 were split into two groups: those who were eligible to vote for the first time in the 2015 general election (youth born between May 3, 1993, and October 19, 1997) and those who were eligible to vote in the 2011 general election (youth born between October 20, 1990, and May 2, 1993).

### Sample design

Elections Canada maintains administrative records that contain the address, date of birth and gender for everyone on the final voters list. They do not indicate which electors cast ballots, except in special circumstances. The administrative data can be used to identify all those who voted at advance polls, by special ballot, or who registered to vote on polling day. For those who voted on polling day but were registered earlier, the information required is only available on the strike lists used to administer the election.

The information on the strike lists is currently not captured electronically. It would be prohibitively expensive and time-consuming to obtain all the lists from each polling station and capture the required information after the fact. Instead, a random sample of polling divisions was selected and the strike list of pre-polling day registered electors from each selected poll was obtained. The information required was then captured, and an estimate of the number of votes cast by regular ballot on polling day was produced for each demographic group of interest. The final estimates required for the numerator of turnout were then produced by adding these estimates to the known numbers of ballots cast in each group at advance polls, by special ballot, and by those registering to vote on polling day.

Based on previous studies and practical considerations of time and resources, an overall sample size of 1,800 polls was determined to be sufficient to produce estimates with acceptable margins of error at the provincial or territorial level.

Stratified simple random sampling was used to select the sample of 1,800 polling divisions. Each of the 338 electoral districts constitutes a stratum. The sample was roughly allocated proportionally to the size of the district, that is, to the number of polling divisions per district. A random sample of polling divisions was selected within each electoral district, and all of these samples form the overall sample containing a total of 548,336 electors.

Table 3 shows the sample breakdown by province or territory as well as the number of ballots cast at advance polls or by special ballot.

Province or territory | Number of electoral districts | Size of sample Polling divisions | Size of sample Electors | Number of votes at advance polls or by special ballot |
---|---|---|---|---|

N.L. | 7 | 35 | 9,751 | 41,492 |

P.E.I. | 4 | 8 | 1,218 | 28,352 |

N.S. | 11 | 58 | 16,139 | 142,911 |

N.B. | 10 | 52 | 12,020 | 134,599 |

Que. | 78 | 456 | 138,510 | 1,077,279 |

Ont. | 121 | 653 | 203,011 | 1,565,776 |

Man. | 14 | 67 | 20,252 | 124,228 |

Sask. | 14 | 58 | 16,607 | 113,409 |

Alta. | 34 | 184 | 57,092 | 425,818 |

B.C. | 42 | 223 | 67,064 | 628,430 |

Y.T. | 1 | 2 | 613 | 7,846 |

N.W.T. | 1 | 2 | 923 | 4,150 |

Nvt. | 1 | 2 | 5,136 | 1,729 |

Total | 338 | 1,800 | 548,336 | 4,296,019 |

### Estimation

The initial estimate for each polling division is obtained by multiplying its sampling weight by the total number of votes in the division. The sample weight (or the inverse of probability of inclusion in the sample) of the polling division is considered as the average number of polling divisions represented by each division in the study's population.

The sum of the initial estimates gives the estimate at the electoral district level. The estimate at the provincial or territorial level is obtained by adding the estimates of the districts belonging to a given province or territory. The estimates by age group and gender are obtained the same way. Finally, the sum of the provincial and territorial estimates is used to determine the national estimate.

However, because of the random character of a sample and other factors such as missing lists, estimates of the number of electors are generally not entirely consistent with the known totals derived from the official results. Therefore, these estimates are adjusted to the known totals using a customary method of sample adjustment known as the "calibration method". Technically, calibration consists in calculating new weights of sampled units which, in minimizing their difference from the initial weighting, produce estimates coherent with known information on the population. Calibration also makes it possible to reduce the sampling variance and, in certain cases, to reduce bias due to non-response.

These estimates are then added to the known totals of electors who voted by advance poll or special ballot, and the resulting total is divided by the electoral population.

### Margins of error for turnout estimates

Margins of error for the estimates were obtained by producing 95% confidence intervals around the estimates, using standard errors calculated according to a method of variance estimation known as Bootstrap, and assuming a normal sampling distribution. The principle of the Bootstrap method is to construct a number of samples of the initial sample selected within the population, with the statistical inference based on the results of the samples thus obtained.

For the 2015 general election, this sampling and estimation methodology serve to produce margins of error between 1 to 3 percentage points at the national level and for most of the age groups, approximately between 1 and 12 percentage points at the provincial or territorial level. Actual participation rates should be within the associated margin of error for the estimates 19 times out of 20.

Throughout this document, a difference was considered statistically significant at the 5% error level if the estimated difference was larger than the associated margin of error.

Tables showing the statistical margins of error by province or territory, age group and gender are provided on Elections Canada's website at www.elections.ca/res/rec/part/estim/42nd_GE_turnout_e.xlsx.