# Margins of Error and Confidence Level

## Margin of Error

The findings from the Active NZ Survey are based on data collected from a randomly-selected sample of adults from each of the 17 regional sports trust (RST) catchment areas throughout New Zealand. The findings from the survey provide an estimate of the true value that would be obtained if all adults in New Zealand were interviewed (as for a census).

A margin of error (MOE) provides an indication of how far away an estimate obtained from a population sample may be from the true value in the whole population (census).

The margin of error is expressed as a percentage (e.g. 5%) and depends upon the *sample size *from the survey and the size of the *estimate* obtained (e.g., 50% of adults volunteered). Hence, a margin of error associated with an estimate of 50 percent for one RST region will not necessarily be the same for another RST region with an estimate of 50 percent if the survey sample size taken from each region differs substantially.

## Confidence Interval

A confidence interval (CI) is a range of values within which the true value of an estimate is likely to lie. A CI provides a given probability (e.g. 95%) that the true value lies within the specified range. Hence, if a percentage estimate of 50% has an MOE of 2.5%, the CI for a percentage estimate of 50% would be from 47.5% – 52.5%. This means that if we ran the survey again 100 times and collected 100 different samples, we would expect 95 of the estimates obtained from these survey samples to lie within the reported confidence interval.

This means there is a 95% probability that the true value of the estimate would lie between 47.5% and 52.5%.

## Margin of Error Tables

#### Using the Table

To determine the margin of error and confidence interval for a specific finding you need two numbers:

- the finding or percent estimate (e.g. 64.1% of New Zealand adults walked as a sport or recreation); and
- the sample size the finding is based on (e.g. total sample, female sample, Maori sample).

The specific sample size numbers are located in the introduction section of the national and regional reports.

Once you have this information, find the numbers in the tables below that are the closest to the actual finding and sample size of interest.

**Example 1**: 48.7% of females in New Zealand participated in gardening. The percent estimate = 48.7% and the sample size of female participants = 2,586. Using the second table, the MOE associated with this estimate is approximately 2.5% (i.e. 48.7% ± 2.5%). The confidence interval is 46.2% to 51.2%.

Margin of Error Table for Samples Sizes of 60 to 295 People

Percentage Estimate |
Sample size | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

60 |
80 |
100 |
120 |
140 |
160 |
180 |
200 |
270 |
295 | |

5% |
6.3 |
5.7 |
5.1 |
4.7 |
4.5 |
4.1 |
3.9 |
3.9 |
3.3 |
3.3 |

10% |
8.6 |
7.6 |
7.1 |
6.5 |
6.1 |
5.7 |
5.5 |
5.3 |
4.7 |
4.5 |

15% |
9.8 |
8.6 |
8.0 |
7.4 |
6.9 |
6.5 |
6.3 |
5.9 |
5.3 |
5.1 |

20% |
10.6 |
9.4 |
8.6 |
7.8 |
7.4 |
7.1 |
6.7 |
6.5 |
5.7 |
5.5 |

25% |
11.0 |
9.8 |
8.8 |
8.2 |
7.8 |
7.3 |
7.1 |
6.7 |
5.9 |
5.7 |

30% |
11.4 |
10.0 |
9.2 |
8.4 |
8.0 |
7.4 |
7.3 |
6.9 |
6.1 |
5.9 |

35% |
11.6 |
10.2 |
9.2 |
8.6 |
8.0 |
7.6 |
7.3 |
7.1 |
6.3 |
5.9 |

40% |
11.6 |
10.4 |
9.4 |
8.6 |
8.2 |
7.6 |
7.4 |
7.1 |
6.3 |
6.1 |

45% |
11.6 |
10.4 |
9.4 |
8.8 |
8.2 |
7.8 |
7.4 |
7.1 |
6.3 |
6.1 |

50% |
11.8 |
10.4 |
9.4 |
8.8 |
8.2 |
7.8 |
7.4 |
7.1 |
6.3 |
6.1 |

55% |
11.8 |
10.4 |
9.4 |
8.8 |
8.2 |
7.8 |
7.4 |
7.1 |
6.3 |
6.1 |

60% |
11.6 |
10.4 |
9.4 |
8.8 |
8.2 |
7.8 |
7.4 |
7.1 |
6.3 |
6.1 |

65% |
11.6 |
10.4 |
9.4 |
8.8 |
8.2 |
7.8 |
7.4 |
7.1 |
6.3 |
6.1 |

70% |
11.6 |
10.2 |
9.4 |
8.6 |
8.2 |
7.6 |
7.4 |
7.1 |
6.3 |
6.1 |

75% |
11.6 |
10.2 |
9.4 |
8.6 |
8.0 |
7.6 |
7.3 |
7.1 |
6.3 |
5.9 |

80% |
11.4 |
10.2 |
9.2 |
8.6 |
8.0 |
7.6 |
7.3 |
7.1 |
6.1 |
5.9 |

85% |
11.4 |
10.2 |
9.2 |
8.6 |
8.0 |
7.6 |
7.3 |
6.9 |
6.1 |
5.9 |

90% |
11.4 |
10.0 |
9.2 |
8.4 |
8.0 |
7.6 |
7.3 |
6.9 |
6.1 |
5.9 |

95% |
11.2 |
10.0 |
9.0 |
8.4 |
7.8 |
7.4 |
7.1 |
6.9 |
6.1 |
5.9 |

Margin of Error Table for Samples Sizes of 360 to 4,400 People

Percentage Estimate |
Sample size | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

360 |
525 |
715 |
780 |
950 |
970 |
1,290 |
1,860 |
2,590 |
3,050 |
4,400 | |

5% |
2.9 |
2.5 |
2.4 |
2.2 |
2.0 |
2.0 |
1.8 |
1.6 |
1.4 |
1.2 |
1.0 |

10% |
4.1 |
3.5 |
3.1 |
2.9 |
2.7 |
2.7 |
2.4 |
2.2 |
1.8 |
1.8 |
1.4 |

15% |
4.7 |
3.9 |
3.5 |
3.3 |
3.1 |
3.1 |
2.7 |
2.4 |
2.2 |
2.0 |
1.8 |

20% |
5.1 |
4.3 |
3.7 |
3.7 |
3.3 |
3.3 |
2.9 |
2.5 |
2.2 |
2.2 |
1.8 |

25% |
5.3 |
4.5 |
3.9 |
3.7 |
3.5 |
3.5 |
3.1 |
2.7 |
2.4 |
2.2 |
2.0 |

30% |
5.5 |
4.7 |
4.1 |
3.9 |
3.5 |
3.5 |
3.1 |
2.7 |
2.4 |
2.2 |
2.0 |

35% |
5.5 |
4.7 |
4.1 |
3.9 |
3.7 |
3.7 |
3.3 |
2.7 |
2.4 |
2.4 |
2.0 |

40% |
5.5 |
4.7 |
4.1 |
4.1 |
3.7 |
3.7 |
3.3 |
2.7 |
2.5 |
2.4 |
2.0 |

45% |
5.5 |
4.7 |
4.1 |
4.1 |
3.7 |
3.7 |
3.3 |
2.7 |
2.5 |
2.4 |
2.0 |

50% |
5.5 |
4.7 |
4.1 |
4.1 |
3.7 |
3.7 |
3.3 |
2.7 |
2.5 |
2.4 |
2.0 |

55% |
5.5 |
4.7 |
4.1 |
4.1 |
3.7 |
3.7 |
3.3 |
2.7 |
2.5 |
2.4 |
2.0 |

60% |
5.5 |
4.7 |
4.1 |
4.1 |
3.7 |
3.7 |
3.3 |
2.7 |
2.5 |
2.4 |
2.0 |

65% |
5.5 |
4.7 |
4.1 |
4.1 |
3.7 |
3.7 |
3.3 |
2.7 |
2.5 |
2.4 |
2.0 |

70% |
5.5 |
4.7 |
4.1 |
4.1 |
3.7 |
3.7 |
3.3 |
2.7 |
2.5 |
2.4 |
2.0 |

75% |
5.5 |
4.7 |
4.1 |
3.9 |
3.7 |
3.7 |
3.3 |
2.7 |
2.4 |
2.4 |
2.0 |

80% |
5.5 |
4.7 |
4.1 |
3.9 |
3.7 |
3.7 |
3.3 |
2.7 |
2.4 |
2.4 |
2.0 |

85% |
5.5 |
4.7 |
4.1 |
3.9 |
3.7 |
3.5 |
3.1 |
2.7 |
2.4 |
2.4 |
2.0 |

90% |
5.5 |
4.7 |
4.1 |
3.9 |
3.5 |
3.5 |
3.1 |
2.7 |
2.4 |
2.2 |
2.0 |

95% |
5.3 |
4.5 |
4.1 |
3.9 |
3.5 |
3.5 |
3.1 |
2.7 |
2.4 |
2.2 |
2.0 |