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Appendix 2: Methodology

Logistic regression used to inform analysis

We used logistic regression in this analysis to establish what measures had strong independent relationships with Māori adults’ trust in the police and the media. This logistic regression was used only to decide which measures would be included in the report and these measures were presented using descriptive statistics. Results from the regression analysis form no part of the main report. But the results are presented here for your information.

As the eleven possible response options for respondents to the questions on trust in the police and the media have a logical order, we used a cumulative multinomial logistic regression. The advantage of using regression analysis is that it holds other factors constant, while looking at the association between the likelihood of levels of trust and the factor of interest.

A cumulative multinomial logistic regression describes the relationship between the lowest against all higher categories of the trust in institution measures and the relationship between the next-lowest category and all higher categories. Because the relationship between all pairs of groups is the same, there is only one set of coefficients. Therefore, results from the model refer to the likelihood of having a higher level of trust in the police and the media.

We have taken account of the complex sample design of Te Kupenga in the logistic regression by using the survey logistic procedure in SAS. This procedure allows for the incorporation of complex survey sample designs, including designs with stratification, clustering, and unequal weighting.

Model of trust in institutions

While people’s trust in institutions is no doubt a complex process, Te Kupenga contains many measures that would allow us to look at what is associated with this trust. To restrict the number of these measures that we put into the model, we began with a simple framework that might help explain how a high level of trust is achieved. This framework has the following themes:

  • demography and geography
  • health
  • socio-economic
  • education
  • crime and discrimination.

We selected a number of measures from Te Kupenga to represent each of these themes in the logistic regression model.

Interpreting odds ratios

We present the results of the logistic regression analysis in appendix 3 in the form of odds ratios. An odds ratio is the odds of an event happening divided by the odds of the opposite event happening. For example, suppose that 400 females trusted the police and 200 did not. The odds of a female trusting the police are 400/200 = 2, or 2 to 1. This means the chances of a female trusting the police are reasonably good. To give another example, suppose that 500 males trusted the police and 1,000 did not. The odds of a male trusting the police would be 500/1,000 = 0.5 or 1 to 2. The chances of their trusting the police are therefore significantly lower than for females.

For continuous explanatory variables (for example age), an odds ratio of greater than 1 indicates a higher likelihood of high levels of trust as the value of the explanatory variable increases and an odds ratio less than 1 indicates a lower likelihood.

For categorical explanatory variables, the odds ratio compares the likelihood of trusting the police or the media compared with the reference category. An odds ratio greater than 1 indicates a higher likelihood of trusting the police or the media compared with the reference group, while an odds ratio of less than 1 indicates a lower likelihood.

Confidence intervals

Error bars on all figures represent the 95 percent confidence interval of the estimate. This represent the range in which we are 95 percent confident the true population mean falls. If an error bar does not overlap with an estimate we are 95% confident that there was a difference in the estimates.

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