Gender and police trust are categorical variables. Gender has ‘male’ and ‘female’ levels. The levels in trust police are ‘not at all’, ‘just a little’, ‘somewhat’ and ‘a lot’ when the participants recorded their level of trusting the police. In this analysis, we would like to test independence in the two categorical variables. We want to find out whether males and females differ in their levels for police trust. Since our variables are nominal, the chi-square test will be our best test. Chi-square is used to test for a relationship between two nominal variables, with each variable having two or more groups (Turner, 2014).

Research questions and test hypothesis

Our primary research question is whether males and females differ in their levels for police trust. The follow-up question would be to ask how the variables are dependent on one another if at all there is a significant relationship.  We set our null and alternative hypotheses as;

Males and females do not differ in trust levels for police

Males and females differ in trust levels for police

Chi-square Results

Chart 1; clustered bar chart

From (chart 1), those who reported to trust the police somewhat, record the highest number across the levels. Therefore the chart shows the differences between the levels of trust in the police (McHugh, 2013).

Table 1; cross-tabulation table

 Q59h. Trust police * Q101. Gender of respondent Cross tabulation Q101. Gender of respondent Total Male Female Q59h. Trust police Not at all Count 5803 5454 11257 Expected Count 5656.3 5600.7 11257.0 Just a little Count 6345 6275 12620 Expected Count 6341.1 6278.9 12620.0 Somewhat Count 6550 6730 13280 Expected Count 6672.7 6607.3 13280.0 A lot Count 6669 6659 13328 Expected Count 6696.9 6631.1 13328.0 Total Count 25367 25118 50485 Expected Count 25367.0 25118.0 50485.0

The (Table 1) cross-tabulation table displays the observed and expected counts. The expected count refers to the values that we will expect to observe if the test is not significant (Michael, 2001). For example, if gender does not relate to the level of trusting the police, we expect to observe 6696 males who trust police a lot. The expected and observed values are a little bit different. However, the difference seems to be very small. We will, therefore, look at the chi-square table to determine if the difference is significant (Turner, 2014).

Table 2; chi- square table

 Chi-Square Tests Value df Asymp. Sig. (2-sided) Pearson Chi-Square 12.428a 3 .006 Likelihood Ratio 12.429 3 .006 Linear-by-Linear Association 6.873 1 .009 N of Valid Cases 50485 a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 5600.74.

The footnote under (Table 2) shows that 0.0% of cells have expected count less than 5. The latter means that the assumption of having at least 80% of the expected count to have more than five has not been violated (McHugh, 2013). Looking at the Pearson chi-square value, Since p-value (sig) < α=0.05, we reject the null hypothesis. We, therefore, deduce that there is a significant association between gender and level of trusting police. Males and females differ in their levels of trusting police.

Table 3; symmetric measures table

 Symmetric Measures Value Approx. Sig. Nominal by Nominal Phi .016 .006 Cramer’s V .016 .006 N of Valid Cases 50485 a. Not assuming the null hypothesis. b. Using the asymptotic standard error assuming the null hypothesis.

(Table 3) Shows the size of the effect is (0.016). The latter shows a very weak association between gender and trust levels in the police. The significance for this effect is p-value (sig) =0.006 < 0.05. We, therefore, conclude that there is a positive and very weak association between gender and police trust. Males and females a little bit differ in trusting the police.

References

McHugh, M. L. (2013). The chi-square test of independence. Biochemia medica: Biochemia medica23(2),

Michael, R. S. (2001). Crosstabulation & chi square. Indiana University, Bloomington, IN. URL http://www. indiana. edu/~ educy520/sec5982/we ek_12/chi_sq_summary011020. pdf (Visited 2010, June 15).143-149.

Turner, G. (2014). Is it statistically significant? The chi-square test. In UAS Conference Series.