Statistical Comparisons Between Samples
In order to permit statistical comparisons between the two samples, the data sets from the two separate samples were merged together on like questions. The sample versions (1 for Safety Belt Usage and 2 for Child Safety Seats) were crosstabulated with each of the survey questions which had been asked in an equivalent fashion in the two samples. A chi square test was conducted for each of these crosstabulations to test for the independence of samples.
An exact test of independence was calculated to test the differences between the two samples. Pearson's chi square is a widely used statistic to test the hypothesis that the row and column variables are independent. It is calculated by summing over all cells the squared residuals divided by the expected frequencies. The calculated chi-square is compared to the critical points of the theoretical chi-square distribution to produce an estimate of how likely (or unlikely) this calculated value is, if the two variables are in fact independent. This probability is also known as the observed significance level of the test. If the probability is small (usually less than 0.05), the hypothesis that the two variables are independent is rejected.
No statistically significant difference (at the .05 level) was found between the two samples on most demographic characteristics, including race, ethnicity (Hispanic), educational attainment, and marital status. There is no difference between samples on most vehicle characteristics (e.g., airbags, type of seatbelts) or driver behaviors (e.g., drive everyday, always wear seatbelts).
There are, nonetheless, a limited set of differences large enough to be statistically significant with samples of this size. The proportion of van/minvan drivers in Version 2 is lower (8.2%) than in Version 1 (10.8%). The proportion of primary vehicles with airbags is higher in Version 1 (53.9%) compared to Version 2 (50.6%). The proportion of those reporting they had been injured in an accident was higher in Version 2 (25.4%) than in Version 1 (22.9%); and those who said their injuries prevented them from performing activities for at least one week were higher in Version 1 (55.5%) than in Version 2 (49.8%). The reported income between the two survey versions was also found to be significantly different. All these differences are likely due to the large sample size.
Finally, although the proportion of past month drinkers is the same in the two surveys (48.8% to 47.6), the proportion who report driving after drinking in the past month is significantly lower in the Child Safety Survey (20.9%) than the Seatbelt Survey (27.3%). This last difference probably reflects a contextual effect (willingness to report drinking and driving after an intense discussion of child safety in cars) rather than sample differences.