Estimating Statistical Significance

The estimates of sampling precision presented in the previous section yield confidence bands around the sample estimates, within which the true population value should lie. This type of sampling estimate is appropriate when the goal of the research is to estimate a population distribution parameter. However, the purpose of some surveys is to provide a comparison of population parameters estimated from independent samples (e.g. annual tracking surveys) or between subsets of the same sample. In such instances, the question is not simply whether or not there is any difference in the sample statistics that estimate the population parameter, but rather is the difference between the sample estimates statistically significant (i.e., beyond the expected limits of sampling error for both sample estimates).

To test whether or not a difference between two sample proportions is statistically significant, a rather simple calculation can be made. The maximum expected sampling error (i.e., confidence interval in the previous formula) of the first sample is designated s1 and the maximum expected sampling error of the second sample is s2. The sampling error of the difference between these estimates is sd and is calculated as:

equation 3 - click [d] for long description [d]

Any difference between observed proportions that exceeds sd is a statistically significant difference at the specified confidence interval. Note that this technique is mathematically equivalent to generating standardized tests of the difference between proportions.

An illustration of the pooled sampling error between sub-samples for various sizes is presented in Table 7. This table can be used to determine the size of the difference in proportions between drivers and non-drivers or other sub-samples that would be statistically significant.

TABLE 7.
Pooled Sampling Error Expressed as Percentages for Given Sample Sizes (Assuming P=Q)
Sample Size
4000 14.1 10.0 7.1 5.9 5.1 4.7 4.3 4.0 3.8 3.6 3.5 3.0 2.7 2.5 2.4 2.3 2.2
3500 14.1 10.0 7.1 5.9 5.2 4.7 4.3 4.1 3.8 3.7 3.5 3.0 2.7 2.6 2.4 2.3  
3000 14.1 10.0 7.2 5.9 5.2 4.7 4.4 4.1 3.9 3.7 3.6 3.1 2,8 2.7 2.5    
2500 14.1 10.0 7.2 6.0 5.3 4.8 4.5 4.2 4.0 3.8 3.7 3.2 2.9 2.8      
2000 14.2 10.1 7.3 6.1 5.4 4.9 4.6 4.3 4.1 3.9 3.8 3.3 3.1        
1500 14.2 10.2 7.4 6.2 5.5 5.1 4.7 4.5 4.3 4.1 4.0 3.6          
1000 14.3 10.3 7.6 6.5 5.8 5.4 5.1 4.8 4.7 4.5 4.4            
900 14.4 10.4 7.7 6.5 5.9 5.5 5.2 4.9 4.8 4.6              
800 14.4 10.4 7.8 6.6 6.0 5.6 5.3 5.1 4.9                
700 14.5 10.5 7.9 6.8 6.1 5.7 5.5 5.2                  
600 14.6 10.6 8.0 6.9 6.3 5.9 5.7                    
500 14.7 10.8 8.2 7.2 6.6 6.2                      
400 14.8 11.0 8.5 7.5 6.9                        
300 15.1 11.4 9.0 8.0                          
200 15.6 12.1 9.8                            
100 17.1 13.9                              
50 19.8                                
  50 100 200 300 400 500 600 700 800 900 1000 1500 2000 2500 3000 3500 4000
Sample Size


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