Statistical Significance Between Two Statistics

The difference between any two estimates given in the detailed tables may or may not be statistically significant. Statistical significance for the difference between two independent variables is computed as:

where S is the standard error, x₁ is the first estimate, and x₂ is the second estimate. The result of this computation is to be multiplied by 1.96, and if this result is less than the difference between the two estimates, the difference is statistically significant.

For example, the average expenditures for natural gas among U.S. households located in suburban areas in 1993 was $6.03 per million Btu. The comparable amount for U.S. households located in rural areas was $5.55 per million Btu, an estimated difference of $0.48 per million Btu. The standard error for the $6.03 per million Btu suburban estimate (x₁) is $0.09, and the standard error for the $5.55 per million Btu rural estimate (x₂) is $0.10:

Multiplying $0.13 by1.96 yields $0.26 per million Btu. Since $0.26 per million Btu is less than the $0.48 per million Btu difference between the 1993 suburban and rural natural gas estimates, the difference is statistically significant.