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| * Significant at 0.05 level | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
For each chart generated by MEPSnet/IC, a table is provided which lists the survey estimates shown in the chart and their corresponding standard errors (SE). These standard errors reflect the estimated sampling error associated with the estimate (i.e., potential error introduced because data were collected for only a sample of establishments).
Analysts frequently generate 95% confidence intervals to assess the precision of survey estimates. These intervals are computed as:
Estimate +/- 1.96*SE.
MEPSnet/IC displays a 95 percent confidence interval for each estimate shown in the chart. A 95 percent confidence interval has the following general interpretation: applying the interval-estimating procedure to all possible samples, a statement that a given interval enclosed the true population mean would be correct 95 percent of the time. Therefore, one can be 95 percent sure that an interval constructed from one sample captures the true population mean.
For example, the chart and table generated using MEPSnet/IC at the end of this description show the average total single premium levels per enrolled employee and the corresponding SEs for 1996-2010, at private-sector establishments which offer health insurance.
In 2010, the estimate for the average single premium is $4940 +/- 1.96*$21.92. So, the interval ranges from $4897.04 to $4982.96.
Test of Significance
An analyst can determine if there is a statistically significant difference between any two estimates by calculating a z-statistic.
A z-statistic can be computed with this formula:
As an example using the estimates generated by MEPSnet/IC, the z-statistic to assess whether the difference in average single premiums between 2008 and 2010 is statistically significant would be computed as:
The threshold z-statistic for establishing statistical significance at the .05 level is 1.96. That is, if the calculated z-statistic is greater than 1.96 or less than –1.96, the estimates are significantly different at the .05 level. All values that are significant at the 0.05 level are marked with an *. For this example, the calculated z-statistic of 20.65 is greater than 1.96, so the difference between the two years is statistically significant.
The p-value shown in the table is the probability of having a z-statistic as large or larger than the one calculated from these estimates (or smaller in cases where the z-statistic is negative). When this p-value is less than or equal to the 0.05 level of significance, then the difference is statistically significant at that level and is marked with an * in MEPSnet/IC.
In above example, the p-value associated with the z-statistic of 20.65 is very small (rounds to 0.00000) and thus this difference is statistically significant. (Note that the z-statistic calculated using the above formula is slightly different than that calculated below by the MEPSnet/IC system; this is because the MEPSnet/IC uses unrounded estimates for the premiums and SEs in its formula. This very small difference does not affect the result of the comparison.)
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