Health Stats Healthcare Premium Increases: Summary Statistics

Health Stats

Healthcare Premium Increases: Summary Statistics and Explanations

A recent survey asked forty respondents how much of a monthly premium increase they could/would absorb before leaving their current healthcare plan. The sample responses are given as:

The mean of this sample is 47.23, with a standard deviation of 10.05. Assuming a normal distribution, the maximized level of retention with an increase in premiums would not necessarily occur at the mean itself. Moving one standard deviation to the left -- i.e. decreasing the premium increase by $10.05 to $37.18 -- would incorporate an additional 34.1% of the population (again assuming a normal distribution). Exact estimations regarding the profitability of various options cannot be given without knowledge of current premium rates and total population size, however it is likely that a premium increase below the observed mean in this population would be most beneficial to the company in terms of minimizing risks and maximizing revenue.

When determining a confidence interval for this sample/population, it is necessary to remember that the interval must be one sided. Everyone to the right of a given vertical line on the distribution will be included in the result, while everyone to the left would be excluded. The vertical line represents a selected price for the premium increase; those on the line or to the right of it are willing to pay the selected increase or more than the selected increase, while those to the left of the line would require lower increases in order to remain with their current health plan. Determining what percentage of individuals would remain with their current health plan with a selected premium increase -- or selecting a premium increase so as to maintain a specific desired level of retention -- involves the z-score and a greater use of the known features of the normal distribution. For a one-sided ninety percent confidence interval -- leaving a tail of ten percent at the left of the distribution -- the corresponding z-score is approximately -1.29, meaning the line would need to be drawn 1.29 standard deviations to the left of the mean in order to retain ninety percent of the population. In monetary terms in this case, the premium increase would have to be lowered from the mean by 1.29 x $10.05 or $12.96, meaning a premium increase of $47.23 - $12.96 or $34.27 should retain ninety percent of all current insurance members.