When they do not have the census of the points of sale that they cover, OpenHealth and its European partners allow their customers to follow modeled data on a national basis, ie that is, extrapolated from a sample of points of sale. While these extrapolated data provide our users with a very solid basis for their market analyzes, it nevertheless carries a margin of statistical uncertainty, the magnitude of which depends on several factors detailed below.

## Definitions

### Confidence interval:

A confidence interval frames a real value that we seek to estimate using measurements taken by a random process. This concept makes it possible to define a statistical uncertainty margin.

### Confidence level:

A confidence level represents the level of certainty and is expressed in%. A 95% confidence level is most commonly used in statistical studies.

### Factors impacting the size of the interval for a given confidence level

There are 4 factors that determine the size of the confidence interval for a given confidence level:

• Sample size
• The percentage
• The size of the population
• The time period

### The size of the sample

The larger the sample size, the more the results will truly reflect the population. This indicates that for a given confidence level, the larger the sample size, the smaller the confidence interval. However, the relationship is not linear (ie, doubling the sample size does not halve the confidence interval).

### The percentage

Precision also depends on the percentage of the sample that chooses a particular answer. If 99% of the sample answered "Yes" and 1% answered "No", the chances of statistical uncertainty are low, regardless of the sample size. However, if the percentages are 51% and 49%, the chances of statistical uncertainty are much greater. Extreme responses are easier to be sure than intermediate responses.

### The size of the population

Population size is only likely to be a factor when working with a relatively small population.

### The time period

The Selling Digital Distribution will depend on the time period studied. A DNV will be lower daily and therefore greater uncertainty.

### Sample size formula

• Z = Z value (eg 1.96 for 95% confidence level)
• p = percentage picking a choice, expressed as decimal (.5 used for sample size needed)
• c = confidence interval, expressed as decimal (eg, .04 = ± 4)

## Limitations

Confidence interval calculations assume that you have a true random sample of the affected population.

If your sample is not truly random, you cannot trust the intervals.

## illustrations

For mainland France except Corsica:

• If my product has a DNV of 100% and extrapolated sales of 100 units, a confidence interval of 0.68% means that there is 95% of lucky that my actual sales are between 99.32 units and 100.68 units. The uncertainty is low.
• If my product has a DNV of 1% and extrapolated sales of 100 units, a confidence interval of 9.05% means there are 95 % chance that my actual sales are between 90.95 units and 109.05 units. The uncertainty is greater.