Some proposed changes in the following sentences in the text:

1. “Adding a p-value to the description of our study results is useful since it suggests how high or low the probability is that the difference that we observed between the groups was due to chance.” to “Adding a p-value to the description of our study results is useful since it suggests how high or low the probability is that the observed difference between the groups or a more extreme one was due to chance”

2. “Please note that again it is a common convention to chose 95% as a confidence interval, but this might as well have been 90%, 99% or even 93.37%: it is a matter of choice” to “Please note that again it is a common convention to choose 95% as a confidence level, but this might as well have been 90%, 99% or even 93.37%; it is a matter of choice.”

3. “The deviation comprises the Standard Error”…Actually, the deviation is expressed as “critical value (of a distribution) plus or minus the standard error”. Some more elaboration here would be beneficial...

4. “If the Null Hypothesis is included within the CI, then we should consider it non-significant. For example, in case of a relative risk, the null hypothesis is that RR=1.0 (and the same goes for Odds Ratio).” What about writing this “If the null value is included within the CI, we will consider that the result is not statistically significant. For example, in case of a relative risk, the null value is 1.0 (RR=1.0) based on the null hypothesis that the exposure under study is not associated with the outcome under study (and the same goes for Odds Ratio).”?

5. “Most analytical software will give the confidence intervals automatically, together with the point estimates and p-value.” to “Most analytical software will provide the confidence intervals automatically, together with the point estimates and p-values.”

6. “This can be interpreted that the true relative risk for olive eating and botulism is with 95% probability between 1.17 and 11.07.” can maybe be rephrased to “The true relative risk lies between 1.17 and 11.07 with 95% confidence. That is, the data are also consistent with hypotheses of a relative risk between 1.17 and 11.07.”

7. “A confidence interval represents the range of effects that are compatible with the data. The CI provides

• the magnitude of the measured effect

• the the range in which the effect of our interest is most likely to be

• the direction of the effect (risk factor or protective factor)”

What about:

“A confidence interval represents the range of hypotheses that are compatible with the data.

The CI provides information on:

• the magnitude of the measured effect or else the strength of the association

• the range in which the effect of our interest is most likely to be

• the direction of the effect (risk factor or protective factor)

A separate part on the interpretation of the confidence intervals (as a headline) can also be useful. One may also include the results from the botulism outbreak example in this part.

It might also be preferable to use the terms wide and narrow instead of large and small when commenting on the width of confidence intervals. For example, “In principle, high data variability will lead to wide confidence intervals. The larger the sample size, the narrower the confidence interval. And finally, the higher the confidence level chosen, the wider the interval will be.”

There are some typos in the following sentences:

- “If we want to answer to this question, we can calculate the confidence interval around or estimated effect” to “If we want to answer to this question, we can calculate the confidence interval around our estimated effect”

- “Please note that again it is a common convention to chose 95% as a confidence interval, but this might as well have been 90%, 99% or even 93.37%: it is a matter of choice.” to “Please note that again it is a common convention to choose 95% as a confidence interval, but this might as well have been 90%, 99% or even 93.37%: it is a matter of choice.”