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The language of statistical "significance" is not directly applicable to a confidence interval, though intervals are often related to similar hypothesis tests. If you were to compare a confidence interval to a corresponding hypothesis test you would find that the "confidence level" $1-\alpha$ and the "significance level" $\alpha$ are in fact negatively related --- i.e., a higher confidence level corresponds to a lower significance level. However, saying that a result in a hypothesis test is "more significant" usually means that it has a lower p-value, which is determined by the data, not the chosen significance level. For all these reasons, I strongly recommend that you avoid bringing the terminology of "significance" into discussion of a confidence interval. (It is bad enough in its proper context!)

Just as with significance levels in a hypothesis test, there are no sacrosanct values for the confidence level of a confidence interval. The choice of an appropriate confidence level depends on context, and it always involves a trade-off between desired levels of confidence and accuracy. For a fixed set of data and a fixed procedure for the confidence interval, if you choose a higher confidence level then you will get wider (less accurate) interval, and vice versa. You can think of a higher confidence level as a more conservative inference, insofar as you are willing to be less accurate in order to be highly confident that the parameter of interest falls within the interval. Contrarily, you can think of a lower confidence interval as a less conservative inference, since you will get better accuracy for the interval but at the cost of having lower confidence that the parameter of interest falls within the interval.

There is no inherent problem with choosing a confidence interval at 60% or 70% confidence level, though obviously that is quite a low level of confidence and so it is a risky inference. Typically people choose higher confidence levels because they want to have a high level of confidence that the unknown value of interest falls within the computed interval. Personally, I tend to be quite conservative in my statistical inferences, so unless there are good contextual reasons to the contrary, if I have a reasonable amount of data I will usually opt for a 99% confidence interval (or perhaps an even higher confidence level).

The language of statistical "significance" is not directly applicable to a confidence interval, though intervals are often related to similar hypothesis tests. If you were to compare a confidence interval to a corresponding hypothesis test you would find that the "confidence level" $1-\alpha$ and the "significance level" $\alpha$ are in fact negatively related --- i.e., a higher confidence level corresponds to a lower significance level. However, saying that a result in a hypothesis test is "more significant" usually means that it has a lower p-value, which is determined by the data, not the chosen significance level. For all these reasons, I strongly recommend that you avoid bringing the terminology of "significance" into discussion of a confidence interval. (It is bad enough in its proper context!)

Just as with significance levels in a hypothesis test, there are no sacrosanct values for the confidence level of a confidence interval. The choice of an appropriate confidence level depends on context, and it always involves a trade-off between desired levels of confidence and accuracy. For a fixed set of data and a fixed procedure for the confidence interval, if you choose a higher confidence level then you will get a wider (less accurate) interval, and vice versa. You can think of a higher confidence level as a more conservative inference, insofar as you are willing to be less accurate in order to be highly confident that the parameter of interest falls within the interval. Contrarily, you can think of a lower confidence interval as a less conservative inference, since you will get better accuracy for the interval but at the cost of having lower confidence that the parameter of interest falls within the interval.

There is no inherent problem with choosing a confidence interval at 60% or 70% confidence level, though obviously that is quite a low level of confidence and so it is a risky inference. Typically people choose higher confidence levels because they want to have a high level of confidence that the unknown value of interest falls within the computed interval. Personally, I tend to be quite conservative in my statistical inferences, so unless there are good contextual reasons to the contrary, if I have a reasonable amount of data I will usually opt for a 99% confidence interval (or perhaps an even higher confidence level).

The language of statistical "significance" is not directly applicable to a confidence interval, though intervals are often related to similar hypothesis tests. If you were to compare a confidence interval to a corresponding hypothesis test you would find that the "confidence level" $1-\alpha$ and the "significance level" $\alpha$ are in fact negatively related --- i.e., a higher confidence level corresponds to a lower significance level. However, saying that a result in a hypothesis test is "more significant" usually means that it has a lower p-value, which is determined by the data, not the chosen significance level. For all these reasons, I strongly recommend that you avoid bringing the terminology of "significance" into discussion of a confidence interval. (It is bad enough in its proper context!)

Just as with significance levels in a hypothesis test, there are no sacrosanct values for the confidence level of a confidence interval. The choice of an appropriate confidence level depends on context, and it always involves a trade-off between desired levels of confidence and accuracy. For a fixed set of data and a fixed procedure for the confidence interval, if you choose a higher confidence level then you will get wider (less accurate) interval, and vice versa. There is no inherent problem with choosing a confidence interval at 60% or 70% confidence level, though obviously that is quite a low level of confidence. Typically people choose higher confidence levels because they want to have a high level of confidence that the unknown value of interest falls within the computed interval.

The language of statistical "significance" is not directly applicable to a confidence interval, though intervals are often related to similar hypothesis tests. If you were to compare a confidence interval to a corresponding hypothesis test you would find that the "confidence level" $1-\alpha$ and the "significance level" $\alpha$ are in fact negatively related --- i.e., a higher confidence level corresponds to a lower significance level. However, saying that a result in a hypothesis test is "more significant" usually means that it has a lower p-value, which is determined by the data, not the chosen significance level. For all these reasons, I strongly recommend that you avoid bringing the terminology of "significance" into discussion of a confidence interval. (It is bad enough in its proper context!)

Just as with significance levels in a hypothesis test, there are no sacrosanct values for the confidence level of a confidence interval. The choice of an appropriate confidence level depends on context, and it always involves a trade-off between desired levels of confidence and accuracy. For a fixed set of data and a fixed procedure for the confidence interval, if you choose a higher confidence level then you will get wider (less accurate) interval, and vice versa. You can think of a higher confidence level as a more conservative inference, insofar as you are willing to be less accurate in order to be highly confident that the parameter of interest falls within the interval. Contrarily, you can think of a lower confidence interval as a less conservative inference, since you will get better accuracy for the interval but at the cost of having lower confidence that the parameter of interest falls within the interval.

There is no inherent problem with choosing a confidence interval at 60% or 70% confidence level, though obviously that is quite a low level of confidence and so it is a risky inference. Typically people choose higher confidence levels because they want to have a high level of confidence that the unknown value of interest falls within the computed interval. Personally, I tend to be quite conservative in my statistical inferences, so unless there are good contextual reasons to the contrary, if I have a reasonable amount of data I will usually opt for a 99% confidence interval (or perhaps an even higher confidence level).

The language of statistical "significance" is not directly applicable to a confidence interval, though intervals are often related to similar hypothesis tests. If you were to compare a confidence interval to a corresponding hypothesis test you would find that the "confidence level" $1-\alpha$ and the "significance level" $\alpha$ are in fact negatively related --- i.e., a higher confidence level corresponds to a lower significance level. Moreover, saying that a result in a hypothesis test is "more significant" usually means that it has a lower p-value, which is determined by the data, not the chosen significance level. For all these reasons, I strongly recommend that you avoid bringing the terminology of "significance" into discussion of a confidence interval. (It is bad enough in its proper context!)

Just as with significance levels in a hypothesis test, there are no sacrosanct values for the confidence level of a confidence interval. The choice of an appropriate confidence level depends on context, and it always involves a trade-off between desired levels of confidence and accuracy. For a fixed set of data and a fixed procedure for the confidence interval, if you choose a higher confidence level then you will get wider (less accurate) interval, and vice versa. There is no inherent problem with choosing a confidence interval at 60% or 70% confidence level, though obviously that is quite a low level of confidence. Typically people choose higher confidence levels because they want to have a high level of confidence that the unknown value of interest falls within the computed interval.

The language of statistical "significance" is not directly applicable to a confidence interval, though intervals are often related to similar hypothesis tests. If you were to compare a confidence interval to a corresponding hypothesis test you would find that the "confidence level" $1-\alpha$ and the "significance level" $\alpha$ are in fact negatively related --- i.e., a higher confidence level corresponds to a lower significance level. However, saying that a result in a hypothesis test is "more significant" usually means that it has a lower p-value, which is determined by the data, not the chosen significance level. For all these reasons, I strongly recommend that you avoid bringing the terminology of "significance" into discussion of a confidence interval. (It is bad enough in its proper context!)

Just as with significance levels in a hypothesis test, there are no sacrosanct values for the confidence level of a confidence interval. The choice of an appropriate confidence level depends on context, and it always involves a trade-off between desired levels of confidence and accuracy. For a fixed set of data and a fixed procedure for the confidence interval, if you choose a higher confidence level then you will get wider (less accurate) interval, and vice versa. There is no inherent problem with choosing a confidence interval at 60% or 70% confidence level, though obviously that is quite a low level of confidence. Typically people choose higher confidence levels because they want to have a high level of confidence that the unknown value of interest falls within the computed interval.