# Value and confidence interval relationship

### Confidence Interval or P-Value?

An understanding of p-values and confidence intervals is necessary for The alternative hypothesis (H1) then states that there is a difference. Confidence intervals are an excellent way of understanding the role of sampling range of all values, just how much the average value is likely to fluctuate. root relationship between confidence intervals and sample sizes. A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from.

If the null value is "embraced", then it is certainly not rejected, i. However, one should view these two estimates differently. The estimate with the wide confidence interval was likely obtained with a small sample size and a lot of potential for random error.

However, even though it is not statistically significant, the point estimate i. In this case one might want to explore this further by repeating the study with a larger sample size. Repeating the study with a larger sample would certainly not guarantee a statistically significant result, but it would provide a more precise estimate.

The other estimate that is depicted is also non-significant, but it is a much narrower, i. Even if there were a difference between the groups, it is likely to be a very small difference that may have little if any clinical significance. So, in this case, one would not be inclined to repeat the study. For example, even if a huge study were undertaken that indicated a risk ratio of 1. Even if this were true, it would not be important, and it might very well still be the result of biases or residual confounding.

Small p-values correspond to strong evidence. If the p-value is below a predefined limit, the results are designated as "statistically significant" 1.

## The Relationship Between Confidence Intervals and p-values

The phrase "statistically striking results" is also used in exploratory studies. If it is to be shown that a new drug is better than an old one, the first step is to show that the two drugs are not equivalent.

Thus, the hypothesis of equality is to be rejected. The null hypothesis H0 to be rejected is then formulated in this case as follows: The alternative hypothesis H1 then states that there is a difference between the two treatments. This can either be formulated as a two-tailed hypothesis any difference or as a one-tailed hypothesis positive or negative effect. In this case, the expression "one-tailed" means that the direction of the expected effect is laid down when the alternative hypothesis is formulated.

## Confidence Intervals and p-Values

For example, if there is clear preliminary evidence that an antihypertensive has on average a stronger hypertensive effect than the comparator drug, the alternative hypothesis can be formulated as follows: For example, the data from a randomized clinical study are to be used to estimate the effect strength relevant to the question to be answered.

This could, for example, be the difference between the mean decrease in blood pressure with a new and with an old antihypertensive. On this basis, the null hypothesis formulated in advance is tested with the help of a significance test.

The p-value gives the probability of obtaining the present test result—or an even more extreme one—if the null hypothesis is correct. A small p-value signifies that the probability is small that the difference can purely be assigned to chance.

### Confidence Intervals and p-Values

In our example, the observed difference in mean systolic pressure might not be due to a real difference in the hypotensive activity of the two antihypertensives, but might be due to chance.

The level of significance of 0. If the p-value is less than this limit, the result is significant and it is agreed that the null hypothesis should be rejected and the alternative hypothesis—that there is a difference—is accepted. The specification of the level of significance also fixes the probability that the null hypothesis is wrongly rejected. P-values alone do not permit any direct statement about the direction or size of a difference or of a relative risk between different groups 1.

However, this would be particularly useful when the results are not significant 2. For this purpose, confidence limits contain more information. Aside from p-values, at least a measure of the effect strength must be reported—for example, the difference between the mean decreases in blood pressure in the two treatment groups 3.

In the final analysis, the definition of a significance limit is arbitrary and p-values can be given even without a significance limit being selected. The smaller the p-value, the less plausible is the null hypothesis that there is no difference between the treatment groups.

Confidence limits—from the dichotomous test decision to the effect range estimate The confidence interval is a range of values calculated by statistical methods which includes the desired true parameter for example, the arithmetic mean, the difference between two means, the odds ratio etc. This means that the confidence interval covers the true value in 95 of studies performed 45.

The advantage of confidence limits in comparison with p-values is that they reflect the results at the level of data measurement 6.