# HOW CONFIDENT IS THE CONFIDENCE INTERVAL

K.I. Egbuchulem

Division of Paediatric Surgery, Department of Surgery, University College Hospital, Ibadan

## EDITORIAL

The classroom teaching of statistics is the pivot for answering these research questions – How confident is the confidence interval and how confident do you want to be as a researcher that sample estimates collected are as accurate as you wish? These are the focus of this editorial, to highlight some of these facts, myths about test of significance as it relates to confidence intervals and the question how confident the confidence interval is needs to be interrogated.

Most biomedical research testing the level of significance report Confidence Intervals (C.Is), and these are useful in interpreting results of statistical analysis. Literally, it should give the researcher some degree of confidence about the research output in terms of reliability, accuracy, and precision. It is usual for biomedical researchers and other investigators to ask questions such as ‘Is the result statistically significant?”, and this is a source of serious concern among researchers., Some tend to disregard or downplay a finding just because it was not significant while some are worried just because the outcomes were not statistically significant.

The reporting of confidence intervals usually follows hypothesis testing or significance testing. Hypotheses refer to statements concerning the situation being investigated which are usually stated as two mutually exclusive options, a null hypothesis, and an alternative hypothesis. These can be stated as two tail which is usually favored or a one tail hypotheses. The null hypothesis is a statement of no association between variables or no difference in means while the alternative hypothesis states that there’s a difference or an association beyond what is attributable to chance.1 Each time a null hypothesis is rejected, there is always an alternative hypothesis for possible acceptance. The interests of medical researchers are varied, and research questions result in statement of hypotheses.

Examples of such questions are: In the article on Burden of Erectile dysfunction among chronic heart failure patients in Ibadan: A pilot study, one may want to find out if there is a significant difference in the International index of erectile function between chronic heart failure patients and patients without cardiac failure.

The probability that the observed result is due to chance alone is what is referred to as P – value.2 The P- value only tells us whether the observed clinical difference is statistically significant or not. The confidence interval reflects the precision of the sample values in terms of their standard deviation and the sample size.3

P- value has a positive correlation with C.I, that is both are usually significant or not significant depending on the outcome of the study. Usually, the initial descriptive statistics used to summarize variables such as proportions, frequencies and means gives an idea of the results of our study, but the statistical significance is what the p value helps to ‘endorse’ and the C.I confirm it thereafter with either a 95% or 97%affirmation order as it is commonly used.

The interpretation of p – values (alpha) is based on reference to a particular cut off for the probability or the so-called level of significance which is conventionally set at 0.05 for a 95 % C.I and 0.01 for a 99% C.I. Hence p-values less than this number are significant while those above are not statistically significant. The confidence interval gives the range of values within which we are reasonably confident that the population parameter lies within.3 The parameter here could be difference in means, or proportions of two groups or it could be a measure of association between two variables such as odds ratio. The most reported interval is the 95% confidence interval at alpha value of 0.05. When the study is repeated several times, about 95% of the different possible results obtained will lie in this interval. Alternatively, we can say that we are 95% confident that the true population value of what we are estimating in our study lies within the interval. Confidence intervals makes it far easier to determine whether a finding has any substantive (e.g. clinical) importance, as opposed to statistical significance. While statistically significant tests are vulnerable to type I error, C.I is not. Confidence level is the complement of the Type 1 error (1-).