The X-axis values ranging from -1.96 to +1.96 is thus the 95% confidence interval in this example. In a normal distribution with mean 0 and standard deviation 1 (aka standard normal distribution), 95% of the values will be symmetrically distributed around the mean like what is shown in the figure below. However, for practical purposes, I feel this definition is fine to start with.
Note that this definition is statistically not correct and purists will find it hard to accept. But what exactly is this confidence interval? For now let’s assume that the a 95% confidence interval means that we are 95% ‘confident’ that the true proportion lies somewhere in that interval. Okay, now that we know that point estimates of proportion from sample data can be assumed to follow a normal distribution because of the normal approximation phenomenon of binomial distribution, we can construct a confidence interval using the point estimate. Here, I just wanted to illustrate a rather extreme case when p is on the extreme (0.1 here) because in reality these extreme values are more common than values near 0.5 in epidemiological studies When p is near 0.5, the distribution can be assumed to be normal even with smaller sample sizes. You can see that the distribution becomes more and more normal with larger sample sizes. This process of inferential statistics of estimating true proportions from sample data is illustrated in the figure below.īinomial distributions for different sample sizes (n) when probability of success (p) is 0.1. Now, how do we know that this proportion that we got from sample can be related to the true proportion, the proportion in population? This is where confidence intervals comes into play. But what we can do is to take a rather practically feasible smaller subset of the population randomly and compute the proportion of the event of interest in the sample. To study proportion of any event in any population, it is not practical to take data from the whole population. In my earlier article about binomial distribution, I tried to illustrate how binomial distributions are inherently related to the prevalence of a disease by citing a hypothetical COVID-19 seroprevalence study. Estimation of the disease burden by estimating the true incidence and prevalence of a disease is probably the most commonly executed epidemiological studies.
Incidences (number of new cases of disease in a specific period of time in the population), prevalence (proportion of people having the disease during a specific period of time) are all proportions. From the context of clinical/epidemiological research, proportions are almost always encountered in any study.
In an earlier article where I detailed binomial distribution, I spoke about how binomial distribution, the distribution of the number of successes in a fixed number of independent trials, is inherently related to proportions. I also recommend reading this review article on confidence interval estimation¹ Proportions and confidence intervals Those who are more than familiar with the concept of confidence can skip the initial part and directly jump to the list of confidence intervals starting with the Wald Interval. The very beginners might find it hard to follow-through this article. Note: This article is intended for those who have at least a fair sense of idea about the concepts confidence intervals and sample population inferential statistics. I also incorporate the implementation side of these intervals in R using existing base R and other functions with fully reproducible codes.
Here, I detail about confidence intervals for proportions and five different statistical methodologies for deriving confidence intervals for proportions that you, especially if you are in healthcare data science field, should know about. Nowadays confidence intervals are receiving more attention (and rightly so!) which used to get overlooked especially because of the obsession with p-values. Confidence intervals are crucial metrics for statistical inference.
0 kommentar(er)
