A Confidence Interval (CI) is a range of values, calculated from sample observations, that is likely to contain the true value of an unknown population parameter. In statistics, it provides a way to quantify and express the uncertainty associated with a given estimate.
When creating a confidence interval, the researcher takes into account sampling error and the size of the sample relative to the population. As an example, if you have surveyed 100 people out of 10 million in your target market, then there is likely to be more uncertainty about the results compared with surveying 1 million out of 10 million in your target market.
The larger the sample size relative to the population size, the lower your confidence interval will be because you are reducing sampling error and increasing precision.
Uses of Confidence Interval
The confidence level typically used for most research studies is 95%, meaning that there is a 95% chance that it contains the true value from within that population. This means that 5% (1 in 20) of similar samples would give different results due to random chance alone when drawn from this same population.
To calculate this interval you need two variables: margin of error (MOE) and confidence level (CL). MOE measures how confident we are about our estimate while CL determines how far away from our estimated value we go when constructing our CI. For instance, if we wanted to measure job satisfaction among bank employees with a 95% CL and desired a ±5% MOE then our CI would range between 90%-100%.
That means we can confidently say that 90%-100% of bank employees are satisfied with their current job situation given our data set and sampling techniques. However, if our sample size was particularly small or had other limitations such as those related to collection methodology—the result may not truly reflect overall job satisfaction within banks across all markets or other variables such as income level or location etc., resulting in an inaccurate CI range being reported.
Advantages and Disadvantages
One major advantage of using a CI is that it provides a more accurate estimation of the population parameter than a point estimate. A point estimate, such as a sample mean, provides only a single estimate of the population parameter and does not account for sampling error.
A CI, on the other hand, shows the range of values that are likely to contain the population parameter, providing a more accurate estimation of its true value.
Another advantage of using a CI is that it allows for the interpretation of results in the context of statistical significance.
By examining whether or not a CI contains a hypothesized population parameter, researchers can infer whether or not their results are statistically significant. However, there are also some disadvantages to using a CI.
One is that it can be difficult to interpret for non-statisticians. For example, a 95% CI does not mean that there is a 95% probability of the true parameter lying within the interval. Another disadvantage is that CI’s can be impacted by sample size.
Smaller sample sizes can lead to wider intervals, which can make it difficult to draw conclusions from the data. Additionally, CI’s assume that the sample is random and unbiased, which may not always be the case in real-world applications.
In summary, confidence intervals are an important statistical tool that provides a range of values to estimate the true population parameter. While they offer several advantages, such as increased accuracy and the ability to interpret results in the context of statistical significance, they also have disadvantages, including difficulty of interpretation and sensitivity to sample size.