Confidence interval (IC) is a type of interval estimate of a population constant. lt is used to ascertain the reliability of a statistical estimate. Rather than estimating a constant using a single value, a range is determined that includes the constant. The interval between the constants is measured by the confidence coefficient.
The confidence coefficient is normally denoted as a percentage of the confidence level, for instance, a 90 percent confidence interval. It is examined that the higher the confidence level, the larger the confidence coefficient and thus the more reliable the parameters are. The extremes of the confidence interval of the variables are known as confidence limits.
Interval estimates can be distinguished from point estimates. While a point estimate represents a single value of the sample population constant such as the mean of a given quantity, an interval estimate gives two extreme limits where the constant is likely to be found.
Confidence intervals can be used in the significance testing of variables. For example in the case given, taking a point estimate of distance from the is 200, with a confidence interval (200, 300) at the confidence coefficient, 90 percent, then any housing units number outside the interval (200, 300) will be said to be significantly from, Distance From City, at a significance level of 10% (100% – 90%), considering the spread assumptions made in ascertaining the confidence interval.
Significance testing will involve two hypotheses, that is, a null and alternative hypothesis. If the value of the distance from the city is less than or greater than the housing units number, the null hypothesis will be rejected since the value of the constant equaled the distance from the city.
Since confidence intervals do not deal with multiple quantities, in cases with multiple quantities, confidence regions can be estimated to generalize the confidence interval of the population. Confidence regions show the estimation errors and also highlight the value of the reliable and estimates estimate.
Confidence intervals can be reported in tables, charts, or graphs, along with point estimates of the conceding constants, to illustrate the reliability of the estimates.
Alongside the confidence intervals method, there are other methods of interval estimation such as credible intervals and prediction intervals. Confidence intervals are a probability representation and adhere to normal probability rules and assumptions. When calculating confidence intervals, the principle of independence of variables must apply. If confidence intervals are calculated to do statistical tests, the several statistics are calculated separately holding that they are independent. Also, the data given should be normally distributed.
The general way to come up with confidence intervals is presupposing the practical applicability of a reliable significance test. That is, to define a 100% – 100α% confidence interval consisting of all values, θ0, for that a hypothesis test θ=θ0 is accepted at a significance level of 100α%.
A reliable confidence interval should be valid, optimal, and invariant.
References
Smithson, Michael. Confidence intervals (Quantitative Applications in the Social Sciences Series). Belmont, CA: SAGE Publications. 2003. Print.