What Are Confidence Intervals?
The confidence interval is the estimated interval of the population parameter constructed from the sample statistics. In statistics, the confidence interval of a probability sample is an interval estimate of a certain population parameter of this sample. The confidence interval shows the degree to which the true value of this parameter has a certain probability of falling around the measurement result. It gives the credibility of the measured value of the measured parameter, which is the "a probability" previously required. [1]
Confidence interval is a commonly used interval estimation method. The so-called confidence interval is an interval formed by the upper and lower confidence limits of the statistics, respectively. [2]
The calculation formula for the confidence interval depends on the statistics used. The confidence interval is calculated at a predetermined significance level. The significance level is usually called (Greek alpha). As mentioned earlier, in most cases, will be set to 0.05. The confidence is (1-), or 100 × (1-)%. Therefore, if = 0.05, then the confidence is 0.95 or 95%, the latter is more commonly used [2]
Step 1: Find one
A narrower confidence interval provides more relevance than a wider confidence interval.
The confidence interval is related to factors such as the confidence level and sample size. The effect of the sample size on the confidence interval is: when the confidence level is fixed, the larger the sample size, the narrower the confidence interval. Second, with the same sample size, the higher the confidence level, the wider the confidence interval. The case analysis is as follows:
(1) Analysis of relationship between confidence interval and sample size
Sample size | Confidence interval | interval | Width and width |
100 | 50% -70% | 20 | width |
800 | 56.2% -63.2% | 7 | Narrower |
1,600 | 57.5% -63% | 5.5 | Narrower |
3,200 | 58.5% -62% | 3.5 | Narrower |
From the table above:
1. With the same confidence level, the larger the sample size, the narrower the confidence interval.
2. The narrowing of the confidence interval is not as fast as the sample size is increasing, that is to say, it is not that the sample size is doubled, and the confidence interval is also narrowed by half. (Narrower half), so when the sample size reaches a certain amount (usually 1,200), no more samples are added. Therefore: Confidence interval = point estimate ± (key value × standard deviation of point estimate). With other factors unchanged, the larger (larger) the sample size, the narrower (smaller) the confidence interval.
(2) Analysis of the relationship between confidence interval and confidence level
The United States did a survey of job satisfaction for the president. Of the 1,200 people sampled in the survey, 60% praised the President's work, with a sampling error of ± 3% and a confidence level of 95%; if the sampling error was reduced to ± 2.3%, the confidence level was reduced to 90%. The comparison of the two sets of numbers is as follows:
Sampling error | Confidence level | Confidence interval | interval | Width and width |
± 3% | 95% | 60% ± 3% = 57% -63% | 6 | width |
± 2.3% | 90% | 60% ± 2.3% = 57.7% -62.3% | 4.6 | narrow |
From the table above:
With the same sample size (both 1,200 people), the higher the confidence level (95%), the wider the confidence interval [1] .
