Properties of Confidence Intervals

CHAPTER 13 Properties of Confidence Intervals




Statistical inference … provides a statement, expressed in the language of probability, of how much confidence we can place in our conclusions.


—David S. Moore and George P. McCabe1


We know that we use sample statistics to estimate the unknown population parameter, such as the population mean, μ. This parameter is very real and does not vary, but we cannot measure it—we can only estimate it. How accurate is our estimate? We can answer that question by using confidence intervals, a concept that was introduced by the distinguished Polish statistician Jerzy Neyman in 1937. Confidence intervals are like umbrellas that attempt to encompass the population parameter we are estimating.


When we are under a big umbrella, we feel protected and safe. That is the same feeling we get with a big confidence interval that contains a wide range of values. It is very likely to contain the population parameter we are trying to estimate. Of course, a wide range of values has limited usefulness for pinning down the parameter. We are not sure where that parameter lies within the interval, but we are confident that the interval is very likely to contain it. That is the trade-off for feeling secure in our estimate. If we want 99% confidence, the interval will be larger than if we accept 90% confidence. As we have seen, it is quite common to accept a 95% confidence interval. That means if the study were repeatedly done with the same-sized sample, 95% of the time our confidence interval would include the true population parameter.


For instance, if we are measuring the birth weights of infants born to mothers who smoke, we may take a random sample of 25 infants, weigh them at birth, and average the weights. We are trying to estimate the true population mean weight of all infants born to smoking mothers. We assume the weights are normally distributed. Say we obtained a sample mean of 6 lbs, with a standard deviation of 1 lb (fictitious data). Using the Central Limit Theorem, we calculate a standard error of the sampling distribution to be 0.2 lb. To calculate the confidence interval, the formula is:



Estimate ± margin of error.


The estimate refers to the sample statistic that is generated as a result of the data analysis. In this case, it is the sample mean. The margin of error is dependent on three things:



1. The standard deviation of the sample data.


2. The sample size.


3. The confidence we desire, which is usually 95%.


The exact formula will vary depending on the type of data we have, but these three values contribute to the range of values that is obtained regardless of the specific formula. Those who wish to view these formulas are referred to a standard statistics textbook.


The calculated confidence interval for the above data came out to be:



image

Related posts:

  1. Types of Statistical Tests
  2. Ethics in Medical Research
  3. Measures of Disease
  4. Mathematical Principles

Stay updated, free articles. Join our Telegram channel
Tags:
Jun 18, 2016 | Posted by in BIOCHEMISTRY | Comments Off on Properties of Confidence Intervals

Full access? Get Clinical Tree
Get Clinical Tree app for offline access