It is well known that c_4 is the bias correction factor for the sample standard deviation and is used to construct control charts. However, why it's called c_4. In addition, who introduced c_4 first?
The term "c4" in the context of control charts and bias correction for the sample standard deviation refers to a constant multiplier that is used to adjust the standard deviation estimate for small sample sizes. The notation "c4" is part of a broader set of statistical constants denoted by various letters and subscripts, each serving a specific purpose in statistical methods.
The specific value of c4 depends on the sample size and is used to correct the bias in the sample standard deviation. The formula for this correction is often expressed as:
��=�4⋅�Sc=c4⋅S
where ��Sc is the corrected standard deviation, �S is the sample standard deviation, and �4c4 is the bias correction factor.
The term "c4" and its associated constants are deeply rooted in statistical literature, and their use has evolved over time. Unfortunately, the historical attribution of the introduction of c4 is not always straightforward, as these constants are often derived from mathematical properties of statistical distributions.
One of the early mentions of these constants can be traced back to the work of W. Allen Wallis. He introduced the concept of �2B2 and �4B4 constants in the mid-1940s. The specific constant related to the correction of the standard deviation (c4) may have been introduced by various statisticians in different contexts.
It's important to note that the values of these constants are often tabulated in statistical reference books or can be derived through statistical methods. For example, c4 for sample sizes �n less than or equal to 10 is commonly found in statistical tables.
To gain insights into the historical development and attribution of c4, you may want to consult classic statistical references and papers from the mid-20th century, especially those focused on the theory of estimation and properties of statistical estimators. Additionally, textbooks on statistical quality control and control charting may provide historical context regarding the introduction of bias correction factors like c4.
- Badges
- Science topic
- Similar topics
- Mathematics
- Statistics
- Regression