在与结果相同的尺度上测量的确定系数:R2的替代方案,使用标准偏差而不是解释差异的标准偏差
1Department of Psychology, Uppsala University.
Psychological methods
|July 18, 2024
概括
本研究引入了模型确定新措施,提供比传统的确定系数 (R2) 更直观的解释. 这些替代方案,包括CoD_SD,可以更清楚地了解原始尺度上的模型性能.
科学领域:
- 统计 统计 统计 统计
- 心理测量 心理测量 心理测量
- 数据科学数据科学数据科学
背景情况:
- 确定系数 (R2) 衡量模型合适性,但依赖于二次方差,限制可解释性.
- 现有的R2指标可能无法直观地表示模型对结果的相对确定性.
研究的目的:
- 在原始尺度上将R2概括为三个相对尺度.
- 引入一个新的系数,CoD_SD (R-pi),以便更易于解释的模型确定.
- 将这些新措施的特性与传统的R2进行比较.
主要方法:
- 在平方尺度上讨论了R2的属性.
- 在最初的尺度上,将R2概括为三个相对指标.
- 引入并定义了 CoD_SD (R-pi) = R2/(R2+1-R2) 的值.
主要成果:
- 提出的概括是R2的转换.
- CoD_SD提供了一种更直观的相对确定性测量方法.
- 当错误贡献是c乘以模型贡献时,CoD_SD = 1/(1+c),而R2 = 1/(1+c2).
结论:
- 新的系数,特别是CoD_SD,为模型确定提供了更易于解释的见解.
- 这些措施为描述性统计提供了R2的实际替代方案.
- CoD_SD更好地反映了模型和错误项的相对贡献.
相关概念视频
01:10Coefficient of Variation
3.8K
The coefficient of variation measures the dispersion of the data points or distribution around the mean. Using the coefficient of variation, we can compare two data series with drastically different means or different units of measurement. The coefficient of variation for a sample and a population is expressed as a percentage of the ratio of standard deviation to the mean.
The coefficient of variation is a practical statistical tool in finance. It allows investors to assess the volatility or...
The coefficient of variation is a practical statistical tool in finance. It allows investors to assess the volatility or...
3.8K
01:19Variation
6.8K
An important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more widely spread out from the mean. The most common measure of variation, or spread, is the standard deviation, which is the square root of variance.
When independent and dependent variables are plotted on a scatter plot, the slope of a line is a value that describes the rate of change between the two...
When independent and dependent variables are plotted on a scatter plot, the slope of a line is a value that describes the rate of change between the two...
6.8K
01:11Variability: Analysis
137
Measures of variability are statistical metrics that reveal the dispersion pattern within a dataset. They are pivotal in biostatistics, providing insights into the heterogeneity within health and biological data. Variability signifies the degree to which data points diverge from one another, helping researchers understand the potential range of values and associated uncertainty within the data.
The range is a simple measure of variability, indicating the difference between the highest and...
The range is a simple measure of variability, indicating the difference between the highest and...
137
01:14Standard Deviation of Calculated Results
6.0K
Standard deviation measures the spread of data around the mean value. Many large data sets follow a Gaussian distribution, also known as a normal distribution. This distribution is bell-shaped curved, with the most frequently observed value (mean or central value) in the middle. The farther away from the central value, the greater the deviation from the central value, and the lower the frequency.
A broad Gaussian distribution curve has a wider standard deviation, representing a data set with...
A broad Gaussian distribution curve has a wider standard deviation, representing a data set with...
6.0K
01:19Testing a Claim about Standard Deviation
2.4K
A complete procedure to test a claim about population standard deviation or population variance is explained here.
The hypothesis testing for the claim of population standard deviation (or variance) requires the data and samples to be random and unbiased. The population distribution also must be normal. There is no specific requirement on the sample size as the estimation is based on the chi-square distribution.
As a first step, the hypothesis (null and alternative) concerning the claim about...
The hypothesis testing for the claim of population standard deviation (or variance) requires the data and samples to be random and unbiased. The population distribution also must be normal. There is no specific requirement on the sample size as the estimation is based on the chi-square distribution.
As a first step, the hypothesis (null and alternative) concerning the claim about...
2.4K
01:10Standard Deviation
16.1K
The most commonly used measure of variation is the standard deviation. It is a numerical value measuring how far data values are from their mean. The standard deviation value is small when the data are concentrated close to the mean, exhibiting slight variation or spread. The standard deviation value is never negative, it is either positive or zero. The standard deviation is larger when the data values are more spread out from the mean, which means the data values are exhibiting more variation.
16.1K