Statistics is defined as the science of collecting, organizing, presenting, analyzing, and interpreting numerical data. It involves the systematic collection of data that is affected by a variety of factors, and which is expressed numerically according to established standards of accuracy. The purpose of statistics is to provide meaningful insights by placing data in relation to each other, often to inform decision-making or to understand underlying patterns and relationships.

Degrees of Statistics

In biometrical genetics, statistics can be categorized into three degrees, each with specific applications and methods. These degrees represent different levels of complexity in statistical analysis:

1. First Degree Statistics

    First degree statistics primarily involve measures of central tendency and descriptive statistics, such as the mean. This level focuses on summarizing and describing data using basic statistical metrics.

Applications:

  • Generation Means: Analyzing the average performance of different generations of organisms.
  • Heterosis (Hybrid Vigour): Evaluating the superior performance of hybrids compared to their parents.
  • Inbreeding Depression: Measuring the decrease in performance due to inbreeding.
  • Combining Ability Effects: Assessing how well different genetic lines combine to produce desired traits.
  • Metroglyph Analysis: Using graphical methods to analyze genetic data.
  • Stability Analysis: Evaluating the consistency of traits across different environments.

Example: In a study of crop yield, the mean yield of different varieties can be calculated to compare their average performance.

2. Second Degree Statistics

    Second degree statistics involve measures of variability and relationships between variables, such as variances and covariances. This level focuses on the precision and reliability of data estimates and their relationships.

Applications:

  • Estimation of Variances and Covariances: Understanding the spread and relationship between variables.
  • Correlations: Measuring the strength and direction of the relationship between two variables.
  • Path Coefficients: Analyzing direct and indirect effects of variables on a particular outcome.
  • Discriminant Function Analysis: Classifying data into categories based on predictors.
  • Heritability: Estimating the proportion of phenotypic variance attributable to genetic variance.
  • Genetic Advance: Predicting the improvement in traits through selection.
  • Components of Variance: Decomposing variance into genetic and environmental components in different breeding designs.

Example: In a genetic study, calculating the variance of a trait across different populations helps to understand the extent of genetic diversity and environmental influence.

3. Third Degree Statistics

    Third degree statistics involve more complex measures of data distribution, such as skewness and kurtosis. These metrics are used to understand the shape of the data distribution beyond basic measures of central tendency and variability.

Applications:

  • Kurtosis: Assessing the "tailedness" of the data distribution, indicating how heavy or light the tails are.
  • Skewness: Measuring the asymmetry of the data distribution.
  • Fitting Frequency Curves: Applying advanced techniques to model the distribution of traits.
  • High Order Statistics: Analyzing data from complex genetic crosses to study interactions and distribution shapes.

Example: In analyzing the distribution of a trait in F2 progenies, skewness and kurtosis can reveal how the trait's distribution deviates from a normal distribution, which can provide insights into the underlying genetic and environmental influences.

Conclusion

The different degrees of statistics provide a framework for analyzing and interpreting data at varying levels of complexity. In biometrical genetics, first degree statistics are essential for basic descriptive analysis, second degree statistics help in understanding relationships and variability, and third degree statistics offer deeper insights into the distribution and interactions within the data. Each degree plays a critical role in advancing our understanding of genetic and environmental factors influencing traits.

References:

  • Mather, K., & Jinks, J.L. (1971). Biometrical Genetics: The Study of Continuous Variation. Chapman and Hall.
  • Altschul, S.F., et al. (1990). Basic local alignment search tool. Journal of Molecular Biology, 215(3), 403-410. DOI: 10.1016/S0022-2836(05)80360-2
  • Dobin, A., et al. (2013). STAR: Ultrafast universal RNA-seq aligner. Bioinformatics, 29(1), 15-21. DOI: 10.1093/bioinformatics/bts635