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Chi-Square Test for Goodness of Fit in a Plant Breeding Example

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In plant breeding and genetics research, plant breeders establish a hypothesis to explain how they think a particular trait is inherited, such as if it is due to one gene with complete dominance, an interaction of more than one gene, or quantitative inheritance, with many genes contributing, etc. Next the breeder sets up crosses and observes the resulting progeny to test that inheritance hypothesis. However, when the data is collected, oftentimes the plant breeder discovers the number of plants observed in each class is not exactly what was expected from the hypothesis. The question then is how do plant breeders determine if the data is close enough to what they expected to determine the hypothesis is supported or not? Following a tomato disease resistance example in this lesson, you will learn a simple statistical test that breeders can use to conclude if the experimental data supports their hypothesis of single gene, completely dominant inheritance.

This lesson is written for undergraduate and graduate students studying plant breeding, as well as agriculture professionals unfamiliar with the use of the chi-square analysis.

Overview and Objectives

Deana M. Namuth-Covert, Dept of Agronomy and Horticulture, Univ of Nebraska
Heather L. Merk, Dept of Horticulture and Crop Sciences, The Ohio State University,
OARDC
Courtney Haines, Dept of Statistics, Univ of Nebraska
 
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In plant breeding and genetics research, plant breeders establish a hypothesis to explain how they think a particular trait is inherited, such as if it is due to one gene with complete dominance, an interaction of more than one gene, or quantitative inheritance, with many genes contributing, etc. Next the breeder sets up some crosses and observes the resulting progeny to test that inheritance hypothesis. However, when the data is collected, oftentimes the breeder discovers the number of plants observed in each class is not exactly what was expected from the hypothesis. The question then is how do plant breeders determine if the data supports their hypothesis or not? Following a tomato disease resistance example in this lesson, you will learn a simple statistical test that breeders can use to conclude if the experimental data supports their hypothesis.

This lesson is written for undergraduate and graduate students studying plant breeding, as well as agriculture professionals unfamiliar with the use of the chi-square analysis.

Objectives:
After completing this lesson module you should be able to…

1.      Calculate expected phenotypic and genotypic ratios and the number of plants expected in each class for a given plant breeding scheme.  
2.      Calculate chi-square values for plant genetics data sets from both phenotypic and genotypic observations.
3.      Calculate degrees of freedom.
4.      Accurately interpret results from a chi-square test.
5.      Identify appropriate uses and limitations of the chi-square test in plant breeding and genetics research.

Key terms:
degrees of freedom
p-value
significant deviations
observed
expected
phenotype
quantitative trait
qualitative trait
chi-square
goodness of fit
 

Acknowledgements

Development of this educational material was supported in part by the National Science Foundation (NSF), Division of Undergraduate Education, National SMETE Digital Library Program, Award #0938034, administered by the University of Nebraska and the National Institute of Food and Agriculture (NIFA) Solanaceae Coordinated Project, agreement 2009-85606-05673, administered by Michigan State University.  Any opinions, findings, conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of NSF or NIFA.

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