Name: chi-square test in genetics
Uploaded: 2021-04-07T12:11:58.000Z
Duration: 2 min 46 s
Channel: JoVE

K12 Standards

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North Carolina K-12 Science Standard Course of Study

9-12

Biology

heredity-inheritance-and-variation-of-traits

Heredity- Inheritance and Variation of Traits

LS.Bio.7.1

Chi-square Analysis

Mendel hypothesized that the phenotypic ratio of a monohybrid cross between individuals with a dominant trait, like purple flowers, and a recessive trait, like white flowers, would be approximately three to one provided the alleles are independently assorted.
When there is an assumption that data will fit a certain ratio, like Mendel&#8217;s 3:1 prediction, a null hypothesis is established. The null hypothesis assumes that there is no real difference between the expected and observed values and that any apparent differences are due to chance.
Consider a monohybrid cross between twenty tall plants and twenty short plants. The F2 generation of this cross yields 33 tall plants and 7 short plants. This is the observed value.
To test the null hypothesis, a chi-square analysis can be performed. First, create a table with three columns: phenotype, observed value, and expected value. The phenotype and observed values are already known, but the expected values must be calculated.
Calculate the expected values by dividing the total number of plants observed with the total number of expected plants - that is three plus one equals four. So, forty divided by four is ten.
Ten represents the &#8220;one&#8221; of the expected three to one frequency. Hence, there are ten plants with the recessive &#8220;short&#8221; gene.
Now, multiply ten by three to obtain the &#8220;three&#8221; of the expected three to one frequency. Thus, there are thirty plants with the dominant &#8220;tall&#8221; gene.
Calculate the difference between the observed and expected value in each row and square the results.
Then, divide this value by the expected value in each row and add them all together to obtain the chi-squared value - 1.2.
The degree of freedom, which is defined as the number of values that can vary in the final calculation of a statistic, must also be calculated. Obtain the degree of freedom using this formula, where n is the number of classes, or in this case phenotypes. Here, there is one degree of freedom.
Using the chi-squared value and degree of freedom, obtain the result on the probability chart. Here, 1.2 falls between 1.07 and 1.64. The p-values for these is 0.30 and 0.20, which is greater than 0.05. Thus, the null hypothesis is not rejected, indicating that the alleles for plant height are independently assorted.

chi-square analysis

The chi-square test is a statistical hypothesis test. It is used to check whether there is a significant difference between an expected value and an observed value. In the context of genetics, it enables us to either accept or reject a hypothesis, based on how much the observed values deviate from the expected values.
The chi-square test was developed by Pearson in 1990.
The first step of performing a Chi-square analysis is to establish a null hypothesis, which assumes that there is no real difference between the expected value and the observed value. Any apparent deviations from the expected value are simply due to chance.
The null hypothesis is rejected if the probability value is less than 5%. Consider, for example, a cross in a plant species with yellow and green seeds. All the F1 generation plants had green seeds. Upon self-fertilization among the F1 generation, the expected value in F2 generation is 660 plants with green seeds and 220 plants with yellow seeds. However, the observed value in the F2 generation is 620 plants with green seeds and 260 plants with yellow seeds. Now chi-square is used to find out if the difference between observed and expected values are significant? Can we conclude that the observed inheritance follows Mendelian monohybrid cross?
 The chi-squared value is calculated using the formula given below:
<img alt="Chi-squared formula, statistical test equation, symbol representation, data analysis method" src="/files/ftp_upload/11971/11971eq1.png" style="opacity: 0.9; text-align: center; height: 50px;" data-altupdatedat="1761830439000" data-alt="Figure1" />
Where O is the observed value and E is the expected value.
The chi-square value is calculated as 9.69. To accept or reject the hypothesis, the degrees of freedom are required. The degree of freedom is the number of classes minus one. It refers to the values involved in the calculation that vary.
In the above example, two different colors of seeds are observed. So the degree of freedom will be 2 - 1 = 1. To check if the result is statistically significant, the calculated chi-square value and the degree of freedom are analyzed on the probability chart under &#945;=0.05. The value from the table is 3.841. Since the chi-squared value 9.69 is greater than 3.841, we have statistically significant evidence to reject the null hypothesis. In other words, the differences observed between the experimental and expected values is due to chance alone.

The chi-square test is a statistical hypothesis test. It is used to check whether there is a significant difference between an expected value and an ...

Education

JoVE Core

Molecular Biology

Unit 2

Mendelian Genetics

KEY TERMS AND CONCEPTS

chi-square test in genetics

The chi-square test in genetics helps compare expected and observed results. It is a statistical hypothesis test used to see whether a difference between an expected value and an observed value is significant. In genetics, it helps decide whether to accept or reject a hypothesis based on how far the observed data moves from the expected data.

The test was developed by Pearson in 1990. The first step is to set up a null hypothesis. This hypothesis says there is no real difference between the expected and observed values. Any small difference is assumed to happen by chance. The null hypothesis is rejected if the probability value is less than 5%.

A plant seed cross provides a clear example. In this case, the F1 plants all had green seeds. After self-fertilization of the F1 generation, the expected F2 result was 660 green-seeded plants and 220 yellow-seeded plants. The observed F2 result was 620 green-seeded plants and 260 yellow-seeded plants. Chi-square analysis asks whether this difference is large enough to be significant and whether the inheritance still fits a Mendelian monohybrid cross.

The chi-square value is calculated with the formula that uses O for observed value and E for expected value. In this example, the chi-square value is 9.69. Degrees of freedom are also needed. A degree of freedom is the number of classes minus one. Since two seed colors are observed, the degree of freedom is 2 - 1 = 1.

The calculated chi-square value is then compared with the probability chart at α = 0.05. For one degree of freedom, the table value is 3.841. Because 9.69 is greater than 3.841, there is statistically significant evidence to reject the null hypothesis. In this case, the difference between the experimental and expected values is due to chance alone.

Chi-Square Test in Genetics

punnett squares

Predicting Traits with Punnett Squares

Punnett squares help students predict how traits may be passed from parents to offspring. They are a simple grid used in genetics to organize possible allele combinations. An allele is a version of a gene. The square compares the alleles each parent can give. By filling in the boxes, students can see possible genotypes, which are the genetic makeup of offspring. The results can also help connect those genotypes to traits that may appear in the next generation.

monohybrid crosses

Tracking One Trait in Monohybrid Crosses

Monohybrid crosses track how one trait is passed from parents to offspring. They are used to study inheritance when only a single characteristic is followed at a time. A monohybrid cross can compare the possible outcomes for a monogenic trait, which is a trait controlled by one gene. This approach helps show how one gene can shape different inherited forms of the same characteristic. The method also connects with Mendel's work on genetics. It is a useful way to predict patterns of inheritance...

dihybrid crosses

Predicting Two-Trait Genetic Crosses

Dihybrid crosses are used to predict how two traits can be passed from parents to offspring. A dihybrid cross tracks two genes at the same time, so it helps students see how different alleles can combine in a genetic pattern. This topic is closely tied to Mendelian genetics and independent assortment. Independent assortment means that allele pairs for different traits can separate into gametes independently of one another. When students work through a dihybrid cross, they can compare the...

trihybrid crosses

Forked Line Method for Trihybrid Crosses

Forked line method for trihybrid crosses helps predict the outcome of three-trait Mendelian crosses. A trihybrid cross studies three pairs of contrasting characteristics. It combines three separate monohybrid crosses. Common examples include plant height, seed shape, and seed color. In a typical trihybrid cross, the F1 plants are heterozygous for all three traits. They can produce eight different gametes. After self-fertilization, these gametes can lead to 64 genotype combinations in the F2...

law of independent assortment

Independent Chromosome Assortment in Meiosis

Independent chromosome assortment in meiosis explains how different gene pairs can be inherited independently. This idea is one of Mendel’s laws of inheritance and is often called the law of independent assortment. The pattern depends on how homologous chromosomes line up during meiosis I. Each chromosome pair orients independently of the others, so the maternal and paternal chromosomes can separate into different gametes in many combinations. This random separation helps create genetic...

The chi-square test in genetics helps compare expected and observed results. It is a statistical hypothesis test used to see whether a difference between an expected value and an observed value is significant. In genetics, it helps decide whether to accept or reject a hypothesis based on how far the observed data moves from the expected data. The test was developed by Pearson in 1990. The first step is to set up a null hypothesis. This hypothesis says there is no real difference between the...

pedigree analysis

Tracing Traits with Pedigree Charts

Pedigree analysis uses family trees, called pedigrees, to trace how traits and diseases pass from one generation to the next. A pedigree chart helps scientists and students see inheritance patterns clearly across relatives. The chart uses standard symbols to show family members and their relationships. It can reveal whether a trait is likely passed through dominant or recessive inheritance, and it can also help identify patterns linked to sex chromosomes. By studying a pedigree, it is...

multiple allele traits

Multiple Alleles in Trait Inheritance

Multiple alleles can shape how a trait is inherited in a population. A gene may have more than two allele forms, even though each person still carries only two alleles for that gene. These allele combinations can produce traits with more than two possible outcomes. The ABO blood group system is a common example of a multiple allele trait. It shows how different alleles can interact to determine an organism’s phenotype, or observable trait. Multiple allele traits help explain why inheritance...

incomplete dominance

Incomplete Dominance in Traits and Disease

Incomplete dominance is a pattern of inheritance where two alleles both affect a trait in a heterozygous organism. In this case, one allele is not fully dominant over the other. The result is a phenotype that looks like a blend or intermediate form. Gregor Mendel’s pea plant experiments helped explain the usual dominant and recessive pattern. He showed that each gene in a diploid cell has two alleles, one inherited from each parent. In his model, a dominant allele shows its effect with one or...

lethal alleles

When Genes Cause Embryonic Death

Lethal alleles can change inheritance patterns by causing death before birth. In mice, Lucien Cuénot studied the agouti gene, which helps control coat color through an agouti-signaling protein that affects melanin distribution in mammals. The wild-type allele produces a gray-brown coat, while the mutant allele produces a yellow coat. Cuénot also found that the yellow allele was linked to yellow mouse obesity syndrome. This syndrome is associated with early-onset obesity and tumors. When he...

polygenic traits

Traits Shaped by Many Genes

Polygenic traits are characteristics shaped by many genes acting together. This pattern is different from a single-gene trait, where one gene has a larger effect on the outcome. In polygenic inheritance, each gene adds a small contribution to the final trait. Height is a common example of a polygenic trait. Many genes influence human height, so the result can vary across a wide range. These small genetic effects combine to produce differences that are easy to see in a population. Polygenic...

background and environment affect phenotype

background-and-environment-affect-phenotype

How Genes and Environment Shape Traits

Genes and the environment work together to shape phenotype, or the visible traits of an organism. A phenotype can change because of genetic background, environmental conditions, or both. Factors such as temperature, oxygen availability, and mutagens can all influence how a trait appears. Horses show how one gene can affect coat color and how a modifier gene can change that result. The Extension gene controls pigment production in the coat. The wild-type genotype EE produces black pigment,...

x and y chromosomes

Sex Chromosomes in Human Inheritance

Sex chromosomes help determine biological sex in mammals, including humans. Humans have two sex chromosomes, X and Y. Each diploid cell has 22 pairs of autosomes and one pair of sex chromosomes. A female usually has two X chromosomes, while a male usually has one X chromosome and one Y chromosome. Egg and sperm cells carry only half the usual number of chromosomes. They contain 22 autosomes and one sex chromosome. Every egg has an X chromosome. Sperm cells can carry either an X or a Y...

the y chromosome determines maleness

Y Chromosome Structure and Male Traits

The Y chromosome is a sex chromosome that helps guide male development in humans and other vertebrates and mammals. Human males usually have one X chromosome and one Y chromosome, along with 22 pairs of autosomes. In these organisms, the presence or absence of the Y chromosome influences whether male traits develop. The Y chromosome evolved from an autosome about 300 million years ago, when two sex chromosomes began to diverge. Since then, it has lost most of its genes and become much smaller.

the ratio of x chromosome to autosomes

Drosophila Sex Determination by X:A Balance

In Drosophila, sex is determined by the balance between X chromosomes and autosomes, not by the X and Y chromosomes alone. The Y chromosome is active in these flies, but it does not set sex. Instead, it carries genes needed for sperm production in adult males. A normal male Drosophila has one X chromosome and two sets of autosomes. A normal female has two X chromosomes and two sets of autosomes. When this X:A ratio changes, flies can develop different sexual phenotypes, including metamales,...

x-linked traits

X-Linked Inheritance in Families

X-linked inheritance in families explains how traits linked to the X chromosome pass from parents to children. These traits are often tracked through family trees because the pattern can differ between males and females. A male has one X chromosome and one Y chromosome. A female has two X chromosomes. Because of this difference, a trait on the X chromosome can show up in a different way depending on the sex of the child. Family examples often include traits such as color blindness. Studying...

sex linked disorders

Sex-Linked Disorders and Inheritance Patterns

Sex-linked disorders are genetic conditions that follow inheritance patterns tied to the sex chromosomes. These disorders help explain how certain traits can appear more often in one sex than the other. The transcript focuses on examples of sex-linked disorders, including Y-linked infertility, Fragile X syndrome, and Duchenne muscular dystrophy. Y-linked infertility is passed through the Y chromosome, while Fragile X syndrome and Duchenne muscular dystrophy are associated with sex-linked...

dosage compensation

X-Chromosome Balance in Animals

X-chromosome balance in animals helps equalize gene expression between males and females. Sex can be determined by the number and type of sex chromosomes. In humans, females have two X chromosomes and males have one X and one Y chromosome. In C. elegans, one X chromosome is male, while two X chromosomes make a hermaphrodite. The X chromosome carries more than sex-related genes. It also includes genes involved in body functions such as brain development and the immune system. Because males and...

x-inactivation

X-Inactivation and Barr Bodies

X-inactivation is a process that reduces gene activity on one X chromosome. It helps balance gene expression in cells that have more than one X chromosome. A key result of this process is the formation of a Barr body, which is the inactive X chromosome seen in the nucleus. This topic also includes Xist, a gene linked to X-inactivation. Xist produces RNA that coats the X chromosome and helps turn it off. Together, Xist and the Barr body show how cells control X-linked genes during development...

blood types

Blood Types and Transfusion Matching

Human blood types help determine safe blood transfusion matching. Blood is classified by antigens on the surface of red blood cells and antibodies in the plasma. Correct blood typing matters because an unsafe match can affect transfusion success. The International Society of Blood Transfusion has identified 38 human blood types, and ABO, Rh, and MNS are among the most common. The ABO blood group depends on antigens made by genes on chromosome 9. Red blood cells carry a base glycoprotein called...

blood transfusion and agglutination

Matching Blood Types for Safe Transfusion

Blood transfusion is a medical treatment used to restore blood volume after major blood loss from an accident or a medical procedure. It works by taking blood from a suitable donor and giving it to a recipient. Safe transfusion depends on matching blood types and checking for immune compatibility. The history of blood transfusion began in the 17th century, when early experiments were done in animals. In 1818, James Blundell, a British doctor, performed the first successful human blood...

key terms and concepts

Learn how the chi-square test compares expected and observed genetic results, uses degrees of freedom, and helps test a Mendelian cross.

Chi-Square Test in Genetics | JoVE K12

molecular biology

JoVE Core Molecular Biology showcases the molecular processes of the cell through clear and concise animated video lessons. Additionally, in scientist-in-action videos, these concepts' application is demonstrated through real experiments in modern laboratories.

Louisiana Student Standards for Science

High School

Life Sciences

Heredity: Inheritance And Variation Of Traits

HS-LS3-1

ohios-learning-standards-and-model-curriculum

Ohio’s Learning Standards and Model Curriculum

Heredity

Genetic mechanisms and inheritance

Alabama Course of Study Science

Heredity: Inheritance and Variation of Traits

9-12.B.3.11

Next Generation Science Standards

Life Science

Florida Department of Education

SC.912.L.16

SC.912.L.16.2

Texas Essential Knowledge and Skills

BIO.8

BIO.8.B

new-york-state-science-learning-standards

New York State Science Learning Standards

Inheritance and Variation of Traits

HS-LS3-1.

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Multiple Allele Traits

Incomplete Dominance

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Lethal Alleles

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Polygenic Traits

Background and Environment Affect Phenotype

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Use mathematics and computational thinking to predict the variation and distribution of expressed traits based on: Mendelian inheritance, co-dominance, incomplete dominance, multiple alleles, and sex-linked inheritance.

Overview

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Probability Laws

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Analyze and interpret data to explain how polygenic traits result in a wide range of phenotypes.

LS.Bio.7.2

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Chi-Square Test in Genetics

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