16.2.5
Chi-Squared Test
Overview of Chi-Squared
Overview of Chi-Squared
The chi-squared test is used in genetics to compare the goodness of fit of observed data with expected data. It tests if the difference between observed and expected values is due to chance.


Inheritance
Inheritance
- Genetic diagrams are used to predict the expected phenotypic ratio of offspring.
- Predictions are rarely 100% accurate because of the random nature of gametes fusing during fertilisation.
- Chi-squared is used to compare observed phenotypic ratios with expected ratios.
- Chi-squared tells us if the difference between the observed and expected ratios are due to chance.


Requirements
Requirements
- The Chi-squared test is used when:
- Variation is discrete not continuous. This means the data are in categories (e.g. Aa and aa).
- Data show absolute numbers (whole numbers), normally frequencies.


Null hypothesis
Null hypothesis
- Before using chi-squared, a null hypothesis is stated.
- The null hypothesis is:
- 'There is no significant difference between observed and expected data, the difference is due to chance'.
- The chi-squared test is used to reject or accept the null hypothesis.


Equation
Equation
- The equation for chi-squared is:
- O = observed values.
- E = expected values.
Chi-Squared Test
Chi-Squared Test
The steps involved in applying the chi-squared test are:


Equation
Equation
- The equation for chi-squared is:
- O = observed values.
- E = expected values.


1) Calculate expected values
1) Calculate expected values
- To use the chi-squared equation, the expected values need to be calculated.
- Expected values are predicted using genetic diagrams.
- The expected values are the phenotypic ratios given by the genetic diagram.
- Compare the expected values with observed values and use these numbers in the equation.


2) Calculate chi-squared
2) Calculate chi-squared
- Using the chi-squared equation, calculate the chi-squared value.


3) Find the critical value
3) Find the critical value
- Calculate the degrees of freedom.
- Degrees of freedom = the number of categories (e.g. phenotypes) − 1.
- Find the critical value that corresponds to the degrees of freedom in a probability distribution table at 0.05 significance level.


4) Accept the null hypothesis?
4) Accept the null hypothesis?
- Compare the chi-squared value to the critical value.
- If the chi-squared value is lower than the critical value - accept the null hypothesis.
- The difference between observed and expected data is due to chance.


Reject the null hypothesis?
Reject the null hypothesis?
- If the chi-squared value is greater than the critical value - reject the null hypothesis.
- The difference between observed and expected data is NOT due to chance.
- This means we would get this chi-squared value in less than 5% of cases, which is very unlikely.
1Cell Structure
1.1Cell Structure
1.1.1Studying Cells - Microscopes
1.1.2Introduction to Eukaryotic & Prokaryotic Cells
1.1.3Ultrastructure of Eukaryotic Cells
1.1.4Ultrastructure of Eukaryotic Cells 2
1.1.5Ultrastructure of Eukaryotic Cells 3
1.1.6Prokaryotic Cells
1.1.7Viruses
1.1.8End of Topic Test - Cell Structure
1.1.9Exam-Style Question - Microscopes
1.1.10A-A* (AO2/3) - Cell Structure
2Biological Molecules
2.1Testing for Biological Modules
2.2Carbohydrates & Lipids
2.3Proteins
3Enzymes
4Cell Membranes & Transport
4.1Biological Membranes
5The Mitotic Cell Cycle
6Nucleic Acids & Protein Synthesis
6.1Nucleic Acids
7Transport in Plants
8Transport in Mammals
8.1Circulatory System
8.2Transport of Oxygen & Carbon Dioxide
9Gas Exchange
9.1Gas Exchange System
10Infectious Diseases
10.1Infectious Diseases
10.2Antibiotics
11Immunity
12Energy & Respiration (A2 Only)
13Photosynthesis (A2 Only)
14Homeostasis (A2 Only)
14.1Homeostasis
14.2The Kidney
14.3Cell Signalling
14.4Blood Glucose Concentration
14.5Homeostasis in Plants
15Control & Coordination (A2 Only)
15.1Control & Coordination in Mammals
15.1.1Neurones
15.1.2Receptors
15.1.3Taste
15.1.4Reflexes
15.1.5Action Potentials
15.1.6Saltatory Conduction
15.1.7Synapses
15.1.8Cholinergic Synnapses
15.1.9Neuromuscular Junction
15.1.10Skeletal Muscle
15.1.11Sliding Filament Theory Contraction
15.1.12Sliding Filament Theory Contraction 2
15.1.13Menstruation
15.1.14Contraceptive Pill
15.2Control & Co-Ordination in Plants
16Inherited Change (A2 Only)
16.1Passage of Information to Offspring
16.2Genes & Phenotype
17Selection & Evolution (A2 Only)
17.2Natural & Artificial Selection
18Classification & Conservation (A2 Only)
18.1Biodiversity
18.2Classification
19Genetic Technology (A2 Only)
19.1Manipulating Genomes
19.2Genetic Technology Applied to Medicine
19.3Genetically Modified Organisms in Agriculture
Jump to other topics
1Cell Structure
1.1Cell Structure
1.1.1Studying Cells - Microscopes
1.1.2Introduction to Eukaryotic & Prokaryotic Cells
1.1.3Ultrastructure of Eukaryotic Cells
1.1.4Ultrastructure of Eukaryotic Cells 2
1.1.5Ultrastructure of Eukaryotic Cells 3
1.1.6Prokaryotic Cells
1.1.7Viruses
1.1.8End of Topic Test - Cell Structure
1.1.9Exam-Style Question - Microscopes
1.1.10A-A* (AO2/3) - Cell Structure
2Biological Molecules
2.1Testing for Biological Modules
2.2Carbohydrates & Lipids
2.3Proteins
3Enzymes
4Cell Membranes & Transport
4.1Biological Membranes
5The Mitotic Cell Cycle
6Nucleic Acids & Protein Synthesis
6.1Nucleic Acids
7Transport in Plants
8Transport in Mammals
8.1Circulatory System
8.2Transport of Oxygen & Carbon Dioxide
9Gas Exchange
9.1Gas Exchange System
10Infectious Diseases
10.1Infectious Diseases
10.2Antibiotics
11Immunity
12Energy & Respiration (A2 Only)
13Photosynthesis (A2 Only)
14Homeostasis (A2 Only)
14.1Homeostasis
14.2The Kidney
14.3Cell Signalling
14.4Blood Glucose Concentration
14.5Homeostasis in Plants
15Control & Coordination (A2 Only)
15.1Control & Coordination in Mammals
15.1.1Neurones
15.1.2Receptors
15.1.3Taste
15.1.4Reflexes
15.1.5Action Potentials
15.1.6Saltatory Conduction
15.1.7Synapses
15.1.8Cholinergic Synnapses
15.1.9Neuromuscular Junction
15.1.10Skeletal Muscle
15.1.11Sliding Filament Theory Contraction
15.1.12Sliding Filament Theory Contraction 2
15.1.13Menstruation
15.1.14Contraceptive Pill
15.2Control & Co-Ordination in Plants
16Inherited Change (A2 Only)
16.1Passage of Information to Offspring
16.2Genes & Phenotype
17Selection & Evolution (A2 Only)
17.2Natural & Artificial Selection
18Classification & Conservation (A2 Only)
18.1Biodiversity
18.2Classification
19Genetic Technology (A2 Only)
19.1Manipulating Genomes
19.2Genetic Technology Applied to Medicine
19.3Genetically Modified Organisms in Agriculture
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