7.1.5

Chi-Squared Test

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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:
    • χ=Σ  (O−E)2E\chi = \Sigma \; \frac{(O - E)^2}{E}
      • O = observed values.
      • E = expected values.

Chi-Squared Test

The steps involved in applying the chi-squared test are:

Equation

Equation

  • The equation for chi-squared is:
  • χ=Σ  (O−E)2E\chi = \Sigma \; \frac{(O - E)^2}{E}
    • 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.
Jump to other topics
1

Biological Molecules

1.1

Monomers & Polymers

1.1.1Monomers & Polymers1.1.2Condensation & Hydrolysis Reactions
1.2

Carbohydrates

1.2.1Structure of Carbohydrates1.2.2Types of Polysaccharides1.2.3End of Topic Test - Monomers, Polymers and Carbs1.2.4Exam-Style Question - Carbohydrates1.2.5A-A* (AO3/4) - Carbohydrates
1.3

Lipids

1.3.1Triglycerides & Phospholipids1.3.2Types of Fatty Acids1.3.3Testing for Lipids1.3.4Exam-Style Question - Fats1.3.5A-A* (AO3/4) - Lipids
1.4

Proteins

1.4.1The Peptide Chain1.4.2Investigating Proteins1.4.3Primary & Secondary Protein Structure1.4.4Tertiary & Quaternary Protein Structure1.4.5Enzymes1.4.6Factors Affecting Enzyme Activity1.4.7Enzyme-Controlled Reactions1.4.8End of Topic Test - Lipids & Proteins1.4.9A-A* (AO3/4) - Enzymes1.4.10A-A* (AO3/4) - Proteins1.4.11Diagnostic Misconceptions - Enzyme Inhibitors
1.5

Nucleic Acids

1.5.1DNA & RNA1.5.2Nucleotides1.5.3Polynucleotides1.5.4DNA Replication1.5.5Exam-Style Question - Nucleic Acids1.5.6A-A* (AO3/4) - Nucleic Acids
1.6

ATP

1.6.1Structure of ATP1.6.2Hydrolysis of ATP1.6.3Resynthesis of ATP1.6.4End of Topic Test - Nucleic Acids & ATP
1.7

Water

1.7.1Importance of Water1.7.2Structure of Water1.7.3Properties of Water1.7.4A-A* (AO3/4) - Water
1.8

Inorganic Ions

1.8.1Inorganic Ions1.8.2End of Topic Test - Water & Inorganic Ions
2

Cells

2.1

Cell Structure

2.1.1Introduction to Cells2.1.2Eukaryotic Cells & Organelles2.1.3Eukaryotic Cells & Organelles 22.1.4Prokaryotes2.1.5A-A* (AO3/4) - Organelles2.1.6Methods of Studying Cells2.1.7Microscopes2.1.8End of Topic Test - Cell Structure2.1.9Exam-Style Question - Cells2.1.10A-A* (AO3/4) - Cells
2.2

Mitosis & Cancer

2.2.1Mitosis2.2.2Stages of Mitosis2.2.3Investigating Mitosis2.2.4Cancer2.2.5A-A* (AO3/4) - The Cell Cycle
2.3

Transport Across Cell Membrane

2.3.1Cell Membrane Structure2.3.2A-A* (AO3/4) - Membrane Structure2.3.3Diffusion2.3.4Osmosis2.3.5Active Transport2.3.6End of Topic Test - Mitosis, Cancer & Transport2.3.7Exam-Style Question - Membranes2.3.8A-A* (AO3/4) - Membranes & Transport2.3.9A-A*- Mitosis, Cancer & Transport
2.4

Cell Recognition & the Immune System

2.4.1Immune System2.4.2Phagocytosis2.4.3T Lymphocytes2.4.4B Lymphocytes2.4.5Antibodies2.4.6Primary & Secondary Response2.4.7Vaccines2.4.8HIV2.4.9Ethical Issues2.4.10End of Topic Test - Immune System2.4.11Exam-Style Question - Immune System2.4.12A-A* (AO3/4) - Immune System2.4.13Diagnostic Misconceptions - Humoral vs Cellular
3

Substance Exchange

3.1

Surface Area to Volume Ratio

3.1.1Size & Surface Area3.1.2A-A* (AO3/4) - Cell Size
3.2

Gas Exchange

3.2.1Single-Celled Organisms3.2.2Multicellular Organisms3.2.3Control of Water Loss3.2.4Human Gas Exchange3.2.5Ventilation3.2.6Dissection3.2.7Measuring Gas Exchange3.2.8Lung Disease3.2.9Lung Disease Data3.2.10End of Topic Test - Gas Exchange3.2.11A-A* (AO3/4) - Gas Exchange
3.3

Digestion & Absorption

3.3.1Overview of Digestion3.3.2Digestion in Mammals3.3.3Absorption3.3.4End of Topic Test - Substance Exchange & Digestion3.3.5A-A* (AO3/4) - Substance Ex & Digestion
3.4

Mass Transport

3.4.1Haemoglobin3.4.2Oxygen Transport3.4.3The Circulatory System3.4.4The Heart3.4.5Blood Vessels3.4.6Cardiovascular Disease3.4.7Heart Dissection3.4.8Xylem3.4.9Phloem3.4.10Investigating Plant Transport3.4.11End of Topic Test - Mass Transport3.4.12A-A* (AO3/4) - Mass Transport3.4.13Diagnostic Misconceptions - Concentration Gradient3.4.14Diagnostic Misconceptions - Cardiac Cycle3.4.15Diagnostic Misconceptions - Carrying Capacity3.4.16Diagnostic Misconceptions - Translocation
4

Genetic Information & Variation

4.1

DNA, Genes & Chromosomes

4.1.1DNA4.1.2Genes4.1.3Non-Coding Genes4.1.4The Genetic Code4.1.5A-A* (AO3/4) - DNA
4.2

DNA & Protein Synthesis

4.2.1Protein Synthesis4.2.2Transcription & Translation4.2.3End of Topic Test - DNA, Genes & Protein Synthesis4.2.4Exam-Style Question - Protein Synthesis4.2.5A-A* (AO3/4) - Coronavirus Translation4.2.6A-A* (AO3/4) - Transcription4.2.7A-A* (AO3/4) - Translation
4.3

Mutations & Meiosis

4.3.1Mutations4.3.2Meiosis4.3.3A-A* (AO3/4) - Meiosis4.3.4Meiosis vs Mitosis4.3.5End of Topic Test - Mutations, Meiosis4.3.6A-A* (AO3/4) - DNA,Genes, CellDiv & ProtSynth4.3.7Diagnostic Misconceptions - Meiosis vs Mitosis
4.4

Genetic Diversity & Adaptation

4.4.1Genetic Diversity4.4.2Natural Selection4.4.3A-A* (AO3/4) - Natural Selection4.4.4Adaptations4.4.5Investigating Natural Selection4.4.6End of Topic Test - Genetic Diversity & Adaptation4.4.7A-A* (AO3/4) - Genetic Diversity & Adaptation
4.5

Species & Taxonomy

4.5.1Courtship Behaviour4.5.2Phylogeny4.5.3Classification4.5.4DNA Technology4.5.5A-A* (AO3/4) - Species & Taxonomy
4.6

Biodiversity Within a Community

4.6.1Biodiversity4.6.2Index of diversity4.6.3Agriculture4.6.4End of Topic Test - Species,Taxonomy& Biodiversity4.6.5A-A* (AO3/4) - Species,Taxon&Biodiversity
4.7

Investigating Diversity

4.7.1Genetic Diversity4.7.2Quantitative Investigation
5

Energy Transfers (A2 only)

5.1

Photosynthesis

5.1.1Overview of Photosynthesis5.1.2Photoionisation of Chlorophyll5.1.3Production of ATP & Reduced NADP5.1.4Cyclic Photophosphorylation5.1.5Light-Independent Reaction5.1.6A-A* (AO3/4) - Photosynthesis Reactions5.1.7Limiting Factors5.1.8Photosynthesis Experiments5.1.9End of Topic Test - Photosynthesis5.1.10A-A* (AO3/4) - Photosynthesis
5.2

Respiration

5.2.1Overview of Respiration5.2.2Anaerobic Respiration5.2.3A-A* (AO3/4) - Anaerobic Respiration5.2.4The Link Reaction5.2.5The Krebs Cycle5.2.6Oxidative Phosphorylation5.2.7Respiration Experiments5.2.8End of Topic Test - Respiration5.2.9A-A* (AO3/4) - Respiration5.2.10Diagnostic Misconceptions - Aerobic vs Anaerobic
5.3

Energy & Ecosystems

5.3.1Biomass5.3.2Production & Productivity5.3.3Agricultural Practices
5.4

Nutrient Cycles

5.4.1Nitrogen Cycle5.4.2Phosphorous Cycle5.4.3Fertilisers & Eutrophication5.4.4End of Topic Test - Nutrient Cycles5.4.5A-A* (AO3/4) - Energy,Ecosystems&NutrientCycles
6

Responding to Change (A2 only)

6.1

Nervous Communication

6.1.1Survival6.1.2Plant Responses6.1.3Animal Responses6.1.4Reflexes6.1.5End of Topic Test - Reflexes, Responses & Survival6.1.6Receptors6.1.7The Human Retina6.1.8Control of Heart Rate6.1.9End of Topic Test - Receptors, Retina & Heart Rate
6.2

Nervous Coordination

6.2.1Neurones6.2.2Action Potentials6.2.3Speed of Transmission6.2.4End of Topic Test - Neurones & Action Potentials6.2.5Synapses6.2.6Types of Synapse6.2.7Medical Application6.2.8End of Topic Test - Synapses6.2.9A-A* (AO3/4) - Nervous Comm&Coord
6.3

Muscle Contraction

6.3.1Skeletal Muscle6.3.2Sliding Filament Theory6.3.3Contraction6.3.4Slow & Fast Twitch Fibres6.3.5End of Topic Test - Muscles6.3.6A-A* (AO3/4) - Muscle Contraction
6.4

Homeostasis

6.4.1Overview of Homeostasis6.4.2Blood Glucose Concentration6.4.3Controlling Blood Glucose Concentration6.4.4End of Topic Test - Blood Glucose6.4.5Primary & Secondary Messengers6.4.6Diabetes Mellitus6.4.7Measuring Glucose Concentration6.4.8Osmoregulation6.4.9Controlling Blood Water Potential6.4.10ADH6.4.11End of Topic Test - Diabetes & Osmoregulation6.4.12A-A* (AO3/4) - Homeostasis6.4.13Diagnostic Misconceptions - Effect of ADH
7

Genetics & Ecosystems (A2 only)

7.1

Genetics

7.1.1Key Terms in Genetics7.1.2Inheritance7.1.3Linkage7.1.4Multiple Alleles & Epistasis7.1.5Chi-Squared Test7.1.6End of Topic Test - Genetics7.1.7A-A* (AO3/4) - Genetics7.1.8Diagnostic Misconceptions - Dihybrid Inheritance7.1.9Diagnostic Misconceptions - Sex Linkage
7.2

Populations

7.2.1Populations7.2.2Hardy-Weinberg Principle
7.3

Evolution

7.3.1Variation7.3.2Natural Selection & Evolution7.3.3End of Topic Test - Populations & Evolution7.3.4Types of Selection7.3.5Types of Selection Summary7.3.6Overview of Speciation7.3.7Causes of Speciation7.3.8Diversity7.3.9End of Topic Test - Selection & Speciation7.3.10A-A* (AO3/4) - Populations & Evolution7.3.11Diagnostic Misconceptions - Types of Speciation
7.4

Populations in Ecosystems

7.4.1Overview of Ecosystems7.4.2Niche7.4.3Population Size7.4.4Investigating Population Size7.4.5End of Topic Test - Ecosystems & Population Size7.4.6Succession7.4.7Conservation7.4.8End of Topic Test - Succession & Conservation7.4.9A-A* (AO3/4) - Ecosystems
8

The Control of Gene Expression (A2 only)

8.1

Mutation

8.1.1Mutations8.1.2Effects of Mutations8.1.3Causes of Mutations8.1.4Diagnostic Misconceptions - Gene Expression
8.2

Gene Expression

8.2.1Stem Cells8.2.2Stem Cells in Disease8.2.3End of Topic Test - Mutation & Gene Epression8.2.4A-A* (AO3/4) - Mutation & Stem Cells8.2.5Regulating Transcription8.2.6Epigenetics8.2.7Epigenetics & Disease8.2.8Regulating Translation8.2.9Experimental Data8.2.10End of Topic Test - Transcription & Translation8.2.11Tumours8.2.12Correlations & Causes8.2.13Prevention & Treatment8.2.14End of Topic Test - Cancer8.2.15A-A* (AO3/4) - Gene Expression & Cancer
8.3

Genome Projects

8.3.1Using Genome Projects
8.4

Gene Technology

8.4.1Recombinant DNA8.4.2Producing Fragments8.4.3Amplification8.4.4End of Topic Test - Genome Project & Amplification8.4.5Using Recombinant DNA8.4.6Medical Diagnosis8.4.7Genetic Fingerprinting8.4.8End of Topic Test - Gene Technologies8.4.9A-A* (AO3/4) - Gene Technology
9

Mathematical Skills

9.1

Mathematical Skills

9.1.1Diagnostic Misconceptions - Converting Units9.1.2Diagnostic Misconceptions - Correct Hypothesis9.1.3Diagnostic Misconceptions - Interpret Hypothesis9.1.4Diagnostic Misconceptions - Calculate Uncertainty

Practice questions on Chi-Squared Test

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  1. 1
    What are the requirements for the chi-squared test?Fill in the list
  2. 2
    Why are predictions of phenotypic ratios rarely 100% accurate?Multiple choice
  3. 3
    Which of the following statements about chi-squared are true?True / false
  4. 4
    Stages of the Chi-Squared TestPut in order
  5. 5
    When is the null hypothesis rejected?Multiple choice
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Multiple Alleles & Epistasis

End of Topic Test - Genetics