Chi-Squared Test

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

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

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

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

The equation for chi-squared is:
- $\chi = \Sigma \; \frac{(O - E)^2}{E}$
  - O = observed values.
  - E = expected values.

Chi-Squared Test

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

Equation

The equation for chi-squared is:
$\chi = \Sigma \; \frac{(O - E)^2}{E}$
- O = observed values.
- E = 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

Using the chi-squared equation, calculate the chi-squared 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?

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?

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.

1Biological Molecules

1.1Monomers & Polymers

1.1.1Monomers & Polymers

1.1.2Condensation & Hydrolysis Reactions

1.2Carbohydrates

1.2.1Structure of Carbohydrates

1.2.2Types of Polysaccharides

1.2.3End of Topic Test - Monomers, Polymers and Carbs

1.2.4Exam-Style Question - Carbohydrates

1.2.5A-A* (AO3/4) - Carbohydrates

1.3Lipids

1.3.1Triglycerides & Phospholipids

1.3.2Types of Fatty Acids

1.3.3Testing for Lipids

1.3.4Exam-Style Question - Fats

1.3.5A-A* (AO3/4) - Lipids

1.4Proteins

1.4.1The Peptide Chain

1.4.2Investigating Proteins

1.4.3Primary & Secondary Protein Structure

1.4.4Tertiary & Quaternary Protein Structure

1.4.5Enzymes

1.4.6Factors Affecting Enzyme Activity

1.4.7Enzyme-Controlled Reactions

1.4.8End of Topic Test - Lipids & Proteins

1.4.9A-A* (AO3/4) - Enzymes

1.4.10A-A* (AO3/4) - Proteins

1.5Nucleic Acids

1.5.1DNA & RNA

1.5.2Nucleotides

1.5.3Polynucleotides

1.5.4DNA Replication

1.5.5Exam-Style Question - Nucleic Acids

1.5.6A-A* (AO3/4) - Nucleic Acids

1.6ATP

1.6.1Structure of ATP

1.6.2Hydrolysis of ATP

1.6.3Resynthesis of ATP

1.6.4End of Topic Test - Nucleic Acids & ATP

1.7Water

1.7.1Importance of Water

1.7.2Structure of Water

1.7.3Properties of Water

1.7.4A-A* (AO3/4) - Water

1.8Inorganic Ions

1.8.1Inorganic Ions

1.8.2End of Topic Test - Water & Inorganic Ions

2Cells

2.1Cell Structure

2.1.1Introduction to Cells

2.1.2Eukaryotic Cells & Organelles

2.1.3Eukaryotic Cells & Organelles 2

2.1.4Prokaryotes

2.1.5A-A* (AO3/4) - Organelles

2.1.6Methods of Studying Cells

2.1.7Microscopes

2.1.8End of Topic Test - Cell Structure

2.1.9Exam-Style Question - Cells

2.1.10A-A* (AO3/4) - Cells

2.2Mitosis & Cancer

2.2.1Mitosis

2.2.2Stages of Mitosis

2.2.3Investigating Mitosis

2.2.4Cancer

2.2.5A-A* (AO3/4) - The Cell Cycle

2.3Transport Across Cell Membrane

2.3.1Cell Membrane Structure

2.3.2A-A* (AO3/4) - Membrane Structure

2.3.3Diffusion

2.3.4Osmosis

2.3.5Active Transport

2.3.6End of Topic Test - Mitosis, Cancer & Transport

2.3.7Exam-Style Question - Membranes

2.3.8A-A* (AO3/4) - Membranes & Transport

2.3.9A-A*- Mitosis, Cancer & Transport

2.4Cell Recognition & the Immune System

2.4.1Immune System

2.4.2Phagocytosis

2.4.3T Lymphocytes

2.4.4B Lymphocytes

2.4.5Antibodies

2.4.6Primary & Secondary Response

2.4.7Vaccines

2.4.8HIV

2.4.9Ethical Issues

2.4.10End of Topic Test - Immune System

2.4.11Exam-Style Question - Immune System

2.4.12A-A* (AO3/4) - Immune System

3Substance Exchange

3.1Surface Area to Volume Ratio

3.1.1Size & Surface Area

3.1.2A-A* (AO3/4) - Cell Size

3.2Gas Exchange

3.2.1Single-Celled Organisms

3.2.2Multicellular Organisms

3.2.3Control of Water Loss

3.2.4Human Gas Exchange

3.2.5Ventilation

3.2.6Dissection

3.2.7Measuring Gas Exchange

3.2.8Lung Disease

3.2.9Lung Disease Data

3.2.10End of Topic Test - Gas Exchange

3.2.11A-A* (AO3/4) - Gas Exchange

3.3Digestion & Absorption

3.3.1Overview of Digestion

3.3.2Digestion in Mammals

3.3.3Absorption

3.3.4End of Topic Test - Substance Exchange & Digestion

3.3.5A-A* (AO3/4) - Substance Ex & Digestion

3.4Mass Transport

3.4.1Haemoglobin

3.4.2Oxygen Transport

3.4.3The Circulatory System

3.4.4The Heart

3.4.5Blood Vessels

3.4.6Cardiovascular Disease

3.4.7Heart Dissection

3.4.8Xylem

3.4.9Phloem

3.4.10Investigating Plant Transport

3.4.11End of Topic Test - Mass Transport

3.4.12A-A* (AO3/4) - Mass Transport

4Genetic Information & Variation

4.1DNA, Genes & Chromosomes

4.1.1DNA

4.1.2Genes

4.1.3Non-Coding Genes

4.1.4The Genetic Code

4.1.5A-A* (AO3/4) - DNA

4.2DNA & Protein Synthesis

4.2.1Protein Synthesis

4.2.2Transcription & Translation

4.2.3End of Topic Test - DNA, Genes & Protein Synthesis

4.2.4Exam-Style Question - Protein Synthesis

4.2.5A-A* (AO3/4) - Coronavirus Translation

4.2.6A-A* (AO3/4) - Transcription

4.2.7A-A* (AO3/4) - Translation

4.3Mutations & Meiosis

4.3.1Mutations

4.3.2Meiosis

4.3.3A-A* (AO3/4) - Meiosis

4.3.4Meiosis vs Mitosis

4.3.5End of Topic Test - Mutations, Meiosis

4.3.6A-A* (AO3/4) - DNA,Genes, CellDiv & ProtSynth

4.4Genetic Diversity & Adaptation

4.4.1Genetic Diversity

4.4.2Natural Selection

4.4.3A-A* (AO3/4) - Natural Selection

4.4.4Adaptations

4.4.5Investigating Natural Selection

4.4.6End of Topic Test - Genetic Diversity & Adaptation

4.4.7A-A* (AO3/4) - Genetic Diversity & Adaptation

4.5Species & Taxonomy

4.5.1Courtship Behaviour

4.5.2Phylogeny

4.5.3Classification

4.5.4DNA Technology

4.5.5A-A* (AO3/4) - Species & Taxonomy

4.6Biodiversity Within a Community

4.6.1Biodiversity

4.6.2Index of diversity

4.6.3Agriculture

4.6.4End of Topic Test - Species,Taxonomy& Biodiversity

4.6.5A-A* (AO3/4) - Species,Taxon&Biodiversity

4.7Investigating Diversity

4.7.1Genetic Diversity

4.7.2Quantitative Investigation

5Energy Transfers (A2 only)

5.1Photosynthesis

5.1.1Overview of Photosynthesis

5.1.2Photoionisation of Chlorophyll

5.1.3Production of ATP & Reduced NADP

5.1.4Cyclic Photophosphorylation

5.1.5Light-Independent Reaction

5.1.6A-A* (AO3/4) - Photosynthesis Reactions

5.1.7Limiting Factors

5.1.8Photosynthesis Experiments

5.1.9End of Topic Test - Photosynthesis

5.1.10A-A* (AO3/4) - Photosynthesis

5.2Respiration

5.2.1Overview of Respiration

5.2.2Anaerobic Respiration

5.2.3A-A* (AO3/4) - Anaerobic Respiration

5.2.4The Link Reaction

5.2.5The Krebs Cycle

5.2.6Oxidative Phosphorylation

5.2.7Respiration Experiments

5.2.8End of Topic Test - Respiration

5.2.9A-A* (AO3/4) - Respiration

5.3Energy & Ecosystems

5.3.1Biomass

5.3.2Production & Productivity

5.3.3Agricultural Practices

5.4Nutrient Cycles

5.4.1Nitrogen Cycle

5.4.2Phosphorous Cycle

5.4.3Fertilisers & Eutrophication

5.4.4End of Topic Test - Nutrient Cycles

5.4.5A-A* (AO3/4) - Energy,Ecosystems&NutrientCycles

6Responding to Change (A2 only)

6.1Nervous Communication

6.1.1Survival

6.1.2Plant Responses

6.1.3Animal Responses

6.1.4Reflexes

6.1.5End of Topic Test - Reflexes, Responses & Survival

6.1.6Receptors

6.1.7The Human Retina

6.1.8Control of Heart Rate

6.1.9End of Topic Test - Receptors, Retina & Heart Rate

6.2Nervous Coordination

6.2.1Neurones

6.2.2Action Potentials

6.2.3Speed of Transmission

6.2.4End of Topic Test - Neurones & Action Potentials

6.2.5Synapses

6.2.6Types of Synapse

6.2.7Medical Application

6.2.8End of Topic Test - Synapses

6.2.9A-A* (AO3/4) - Nervous Comm&Coord

6.3Muscle Contraction

6.3.1Skeletal Muscle

6.3.2Sliding Filament Theory

6.3.3Contraction

6.3.4Slow & Fast Twitch Fibres

6.3.5End of Topic Test - Muscles

6.3.6A-A* (AO3/4) - Muscle Contraction

6.4Homeostasis

6.4.1Overview of Homeostasis

6.4.2Blood Glucose Concentration

6.4.3Controlling Blood Glucose Concentration

6.4.4End of Topic Test - Blood Glucose

6.4.5Primary & Secondary Messengers

6.4.6Diabetes Mellitus

6.4.7Measuring Glucose Concentration

6.4.8Osmoregulation

6.4.9Controlling Blood Water Potential

6.4.10ADH

6.4.11End of Topic Test - Diabetes & Osmoregulation

6.4.12A-A* (AO3/4) - Homeostasis

7Genetics & Ecosystems (A2 only)

7.1Genetics

7.1.1Key Terms in Genetics

7.1.2Inheritance

7.1.3Linkage

7.1.4Multiple Alleles & Epistasis

7.1.5Chi-Squared Test

7.1.6End of Topic Test - Genetics

7.1.7A-A* (AO3/4) - Genetics

7.2Populations

7.2.1Populations

7.2.2Hardy-Weinberg Principle

7.3Evolution

7.3.1Variation

7.3.2Natural Selection & Evolution

7.3.3End of Topic Test - Populations & Evolution

7.3.4Types of Selection

7.3.5Types of Selection Summary

7.3.6Overview of Speciation

7.3.7Causes of Speciation

7.3.8Diversity

7.3.9End of Topic Test - Selection & Speciation

7.3.10A-A* (AO3/4) - Populations & Evolution

7.4Populations in Ecosystems

7.4.1Overview of Ecosystems

7.4.2Niche

7.4.3Population Size

7.4.4Investigating Population Size

7.4.5End of Topic Test - Ecosystems & Population Size

7.4.6Succession

7.4.7Conservation

7.4.8End of Topic Test - Succession & Conservation

7.4.9A-A* (AO3/4) - Ecosystems

8The Control of Gene Expression (A2 only)

8.1Mutation

8.1.1Mutations

8.1.2Effects of Mutations

8.1.3Causes of Mutations

8.2Gene Expression

8.2.1Stem Cells

8.2.2Stem Cells in Disease

8.2.3End of Topic Test - Mutation & Gene Epression

8.2.4A-A* (AO3/4) - Mutation & Stem Cells

8.2.5Regulating Transcription

8.2.6Epigenetics

8.2.7Epigenetics & Disease

8.2.8Regulating Translation

8.2.9Experimental Data

8.2.10End of Topic Test - Transcription & Translation

8.2.11Tumours

8.2.12Correlations & Causes

8.2.13Prevention & Treatment

8.2.14End of Topic Test - Cancer

8.2.15A-A* (AO3/4) - Gene Expression & Cancer

8.3Genome Projects

8.3.1Using Genome Projects

8.4Gene Technology

8.4.1Recombinant DNA

8.4.2Producing Fragments

8.4.3Amplification

8.4.4End of Topic Test - Genome Project & Amplification

8.4.5Using Recombinant DNA

8.4.6Medical Diagnosis

8.4.7Genetic Fingerprinting

8.4.8End of Topic Test - Gene Technologies

8.4.9A-A* (AO3/4) - Gene Technology

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