How is the chi-squared statistic calculated?

For each category the observed frequency is subtracted from the expected frequency, the difference is squared and divided by the expected frequency, and these values are summed for all categories.

How are the degrees of freedom found for a chi-squared test, and what value would a dihybrid cross give?

The degrees of freedom are one fewer than the number of categories, so a dihybrid cross with four phenotypes has three degrees of freedom.

A cross expected to give a 3:1 ratio produced 132 and 28 offspring out of 160. Calculate chi-squared.

The expected numbers are 120 and 40, so chi-squared is (12² ÷ 120) + (12² ÷ 40) = 1.2 + 3.6 = 4.8.

With one degree of freedom the critical value at p = 0.05 is 3.84. Interpret a calculated chi-squared value of 4.8.

The calculated value is greater than the critical value, so the null hypothesis is rejected and the difference from the expected 3:1 ratio is significant.

WJEC A-Level Biology 601-5290-0

Chemical Elements Are Joined Together to Form Biological Compounds

Topic overview Inorganic Ions Biological Importance of Water Carbohydrates: Monosaccharides and Disaccharides Carbohydrates: Polysaccharides and Alpha/Beta Glucose Isomerism Lipids: Triglycerides and Phospholipids Lipids: Saturated and Unsaturated Fat in Human Health Amino Acids and Proteins: Primary to Quaternary Structure Amino Acids and Proteins: Fibrous and Globular Forms Condensation and Hydrolysis: Peptide and Glycosidic Food Tests for Biological Molecules

Cell Structure and Organisation

Topic overview Eukaryotic Cell Ultrastructure: Organelles Eukaryotic Cell Ultrastructure: Functions Prokaryotic Cells, Viruses and Cell Theory: Comparing Cell Structures Prokaryotic Cells, Viruses and Cell Theory: Electron Micrographs Levels of Organisation and Light Microscopy: Tissues and Organs Levels of Organisation and Light Microscopy: Organ Systems and Microscope Calibration Levels of Organisation and Light Microscopy: Magnification and Scientific Drawing

Cell Membranes and Transport

Topic overview Plasma Membrane Structure and Permeability: Fluid-Mosaic Model Plasma Membrane Structure and Permeability: Factors Affecting Permeability Transport Across Membranes: Diffusion, Osmosis and Water Potential Transport Across Membranes: Facilitated Diffusion, Active Transport and Pinocytosis Transport Across Membranes: Phagocytosis and Exocytosis

Biological Reactions Are Regulated by Enzymes

Topic overview Enzymes as Biological Catalysts: Metabolism, Extracellular Action and Induced Fit Enzymes as Biological Catalysts: Activation Energy Factors Affecting Enzyme Activity: Temperature and Substrate Factors Affecting Enzyme Activity: Enzyme Concentration, Denaturation and Buffers Enzyme Inhibition Immobilised Enzymes in Industry

Nucleic Acids and Their Functions

Topic overview Nucleotides, Chemical Energy and ATP: Structure Nucleotides, Chemical Energy and ATP: Role as Energy Carrier DNA and RNA Structure Semi-conservative Replication, Meselson and Stahl experiment The Genetic Code: Triplet Code The Genetic Code: Exons and Introns Protein Synthesis: Transcription, Translation and tRNA Protein Synthesis: One Gene-One Polypeptide and Polypeptide Modification

Genetic Information Is Copied and Passed on to Daughter Cells

Topic overview The Cell Cycle and Mitosis: Interphase and Stages The Cell Cycle and Mitosis: Cytokinesis, Significance in Renewal and Repair The Cell Cycle and Mitosis: Root Tip Squash and Mitotic Index Meiosis: Meiosis I and Meiosis II, crossing over and independent assortment Meiosis: differences from mitosis

All Organisms Are Related Through Their Evolutionary History

Topic overview Classification: Hierarchical Groups, Need and Tentative Nature Classification: Three Domains and Five Kingdoms Assessing Relatedness Species Concept and Binomial System Biodiversity and Its Assessment: Habitat Level Biodiversity and Its Assessment: Genetic Level and Molecular Level Natural Selection as the Source of Biodiversity and Anatomical, Physiological and Behavioural Adaptations

Adaptations for Gas Exchange

Topic overview Surface Area to Volume Ratio and Gas Exchange in Small Organisms: Amoeba Surface Area to Volume Ratio and Gas Exchange in Small Organisms: Flatworm and Earthworm Specialised Respiratory Surfaces and Ventilation in Bony Fish: Counter-current Specialised Respiratory Surfaces and Ventilation in Bony Fish: Parallel Flow Gas Exchange in Terrestrial Animals: Human Breathing System Gas Exchange in Terrestrial Animals: Ventilation Gas Exchange in Terrestrial Animals: the Insect Tracheal System The Angiosperm Leaf: Structure The Angiosperm Leaf: Photosynthetic Role The Angiosperm Leaf: Stomatal Control of Gas Exchange

Adaptations for Transport

Topic overview Vascular Systems Across Animal Groups: Earthworm and Insect Vascular Systems Across Animal Groups: Fish and Mammal The Mammalian Heart and Circulation: Blood Vessels and Cardiac Cycle The Mammalian Heart and Circulation: Sino-atrial Node, Purkyne Fibres and Electrocardiograms Blood and the Transport of Respiratory Gases: Erythrocytes, Plasma and Dissociation Curves Blood and the Transport of Respiratory Gases: Bohr Effect and Chloride Shift Transport of Nutrients, Hormones, Excretory Products and Heat Tissue Fluid, Lymph and Oedema Water Uptake and Movement Through the Root: Dicotyledon Root Structure and Apoplast Water Uptake and Movement Through the Root: Symplast, Vacuolar Pathways and Endodermis Xylem, the Transpiration Stream and Plant Water Adaptations: Cohesion-Tension Theory Xylem, the Transpiration Stream and Plant Water Adaptations: Hydrophytes and Xerophytes Phloem Structure and Translocation from Source to Sink: Mass Flow Models Phloem Structure and Translocation from Source to Sink: Experimental Evidence

Adaptations for Nutrition

Topic overview Modes of Nutrition: Autotrophic, Heterotrophic and Holozoic Modes of Nutrition: Parasitic, and Digestion in Amoeba and Hydra to Tube Guts The Human Gut: Adaptations to an Omnivorous Diet The Human Gut: Enzymes The Human Gut: Conditions Herbivore, Carnivore and Parasite Adaptations: Guts and Dentition Herbivore, Carnivore and Parasite Adaptations: Ruminants, Taenia and Pediculus

Importance of ATP

Topic overview ATP Synthesis and Chemiosmosis: ATP Synthetase ATP Synthesis and Chemiosmosis: Proton and Electrochemical Gradients ATP Synthesis and Chemiosmosis: Proton Pumps and Electron Transport Chain

Photosynthesis Uses Light Energy to Synthesise Organic Molecules

Topic overview Chloroplasts and Light Harvesting: Distribution and Transduction Chloroplasts and Light Harvesting: Pigments and Wavelengths Chloroplasts and Light Harvesting: Chromatography of Pigments The Light-dependent Stage: Cyclic and Non-cyclic Photophosphorylation The Light-dependent Stage: Photolysis and Reduction of NADP The Light-independent Stage: Rubisco, Glycerate-3-phosphate and Triose Phosphate The Light-independent Stage: RuBP Regeneration, Synthesis of Carbohydrates and Amino Acids Limiting Factors in Photosynthesis Investigating the Rate of Photosynthesis and the Role of Nitrogen Magnesium in Plant Metabolism

Respiration Releases Chemical Energy in Biological Processes

Topic overview Glycolysis, Acetyl Coenzyme A and the Krebs Cycle: Triose Phosphate and Pyruvate Glycolysis, Acetyl Coenzyme A and the Krebs Cycle: Reduced NAD, FAD as Electron and Proton Sources Energy Budgets of Aerobic and Anaerobic Glucose Breakdown Use of Lipids and Amino Acids in Respiration Measuring the Rate of Respiration in Yeast

Microbiology

Topic overview Bacterial Classification by Shape and Gram Stain Culturing Microorganisms and Monitoring Population Growth Serial Dilution and Plating Viable Counts

Population Size and Ecosystems

Topic overview Population Growth and Its Regulation: Birth and Immigration Population Growth and Its Regulation: Emigration, Competition and Carrying Capacity Population Growth and Its Regulation: Density Dependent and Density Independent Factors Sampling Techniques for the Abundance Distribution of Organisms in a Habitat Habitats, Communities and Sun as Energy Source Biomass, Productivity and Transfer Through Trophic Levels Succession: Secondary Succession and Pioneers Succession: Seres and Climax Communities Nutrient Cycles and Human Impact: Organic Breakdown and Carbon Cycle Nutrient Cycles and Human Impact: Climate Change, Nitrogen Cycle and Nitrification Nutrient Cycles and Human Impact: Fertilisers and Eutrophication

Human Impact on the Environment

Topic overview Endangered Species and Causes of Extinction Conservation of Gene Pools in the Wild and in Captivity Agricultural Exploitation, Conservation Conflicts and Sustainability Science-informed Political Decisions and Planetary Boundaries

Homeostasis and the Kidney

Topic overview Homeostasis: Dynamic Equilibrium, Negative Feedback and Positive Feedback Kidney and Nephron Structure and Function: Nephron Structure and Ultrafiltration Kidney and Nephron Structure and Function: Selective Reabsorption Kidney and Nephron Structure and Function: Nitrogenous Excretion and Kidney Practical Work Hormonal Control of Water Balance: ADH and Osmoreceptors The Loop of Henle, Excretory Adaptations and Kidney Failure Treating Kidney Failure: Dialysis and Transplants

The Nervous System

Topic overview Organisation of the Nervous Response: Receptors to Effectors and Spinal Cord Organisation of the Nervous Response: Spinal Nerves, Dorsal and Ventral Roots Organisation of the Nervous Response: Simple Reflex Arc and the Cnidarian Nerve Net Compared Neurones and the Nerve Impulse: Motor Neurone Structure and Nature Neurones and the Nerve Impulse: Transmission of the Impulse and Oscilloscope Traces Neurones and the Nerve Impulse: Speed of Conduction Synapses: Structure and Synaptic Transmission Synapses: Effects of Organophosphates and Psychoactive Drugs

Sexual Reproduction in Humans

Topic overview Human Reproductive Systems and Gametogenesis: Ovary and Testis Histology Human Reproductive Systems and Gametogenesis: Spermatogenesis and Oogenesis Human Reproductive Systems and Gametogenesis: Fertilisation and Implantation Endocrine Control of Reproduction: Menstrual Cycle Endocrine Control of Reproduction: Menstruation, Pregnancy and Birth Endocrine Control of Reproduction: Birth, Lactation and Role of the Placenta

Sexual Reproduction in Plants

Topic overview Flower Structure and Pollination: Wind and Insect Pollinated Flowers Flower Structure and Pollination: Cross and Self Pollination Development of Pollen Ovules Double Fertilisation and Drawing an Anther Seed and Fruit Formation Germination of Vicia faba Effect of Gibberellin

Inheritance

Topic overview Mendelian Inheritance: Alleles Mendelian Inheritance: Monohybrid Crosses with Codominance Mendelian Inheritance: Dihybrid Crosses with Linkage Testing Genetic Outcomes and Sex Linkage: Chi-squared Test Testing Genetic Outcomes and Sex Linkage: Haemophilia and Duchenne Muscular Dystrophy Mutation and Control of Gene Expression: Sickle Cell Anaemia Mutation and Control of Gene Expression: Down's Syndrome and Mutagens Mutation and Control of Gene Expression: Carcinogens, Oncogenes and Epigenetics

Variation and Evolution

Topic overview Variation and Selection Pressures: Genetic, Environmental Causes and Continuous Variation and Selection Pressures: Discontinuous, Non-heritable Variation and Intra-specific Competition Variation and Selection Pressures: Selective Agencies Population Genetics: Gene Pool, Genetic Drift and Changing Allele Frequencies Population Genetics: Hardy-Weinberg Principle Isolation Speciation and Darwin's Theory of Evolution

Application of Reproduction and Genetics

Topic overview Genome Sequencing and Its Ethics: Human Genome Project and 100K Genome Project Genome Sequencing and Its Ethics: Genomes of Other Organisms and Screening of Embryos Genetic Fingerprinting and Recombinant DNA Technology Genetic Fingerprinting and Recombinant DNA Technology: Electrophoresis and Bacterial Plasmids Genetic Fingerprinting and Recombinant DNA Technology: Insulin and GM Crops Gene Therapy Genomics in Future Healthcare and Use of Stem Cells

DiseaseOption A

Topic overview Disease Terminology Human Body as a Host Viral Pathogenicity Named Infectious Diseases: Cholera Named Infectious Diseases: Tuberculosis Named Infectious Diseases: Smallpox and Influenza Named Infectious Diseases: Malaria - Organism, Control and Treatment

AntibioticsOption A

Topic overview Antibiotics: Bacteriostatic, Bactericidal Action and Penicillin Antibiotics: Tetracycline and Gram Negative Cell Walls Antibiotics: Antibiotic Resistance

Immune ResponseOption A

Topic overview Non-specific Defences: Skin Flora, Connective Tissue and Inflammation Non-specific Defences: Phagocytosis, Clotting and Ciliated Epithelium Specific Immunity: Development of Responses to Foreign Antigens and Humoral Specific Immunity: Cell-mediated Immunity, Roles of T and B Lymphocytes Active and Passive Immunity Immunisation Programmes, Effectiveness and Ethics

Skeletal TissuesOption B

Topic overview Cartilage and Compact Bone: Hyaline and Yellow Elastic Cartilage and Compact Bone: White Fibrous Cartilage, Organic and Inorganic Matrix Components Cartilage and Compact Bone: Haversian Systems Bone Remodelling and Bone Disorders: Osteoblasts, Osteoclasts and Rickets Bone Remodelling and Bone Disorders: Osteomalacia, Osteoporosis and Brittle Bone Disease Skeletal Muscle: Structure and Ultrastructure Skeletal Muscle: Sliding Filament Theory and Fast Skeletal Muscle: Slow Twitch Fibres and Creatine Phosphate Skeletal Muscle: Lactic Acid and Energy Sources

Structure and Function of Human SkeletonOption B

Topic overview The Human Skeleton: Axial and Appendicular Structure The Human Skeleton: Vertebral Column and Vertebra Types The Human Skeleton: Fractures, Postural Deformities and Functions of the Skeleton

JointsOption B

Topic overview Types of Joint and Synovial Joint Structure Joints as First, Second, Third Order Levers and Antagonistic Muscle Action in the Forelimb Arthritis: Causes and Treatment of Osteoarthritis Arthritis: Rheumatoid Arthritis

The BrainOption C

Topic overview Structure and Functions of the Human Brain: Cerebrum, Hypothalamus and Hippocampus Structure and Functions of the Human Brain: Cerebellum and Medulla Oblongata Sympathetic Nervous System Parasympathetic Nervous System and Hypothalamus as the Nervous-Endocrine Link The Cerebral Cortex: Sensory and Motor Areas The Cerebral Cortex: Motor Homunculi, Language and Speech Areas

NeuroscienceOption C

Topic overview Studying the Brain and Brain Development: fMRI Studying the Brain and Brain Development: Critical Periods Studying the Brain and Brain Development: Neuroplasticity and Mental Illness

BehaviourOption C

Topic overview Innate and Learned Behaviour: Escape Reflexes and Kineses Innate and Learned Behaviour: Taxes in Woodlice Innate and Learned Behaviour: Habituation, Imprinting and Operant Conditioning Social Behaviour: Primate Societies, Advantages and Disadvantages of Group Living Social Behaviour: Insect Caste Systems and Vertebrate Dominance Hierarchies Territorial and Courtship Behaviour Role of Sexual Selection in Their Evolution

Working Scientifically: Practical Skills

Topic overview The A2 Unit 5 Practical Examination Tasks: Experimental Task The A2 Unit 5 Practical Examination Tasks: Practical Analysis Task Independent Thinking and Use of Scientific Methods and Practices: Solving Problems in Practical Contexts Independent Thinking and Use of Scientific Methods and Practices: Identifying and Following Instructions Independent Thinking and Use of Scientific Methods and Practices: Making and Keeping Records Independent Thinking and Use of Scientific Methods and Practices: Presenting Data Numeracy in Practical Contexts, Research and Referencing: Plotting, Interpreting Graphs and Processing Numeracy in Practical Contexts, Research and Referencing: Analysing Data, Margins of Error and Accuracy Numeracy in Practical Contexts, Research and Referencing: Precision and Online Numeracy in Practical Contexts, Research and Referencing: Offline Research Skills

Use of Apparatus and Techniques

Topic overview Measurement and Laboratory Technique: Quantitative Apparatus Measurement and Laboratory Technique: Instrumentation Measurement and Laboratory Technique: Glassware Including Serial Dilutions Microscopy, Scientific Drawing and Separation and Identification Techniques: Light Microscope Microscopy, Scientific Drawing and Separation and Identification Techniques: Annotated Drawings and Food Tests Microscopy, Scientific Drawing and Separation and Identification Techniques: Chromatography Working with Organisms and Aseptic Technique Viable Counts, Dissection and Fieldwork Sampling Mark-Release-Recapture, Quadrats and ICT for Data Collection

Mathematical Requirements (Appendix C)

Topic overview Arithmetic and Numerical Computation: Appropriate Units, Decimal and Standard Form Arithmetic and Numerical Computation: Ratios, Percentages and Estimating Results Arithmetic and Numerical Computation: Power, Exponential and Logarithmic Functions Handling Data: Significant Figures, Arithmetic Means and Mean Handling Data: Median, Frequency Tables and Histograms Handling Data: Scatter Diagrams Probability, Sampling, Statistical Tests and Uncertainty: Simple Probability and Selecting Probability, Sampling, Statistical Tests and Uncertainty: Using the Chi-squared Test Probability, Sampling, Statistical Tests and Uncertainty: Correlation Coefficient Probability, Sampling, Statistical Tests and Uncertainty: Standard Deviation Algebra and Magnification: Mathematical Symbols and Changing the Subject of an Equation Algebra and Magnification: Substituting Values, Solving Equations and Using Logarithms Graphs: Translating Between Graphical, Plotting Two Variables and Linear Relationships Graphs: Intercepts, Rate of Change and Slope of a Tangent to a Curve Geometry: Circumferences, Surface Areas and Volumes of Regular Shapes

How Science Works (Appendix D)

Topic overview Developing and Communicating Scientific Explanations: Using Theories, Models and Ideas Developing and Communicating Scientific Explanations: Posing Scientific Questions Scientific Methodology, Evidence and Evaluation: Appropriate Methodology Including ICT Scientific Methodology, Evidence and Evaluation: Analysing and Conflicting Data Science, Society and Ethics: How Scientific Knowledge Develops Over Time Science, Society and Ethics: Risks, Ethical Treatment of Humans and Other Organisms Science, Society and Ethics: Environment and How Society Uses Science

Mathematical Requirements (Appendix C)

Probability, Sampling, Statistical Tests and Uncertainty: Using the Chi-squared Test

3 things to know
All units

Overview

Recall questions on Using the Chi-squared Test and Student's t-test.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

Why must chi-squared be calculated from actual counts rather than from percentages?

Key term

What does a large value of t indicate about two sets of measurements?

Key term

When should the chi-squared test be selected?

Questions from this subtopic

Each one with the model answer underneath.

1
When should the chi-squared test be selected?
Model answer
When observed frequencies falling into discrete categories are being compared with the frequencies expected from a theoretical ratio.
2
How is the chi-squared statistic calculated?
Model answer
For each category the observed frequency is subtracted from the expected frequency, the difference is squared and divided by the expected frequency, and these values are summed for all categories.
3
How are the degrees of freedom found for a chi-squared test, and what value would a dihybrid cross give?
Model answer
The degrees of freedom are one fewer than the number of categories, so a dihybrid cross with four phenotypes has three degrees of freedom.
4
A cross expected to give a 3:1 ratio produced 132 and 28 offspring out of 160. Calculate chi-squared.
Model answer
The expected numbers are 120 and 40, so chi-squared is (12² ÷ 120) + (12² ÷ 40) = 1.2 + 3.6 = 4.8.
5
With one degree of freedom the critical value at p = 0.05 is 3.84. Interpret a calculated chi-squared value of 4.8.
Model answer
The calculated value is greater than the critical value, so the null hypothesis is rejected and the difference from the expected 3:1 ratio is significant.
6
Why must chi-squared be calculated from actual counts rather than from percentages?
Model answer
The test depends on the size of the sample, and converting to percentages discards that information and would distort the calculated value.

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