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.

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

2.1.1Tests for Sugars & Starch

2.1.2Tests for Lipids & Proteins

2.2Carbohydrates & Lipids

2.2.1Monomers & Polymers

2.2.2Carbohydrates

2.2.3Examples of Carbohydrates

2.2.4Triglycerides & Phospholipids

2.2.5Types of Fatty Acids

2.2.6Exam-Style Question - Carbohydrates

2.2.7End of Topic Test - Carbohydrates & Lipids

2.3Proteins

2.3.1Amino Acids & Overview of Protein Structure

2.3.2Primary & Secondary Structure

2.3.3Tertiary & Quaternary Structure

2.3.4Globular & Fibrous Proteins

2.3.5Haemoglobin

2.3.6Collagen

2.3.7End of Topic Test - Proteins

2.4Water

2.4.1Water Structure & Function

2.4.2End of Topic Test - Water

3Enzymes

3.1Enzymes

3.1.1Enzyme Action

3.1.2Factors Affecting Enzyme Activity

3.1.3Factors Affecting Enzyme Activity 2

3.1.4A-A* (AO2/3) - Enzymes

4Cell Membranes & Transport

4.1Biological Membranes

4.1.1Fluid Mosaic Model

4.1.2Cell Signalling

4.1.3End of Topic Test - Biological Membranes

4.1.4Exam-Style Question - Membranes

4.2Movement Into & Out of Cells

4.2.1Passive Movement Across the Membrane

4.2.2Active Movement Across the Membrane

4.2.3Osmosis

4.2.4Osmosis & Plant Cells

4.2.5Surface Area to Volume Ratio

4.2.6Adaptions to Surface Area to Volume Ratio

4.2.7Calculations - Volume

4.2.8Calculations - Surface Area

5The Mitotic Cell Cycle

5.1Replication & Division of Nuclei

5.1.1Chromosomes

5.1.2The Cell Cycle

5.1.3Mitosis

5.1.4Role of Mitosis

5.1.5Stem Cells

5.1.6Mitosis & Cancer

5.1.7End of Topic Test - Replication & Division

5.1.8A-A* (AO2/3) - Cell Cycle & Transport

6Nucleic Acids & Protein Synthesis

6.1Nucleic Acids

6.1.1Introduction to DNA & RNA

6.1.2Nucleotides

6.1.3Polynucleotides

6.1.4ADP & ATP

6.1.5DNA

6.1.6DNA Replication

6.1.7RNA

6.1.8End of Topic Test - Nucleic Acids & ATP

6.2Protein Synthesis

6.2.1The Genetic Code

6.2.2Polypeptide Synthesis

6.2.3RNA Processing in Eukaryotes

6.2.4Mutations

6.2.5Exam-Style Question - Protein Synthesis

6.2.6A-A* (AO2/3) - Coronavirus Translation

7Transport in Plants

7.1Transport in Plants

7.1.1Plant Vessels

7.1.2Xylem

7.1.3Investigating Transpiration

7.1.4Adaptations to Water Availability

7.1.5Phloem

7.1.6End of Topic Test - Transport in Animals & Plants

7.1.7A-A* (AO2/3) - Transport in Animals & Plants

8Transport in Mammals

8.1Circulatory System

8.1.1Double Circulation

8.1.2Blood Vessels

8.1.3Important Blood Vessels

8.1.4Blood Cells

8.1.5Tissue Fluid

8.2Transport of Oxygen & Carbon Dioxide

8.2.1Haemoglobin

8.2.2Oxygen Dissociation

8.3The Heart

8.3.1Structure of the Heart

8.3.2The Cardiac Cycle

8.3.3Coordination of Heart Action

9Gas Exchange

9.1Gas Exchange System

9.1.1Mammalian Gas Exchange

9.1.2Smoking

10Infectious Diseases

10.1Infectious Diseases

10.1.1Transmission of Disease

10.1.2Tuberculosis

10.1.3HIV

10.1.4Malaria

10.1.5Cholera

10.1.6Measles

10.2Antibiotics

10.2.1Antibiotics

11Immunity

11.1The Immune System

11.1.1Phagocytes

11.1.2Antigens

11.1.3Lymphocytes

11.1.4Primary & Secondary Response

11.2Antibodies & Vaccination

11.2.1Antibodies

11.2.2Monoclonal Antibodies

11.2.3Immunity

11.2.4Vaccines

11.2.5Exam-Style Question - Immune System

11.2.6A-A* (AO2/3) - Disease & Immune System

12Energy & Respiration (A2 Only)

12.1Energy

12.1.1Energy & ATP

12.1.2Respiratory Substrates & Quotient

12.1.3Respirometers

12.2Respiration

12.2.1Introduction to Respiration

12.2.2Anaerobic Respiration

12.2.3Aerobic Respiration

12.2.4Chemiosmosis & Coenzymes

12.2.5Mitochondria

12.2.6Respiration Experiments

12.2.7End of Topic Test - Respiration

12.2.8A-A* (AO3/4) - Respiration

13Photosynthesis (A2 Only)

13.1Photosynthesis

13.1.1Introduction to Photosynthesis

13.1.2Light-Dependent Reactions

13.1.3Light-Independent Reactions

13.1.4Limiting Factors

13.1.5Investigating Photosynthesis

13.1.6End of Topic Test - Photosynthesis

13.1.7A-A* (AO3/4) - Photosynthesis

14Homeostasis (A2 Only)

14.1Homeostasis

14.1.1Homeostasis

14.1.2Negative Feedback

14.2The Kidney

14.2.1Kidneys & Osmoregulation

14.3Cell Signalling

14.3.1Messengers & cAMP

14.4Blood Glucose Concentration

14.4.1Blood Glucose Concentration

14.4.2Controlling Blood Glucose

14.4.3Urinalysis

14.5Homeostasis in Plants

14.5.1Stomata & Guard Cells

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

15.2.1Venus Flytrap

15.2.2Auixns

15.2.3Gibberellins

16Inherited Change (A2 Only)

16.1Passage of Information to Offspring

16.1.1Meiosis

16.1.2Gametogenesis

16.1.3Meiosis & Genetic Diversity

16.2Genes & Phenotype

16.2.1Key Terms in Genetics

16.2.2Inheritance

16.2.3Linkage

16.2.4Multiple Alleles

16.2.5Chi-Squared Test

16.2.6Mutations

16.2.7Specific Mutations

16.2.8End of Topic Test - Genetics

16.2.9A-A* (AO2/3) - Genetics

16.3Gene Control

16.3.1lac Operon

16.3.2Transcription Factors

16.3.3Gibberellins & DELLA Proteins

17Selection & Evolution (A2 Only)

17.1Variation

17.1.1Phenotypic Variation

17.1.2Continuous & Discontinuous Variation

17.1.3t-Tests

17.2Natural & Artificial Selection

17.2.1Natural Selection & Evolution

17.2.2Types of Selection

17.2.3Types of Selection Summary

17.2.4Genetic Drift & Founder Effect

17.2.5Populations

17.2.6Hardy-Weinberg Principle

17.2.7Artificial Selection

17.3Evolution

17.3.1Evolution by Natural Selection

17.3.2Evidence for Evolution

17.3.3Speciation

17.3.4Extinction

18Classification & Conservation (A2 Only)

18.1Biodiversity

18.1.1Key Terms

18.1.2Biodiversity

18.1.3Sampling Methods

18.1.4Correlation

18.1.5Spearman’s Rank

18.1.6Measuring Biodiversity

18.2Classification

18.2.13-Domain Classification System

18.2.2Linnaean Classification System

18.3Conservation

18.3.1Importance of Biodiversity

18.3.2Conservation

18.3.3Zoos, Seedbanks, & Other Conservation Methods

18.3.4Assisted Reproduction & Contraception

18.3.5Non-Governmental Organisations

19Genetic Technology (A2 Only)

19.1Manipulating Genomes

19.1.1Recombinant DNA & Genetic Engineering

19.1.2Restriction Endonucleases

19.1.3Gel Electrophoresis

19.1.4DNA Probes & Microarrays

19.1.5End of Topic Test - Manipulating Genomes

19.1.6A-A* (AO2/3) - Manipulating Genomes

19.2Genetic Technology Applied to Medicine

19.2.1Bioinformatics

19.2.2Applications of Recombinant DNA

19.2.3Genetic Screening

19.2.4Gene Therapy

19.2.5Ethics

19.2.6DNA Profiling & Forensics

19.3Genetically Modified Organisms in Agriculture

19.3.1GM Crops & Livestock

19.3.2Ethics

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