Correlation

Correlation and Causation

Correlation means that there is a relationship between two variables. Causation means that changing one causes the other to change.

Causation

Correlation does not imply causation.
If two variables are correlated that does not mean that changes in one directly cause changes in the other.

Example

The number of ice cream sales might be positively correlated with temperature but this does not mean that ice cream sales cause higher temperatures.

Pearson's Linear Correlation

Two variables are correlated if you can draw a straight line that lies close to most of the points.

Variables and constants

The variable x is the independent or explanatory variable.
The variable y is the dependent or response variable.
The slope of the regression line is given by the constant b.
- The sign and size of this number tell us how y changes for every unit increase in x on average.

Pearson's correlation coefficient

The Pearson's correlation coefficient, $r$ , provides a measure of strength and direction of the correlation between x and y.
The value of $r$ is always between –1 and +1.

Pearson's correlation coefficient

Values of $r$ close to –1 or to +1 indicate a stronger linear relationship between x and y.
- If $r = 0$ , there is likely no linear correlation.
- If $r = 1$ , there is a perfect positive correlation so all points lie on a straight line.
- If $r = \text{-}1$ , there is a perfect negative correlation so all points lie on a straight line.

Pearson's correlation coefficient

Formula

The formula for the correlation coefficient is:
- $r = \frac{\large 1}{\large n-1}\sum\left(\frac{\large x_i-\overline{x}}{\large s_x}\right)\left(\frac{\large y_i-\overline{y}}{\large s_y}\right)$
Where $\overline{x},\overline{y}$ are the mean and $s_x,s_y$ are the standard deviations of the explanatory and response variables respectively.
It is much more common to calculate $r$ using a calculator.

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

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

2.1.1Tests 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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Sampling Methods

Spearman’s Rank