18.1.4

Correlation

Test yourself on Correlation

Test your knowledge with free interactive questions on Seneca — used by over 10 million students.

Correlation and Causation

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

Causation

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

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

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

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

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

Pearson's correlation coefficient

Formula

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.

1

Cell Structure

1.1

Cell 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

2

Biological Molecules

2.1

Testing for Biological Modules

2.1.1Tests for Sugars & Starch 2.1.2Tests for Lipids & Proteins

2.2

Carbohydrates & 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

2.3

Proteins

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

2.4

Water

2.4.1Water Structure & Function 2.4.2End of Topic Test - Water

3

Enzymes

3.1

Enzymes

3.1.1Enzyme Action 3.1.2Factors Affecting Enzyme Activity 3.1.3Factors Affecting Enzyme Activity 2 3.1.4A-A* (AO2/3) - Enzymes

4

Cell Membranes & Transport

4.1

Biological Membranes

4.1.1Fluid Mosaic Model 4.1.2Cell Signalling 4.1.3End of Topic Test - Biological Membranes 4.1.4Exam-Style Question - Membranes

4.2

Movement 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

5

The Mitotic Cell Cycle

5.1

Replication & 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

6

Nucleic Acids & Protein Synthesis

6.1

Nucleic 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

6.2

Protein 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

7

Transport in Plants

7.1

Transport 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

8

Transport in Mammals

8.1

Circulatory System

8.1.1Double Circulation 8.1.2Blood Vessels 8.1.3Important Blood Vessels 8.1.4Blood Cells 8.1.5Tissue Fluid

8.2

Transport of Oxygen & Carbon Dioxide

8.2.1Haemoglobin 8.2.2Oxygen Dissociation

8.3

The Heart

8.3.1Structure of the Heart 8.3.2The Cardiac Cycle 8.3.3Coordination of Heart Action

9

Gas Exchange

9.1

Gas Exchange System

9.1.1Mammalian Gas Exchange 9.1.2Smoking

10

Infectious Diseases

10.1

Infectious Diseases

10.1.1Transmission of Disease 10.1.2Tuberculosis 10.1.3HIV 10.1.4Malaria 10.1.5Cholera 10.1.6Measles

10.2

Antibiotics

10.2.1Antibiotics

11

Immunity

11.1

The Immune System

11.1.1Phagocytes 11.1.2Antigens 11.1.3Lymphocytes 11.1.4Primary & Secondary Response

11.2

Antibodies & 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

12

Energy & Respiration (A2 Only)

12.1

Energy

12.1.1Energy & ATP 12.1.2Respiratory Substrates & Quotient 12.1.3Respirometers

12.2

Respiration

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

13

Photosynthesis (A2 Only)

13.1

Photosynthesis

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

14

Homeostasis (A2 Only)

14.1

Homeostasis

14.1.1Homeostasis 14.1.2Negative Feedback

14.2

The Kidney

14.2.1Kidneys & Osmoregulation

14.3

Cell Signalling

14.3.1Messengers & cAMP

14.4

Blood Glucose Concentration

14.4.1Blood Glucose Concentration 14.4.2Controlling Blood Glucose 14.4.3Urinalysis

14.5

Homeostasis in Plants

14.5.1Stomata & Guard Cells

15

Control & Coordination (A2 Only)

15.1

Control & 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

15.2

Control & Co-Ordination in Plants

15.2.1Venus Flytrap 15.2.2Auixns 15.2.3Gibberellins

16

Inherited Change (A2 Only)

16.1

Passage of Information to Offspring

16.1.1Meiosis 16.1.2Gametogenesis 16.1.3Meiosis & Genetic Diversity

16.2

Genes & 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

16.3

Gene Control

16.3.1lac Operon 16.3.2Transcription Factors 16.3.3Gibberellins & DELLA Proteins

17

Selection & Evolution (A2 Only)

17.1

Variation

17.1.1Phenotypic Variation 17.1.2Continuous & Discontinuous Variation 17.1.3t-Tests

17.2

Natural & 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

17.3

Evolution

17.3.1Evolution by Natural Selection 17.3.2Evidence for Evolution 17.3.3Speciation 17.3.4Extinction

18

Classification & Conservation (A2 Only)

18.1

Biodiversity

18.1.1Key Terms 18.1.2Biodiversity 18.1.3Sampling Methods 18.1.4Correlation 18.1.5Spearman’s Rank 18.1.6Measuring Biodiversity

18.2

Classification

18.2.13-Domain Classification System 18.2.2Linnaean Classification System

18.3

Conservation

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

19

Genetic Technology (A2 Only)

19.1

Manipulating 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

19.2

Genetic 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

19.3

Genetically Modified Organisms in Agriculture

19.3.1GM Crops & Livestock 19.3.2Ethics

Jump to other topics

1

Cell Structure

1.1

Cell 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

2

Biological Molecules

2.1

Testing for Biological Modules

2.1.1Tests for Sugars & Starch 2.1.2Tests for Lipids & Proteins

2.2

Carbohydrates & 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

2.3

Proteins

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

2.4

Water

2.4.1Water Structure & Function 2.4.2End of Topic Test - Water

3

Enzymes

3.1

Enzymes

3.1.1Enzyme Action 3.1.2Factors Affecting Enzyme Activity 3.1.3Factors Affecting Enzyme Activity 2 3.1.4A-A* (AO2/3) - Enzymes

4

Cell Membranes & Transport

4.1

Biological Membranes

4.1.1Fluid Mosaic Model 4.1.2Cell Signalling 4.1.3End of Topic Test - Biological Membranes 4.1.4Exam-Style Question - Membranes

4.2

Movement 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

5

The Mitotic Cell Cycle

5.1

Replication & 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

6

Nucleic Acids & Protein Synthesis

6.1

Nucleic 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

6.2

Protein 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

7

Transport in Plants

7.1

Transport 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

8

Transport in Mammals

8.1

Circulatory System

8.1.1Double Circulation 8.1.2Blood Vessels 8.1.3Important Blood Vessels 8.1.4Blood Cells 8.1.5Tissue Fluid

8.2

Transport of Oxygen & Carbon Dioxide

8.2.1Haemoglobin 8.2.2Oxygen Dissociation

8.3

The Heart

8.3.1Structure of the Heart 8.3.2The Cardiac Cycle 8.3.3Coordination of Heart Action

9

Gas Exchange

9.1

Gas Exchange System

9.1.1Mammalian Gas Exchange 9.1.2Smoking

10

Infectious Diseases

10.1

Infectious Diseases

10.1.1Transmission of Disease 10.1.2Tuberculosis 10.1.3HIV 10.1.4Malaria 10.1.5Cholera 10.1.6Measles

10.2

Antibiotics

10.2.1Antibiotics

11

Immunity

11.1

The Immune System

11.1.1Phagocytes 11.1.2Antigens 11.1.3Lymphocytes 11.1.4Primary & Secondary Response

11.2

Antibodies & 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

12

Energy & Respiration (A2 Only)

12.1

Energy

12.1.1Energy & ATP 12.1.2Respiratory Substrates & Quotient 12.1.3Respirometers

12.2

Respiration

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

13

Photosynthesis (A2 Only)

13.1

Photosynthesis

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

14

Homeostasis (A2 Only)

14.1

Homeostasis

14.1.1Homeostasis 14.1.2Negative Feedback

14.2

The Kidney

14.2.1Kidneys & Osmoregulation

14.3

Cell Signalling

14.3.1Messengers & cAMP

14.4

Blood Glucose Concentration

14.4.1Blood Glucose Concentration 14.4.2Controlling Blood Glucose 14.4.3Urinalysis

14.5

Homeostasis in Plants

14.5.1Stomata & Guard Cells

15

Control & Coordination (A2 Only)

15.1

Control & 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

15.2

Control & Co-Ordination in Plants

15.2.1Venus Flytrap 15.2.2Auixns 15.2.3Gibberellins

16

Inherited Change (A2 Only)

16.1

Passage of Information to Offspring

16.1.1Meiosis 16.1.2Gametogenesis 16.1.3Meiosis & Genetic Diversity

16.2

Genes & 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

16.3

Gene Control

16.3.1lac Operon 16.3.2Transcription Factors 16.3.3Gibberellins & DELLA Proteins

17

Selection & Evolution (A2 Only)

17.1

Variation

17.1.1Phenotypic Variation 17.1.2Continuous & Discontinuous Variation 17.1.3t-Tests

17.2

Natural & 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

17.3

Evolution

17.3.1Evolution by Natural Selection 17.3.2Evidence for Evolution 17.3.3Speciation 17.3.4Extinction

18

Classification & Conservation (A2 Only)

18.1

Biodiversity

18.1.1Key Terms 18.1.2Biodiversity 18.1.3Sampling Methods 18.1.4Correlation 18.1.5Spearman’s Rank 18.1.6Measuring Biodiversity

18.2

Classification

18.2.13-Domain Classification System 18.2.2Linnaean Classification System

18.3

Conservation

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

19

Genetic Technology (A2 Only)

19.1

Manipulating 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

19.2

Genetic 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

19.3

Genetically Modified Organisms in Agriculture

19.3.1GM Crops & Livestock 19.3.2Ethics

Practice questions on Correlation

Can you answer these? Test yourself with free interactive practice on Seneca — used by over 10 million students.

Answer all questions on Correlation

Unlock your full potential with Seneca Premium

Unlimited access to 10,000+ open-ended exam questions
Mini-mock exams based on your study history
Unlock 800+ premium courses & e-books

Get started with Seneca Premium

Sampling Methods

Spearman’s Rank