17.1.3

t-Tests

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Hypothesis Testing

A hypothesis is an assumption made about the value of a particular parameter. We can use a tt-test to determine whether the difference between the means of two populations are statistically significant.

Null and alternative hypotheses

Null and alternative hypotheses

  • The null hypothesis, H0H_0, is a hypothesis that is assumed to be correct. In a tt-test, the null hypothesis is that there is no significant difference between the two population means.
  • The alternative hypothesis, H1H_1 is that there is a significant difference between the two population means.
  • A decision is then made as to whether or not there is sufficient evidence to reject the null hypothesis.
$$p$$-value

pp-value

  • In order to test a hypothesis, we consider how likely the hypothesis is to be true.
  • The probability of the null hypothesis being true is referred to as the pp-value.
Significance level

Significance level

  • If the probability of the null hypothesis being true is less likely than a given "significance level", we reject the null hypothesis.
  • The significance level used in biology is often 5%.
Test statistic

Test statistic

  • The test statistic used to calculate pp-values is equal to:
    • t=x‾1−x‾2s12n1+s22n2t = \frac{\large\overline{x}_1-\overline{x}_2}{\large \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}
    • x‾1\overline{x}_1 = is the mean of sample one.
    • x‾2\overline{x}_2 = is the mean of sample two.
    • s1s_1 is the standard deviation of sample one.
    • s2s_2 is the standard deviation of sample two.
    • n1n_1 is the number of measures in sample one.
    • n1n_1 is the number of measures in sample two.
Degrees of freedom

Degrees of freedom

  • The degrees of freedom is equal to n1+n2−2n_1+n_2-2.
Determine the critical value

Determine the critical value

  • Once you have determined the value of the test statistic, you need to use a statistics table to determine the critical value.
  • The critical value will be the value at the significance level (5%) of your particular degrees of freedom.
    • If the calculated value is greater than the critical value, you reject the null hypothesis.
    • If the calculated value is less than the critical value, you accept the null hypothesis.
Jump to other topics
1

Cell Structure

1.1

Cell Structure

1.1.1Studying Cells - Microscopes1.1.2Introduction to Eukaryotic & Prokaryotic Cells1.1.3Ultrastructure of Eukaryotic Cells1.1.4Ultrastructure of Eukaryotic Cells 21.1.5Ultrastructure of Eukaryotic Cells 31.1.6Prokaryotic Cells1.1.7Viruses1.1.8End of Topic Test - Cell Structure1.1.9Exam-Style Question - Microscopes1.1.10A-A* (AO2/3) - Cell Structure
2

Biological Molecules

2.1

Testing for Biological Modules

2.1.1Tests for Sugars & Starch2.1.2Tests for Lipids & Proteins
2.2

Carbohydrates & Lipids

2.2.1Monomers & Polymers2.2.2Carbohydrates2.2.3Examples of Carbohydrates2.2.4Triglycerides & Phospholipids2.2.5Types of Fatty Acids2.2.6Exam-Style Question - Carbohydrates2.2.7End of Topic Test - Carbohydrates & Lipids
2.3

Proteins

2.3.1Amino Acids & Overview of Protein Structure2.3.2Primary & Secondary Structure2.3.3Tertiary & Quaternary Structure2.3.4Globular & Fibrous Proteins2.3.5Haemoglobin2.3.6Collagen2.3.7End of Topic Test - Proteins
2.4

Water

2.4.1Water Structure & Function2.4.2End of Topic Test - Water
3

Enzymes

3.1

Enzymes

3.1.1Enzyme Action3.1.2Factors Affecting Enzyme Activity3.1.3Factors Affecting Enzyme Activity 23.1.4A-A* (AO2/3) - Enzymes
4

Cell Membranes & Transport

4.1

Biological Membranes

4.1.1Fluid Mosaic Model4.1.2Cell Signalling4.1.3End of Topic Test - Biological Membranes4.1.4Exam-Style Question - Membranes
4.2

Movement Into & Out of Cells

4.2.1Passive Movement Across the Membrane4.2.2Active Movement Across the Membrane4.2.3Osmosis4.2.4Osmosis & Plant Cells4.2.5Surface Area to Volume Ratio4.2.6Adaptions to Surface Area to Volume Ratio4.2.7Calculations - Volume4.2.8Calculations - Surface Area
5

The Mitotic Cell Cycle

5.1

Replication & Division of Nuclei

5.1.1Chromosomes5.1.2The Cell Cycle5.1.3Mitosis5.1.4Role of Mitosis5.1.5Stem Cells5.1.6Mitosis & Cancer5.1.7End of Topic Test - Replication & Division5.1.8A-A* (AO2/3) - Cell Cycle & Transport
6

Nucleic Acids & Protein Synthesis

6.1

Nucleic Acids

6.1.1Introduction to DNA & RNA6.1.2Nucleotides6.1.3Polynucleotides6.1.4ADP & ATP6.1.5DNA6.1.6DNA Replication6.1.7RNA6.1.8End of Topic Test - Nucleic Acids & ATP
6.2

Protein Synthesis

6.2.1The Genetic Code6.2.2Polypeptide Synthesis6.2.3RNA Processing in Eukaryotes6.2.4Mutations6.2.5Exam-Style Question - Protein Synthesis6.2.6A-A* (AO2/3) - Coronavirus Translation
7

Transport in Plants

7.1

Transport in Plants

7.1.1Plant Vessels7.1.2Xylem7.1.3Investigating Transpiration7.1.4Adaptations to Water Availability7.1.5Phloem7.1.6End of Topic Test - Transport in Animals & Plants7.1.7A-A* (AO2/3) - Transport in Animals & Plants
8

Transport in Mammals

8.1

Circulatory System

8.1.1Double Circulation8.1.2Blood Vessels8.1.3Important Blood Vessels8.1.4Blood Cells8.1.5Tissue Fluid
8.2

Transport of Oxygen & Carbon Dioxide

8.2.1Haemoglobin8.2.2Oxygen Dissociation
8.3

The Heart

8.3.1Structure of the Heart8.3.2The Cardiac Cycle8.3.3Coordination of Heart Action
9

Gas Exchange

9.1

Gas Exchange System

9.1.1Mammalian Gas Exchange9.1.2Smoking
10

Infectious Diseases

10.1

Infectious Diseases

10.1.1Transmission of Disease10.1.2Tuberculosis10.1.3HIV10.1.4Malaria10.1.5Cholera10.1.6Measles
10.2

Antibiotics

10.2.1Antibiotics
11

Immunity

11.1

The Immune System

11.1.1Phagocytes11.1.2Antigens11.1.3Lymphocytes11.1.4Primary & Secondary Response
11.2

Antibodies & Vaccination

11.2.1Antibodies11.2.2Monoclonal Antibodies11.2.3Immunity11.2.4Vaccines11.2.5Exam-Style Question - Immune System11.2.6A-A* (AO2/3) - Disease & Immune System
12

Energy & Respiration (A2 Only)

12.1

Energy

12.1.1Energy & ATP12.1.2Respiratory Substrates & Quotient12.1.3Respirometers
12.2

Respiration

12.2.1Introduction to Respiration12.2.2Anaerobic Respiration12.2.3Aerobic Respiration12.2.4Chemiosmosis & Coenzymes12.2.5Mitochondria12.2.6Respiration Experiments12.2.7End of Topic Test - Respiration12.2.8A-A* (AO3/4) - Respiration
13

Photosynthesis (A2 Only)

13.1

Photosynthesis

13.1.1Introduction to Photosynthesis13.1.2Light-Dependent Reactions13.1.3Light-Independent Reactions13.1.4Limiting Factors13.1.5Investigating Photosynthesis13.1.6End of Topic Test - Photosynthesis13.1.7A-A* (AO3/4) - Photosynthesis
14

Homeostasis (A2 Only)

14.1

Homeostasis

14.1.1Homeostasis14.1.2Negative 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 Concentration14.4.2Controlling Blood Glucose14.4.3Urinalysis
14.5

Homeostasis in Plants

14.5.1Stomata & Guard Cells
15

Control & Coordination (A2 Only)

15.1

Control & Coordination in Mammals

15.1.1Neurones15.1.2Receptors15.1.3Taste15.1.4Reflexes15.1.5Action Potentials15.1.6Saltatory Conduction15.1.7Synapses15.1.8Cholinergic Synnapses15.1.9Neuromuscular Junction15.1.10Skeletal Muscle15.1.11Sliding Filament Theory Contraction15.1.12Sliding Filament Theory Contraction 215.1.13Menstruation15.1.14Contraceptive Pill
15.2

Control & Co-Ordination in Plants

15.2.1Venus Flytrap15.2.2Auixns15.2.3Gibberellins
16

Inherited Change (A2 Only)

16.1

Passage of Information to Offspring

16.1.1Meiosis16.1.2Gametogenesis16.1.3Meiosis & Genetic Diversity
16.2

Genes & Phenotype

16.2.1Key Terms in Genetics16.2.2Inheritance16.2.3Linkage16.2.4Multiple Alleles16.2.5Chi-Squared Test16.2.6Mutations16.2.7Specific Mutations16.2.8End of Topic Test - Genetics16.2.9A-A* (AO2/3) - Genetics
16.3

Gene Control

16.3.1lac Operon16.3.2Transcription Factors16.3.3Gibberellins & DELLA Proteins
17

Selection & Evolution (A2 Only)

17.1

Variation

17.1.1Phenotypic Variation17.1.2Continuous & Discontinuous Variation17.1.3t-Tests
17.2

Natural & Artificial Selection

17.2.1Natural Selection & Evolution17.2.2Types of Selection17.2.3Types of Selection Summary17.2.4Genetic Drift & Founder Effect17.2.5Populations17.2.6Hardy-Weinberg Principle17.2.7Artificial Selection
17.3

Evolution

17.3.1Evolution by Natural Selection17.3.2Evidence for Evolution17.3.3Speciation17.3.4Extinction
18

Classification & Conservation (A2 Only)

18.1

Biodiversity

18.1.1Key Terms18.1.2Biodiversity18.1.3Sampling Methods18.1.4Correlation18.1.5Spearman’s Rank18.1.6Measuring Biodiversity
18.2

Classification

18.2.13-Domain Classification System18.2.2Linnaean Classification System
18.3

Conservation

18.3.1Importance of Biodiversity18.3.2Conservation18.3.3Zoos, Seedbanks, & Other Conservation Methods18.3.4Assisted Reproduction & Contraception18.3.5Non-Governmental Organisations
19

Genetic Technology (A2 Only)

19.1

Manipulating Genomes

19.1.1Recombinant DNA & Genetic Engineering19.1.2Restriction Endonucleases19.1.3Gel Electrophoresis19.1.4DNA Probes & Microarrays19.1.5End of Topic Test - Manipulating Genomes19.1.6A-A* (AO2/3) - Manipulating Genomes
19.2

Genetic Technology Applied to Medicine

19.2.1Bioinformatics19.2.2Applications of Recombinant DNA19.2.3Genetic Screening19.2.4Gene Therapy19.2.5Ethics19.2.6DNA Profiling & Forensics
19.3

Genetically Modified Organisms in Agriculture

19.3.1GM Crops & Livestock19.3.2Ethics

Practice questions on t-Tests

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  1. 1
    Which symbol denotes the alternative hypothesis?Multiple choice
  2. 2
    What is the probability of the null hypothesis being true called?Multiple choice
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Continuous & Discontinuous Variation

Natural Selection & Evolution