17.1.417-18 · Selection, Evolution, Classification and Conservation
Variation- t-test Worked Example — Cambridge AS & A Level Biology 9700 Revision Notes & Topical Questions
5 min read 9 parts Lesson 5 of 36 1 quiz
Lesson summary
17.1.4 Variation: Applying the t-test — CAMBRIDGE AS & A LEVEL BIOLOGY 9700 — REVISION NOTES notes: Apply the t-test to a comparison of two samples, from hypotheses and means to degrees of freedom and a conclusion.Use the t-test when two samples of continuous measurements are compared, e.g.
- Null hypothesis
- Standard deviation
- Critical value
- Error bars
- Record the sample sizes n1 and n2 for the two populations
- Add up all the values in each sample
Part 1 of 7Setting up the comparison
Setting up the comparison
Use the t-test when two samples of continuous measurements are compared, e.g. a characteristic measured in two populations.
Record the sample sizes n1 and n2 for the two populations.
State the null hypothesis first.
- There is no significant difference between the means of the measurements in populations 1 and 2.
Part 2 of 7Calculating the means
Calculating the means
Add up all the values in each sample.
Divide each total by its number of values to give x̄1 and x̄2.
Record the difference between the two means, which forms the top of the t formula.
Part 3 of 7Calculating the standard deviations
1
Subtract the sample mean from each value in the sample (x − x̄).
2
Square each difference, which removes negative signs.
3
Add the squared differences to give Σ(x − x̄)2.
4
Divide the sum by n − 1 to give the variance.
5
Take the square root of the variance to give the standard deviation s.
6
Repeat for the second sample.
Part 4 of 7Calculating t and degrees of freedom
1
Square each standard deviation and divide by its sample size.
2
Add the two results and take the square root.
3
Divide the difference between the means by this value to give t.
4
Calculate degrees of freedom: ν = (n1 − 1) + (n2 − 1).
Part 5 of 7Reaching the conclusion
1
Find the critical value of t for the calculated degrees of freedom at p = 0.05 in the table.
2
Compare the calculated t with the critical value.
- If t is less than the critical value, the null hypothesis is accepted.
- If t is greater than or equal to the critical value, the null hypothesis is rejected.
3
When t is below the critical value, the differences between the means are due to chance and there is no significant difference between the populations.
4
When t is above it, there is a significant difference and the probability that chance caused it is below 5%.
5
Write the conclusion in terms of the characteristic measured.
Part 6 of 7Evaluating and presenting the investigation
1
Present the working in a table with the mean, standard deviation, n, t, degrees of freedom and critical value.
2
A bar chart of means with error bars showing standard deviation suits two categories of continuous data.
- Widely separated error bars suggest a significant difference.
- Overlapping error bars suggest the difference may not be significant.
3
Evaluate the method by commenting on sample size, random sampling and control of other variables.
4
A significant difference shows a difference exists but does not by itself prove the cause.
Part 7 of 7More from the specification
More from the specification
Genetic vs. Environmental Variation in Phenotype
- An organism's observable phenotype results from the interaction between its genetic makeup and environmental factors such as diet, temperature,
- (alleles inherited from parents)
- and climate.
Continuous vs. Discontinuous Variation
- Discontinuous variation is qualitative, controlled by one or few genes,
- and unaffected by the environment,
- (e.g., ABO blood groups)
- whereas continuous variation is polygenic, quantitative,
- and significantly influenced by the environment.
- (e.g., height in humans)
Student's t-Test for Comparing Sample Means
- The Student's t-test statistically compares the mean values of continuous phenotypic measurements between two independent populations to determine whether the observed difference between individuals is statistically significant or due to chance.
Role of Mutation in Generating Genetic Diversity
- Random mutations in DNA nucleotide sequences create new alleles, providing the raw genetic variation upon which natural selection acts within a species.
Quantitative
- Measured with numbers
Genetic variation
- Differences in alleles within a population.
Discontinuous variation
- A limited number of distinct phenotypes with no intermediates.
Additive effect
- Combined effect of several genes or alleles adding together to determine a phenotype.
Statistically significant
- A difference with a probability of less than 5% of being due to chance.
Blood group
- A phenotype set by alleles I-A, I-B and I-O.
Phenotype
- The observable characteristic.
Allele
- A version of a gene.
Species
- A group of organisms that can reproduce to produce fertile offspring.
Gamete
- A haploid sex cell.
Organism
- A living thing, such as a plant or an animal.
Chromosome
- A thread-like structure of DNA carrying genes.
Additive
- Substance added to food.
Qualitative
- A result describing presence or absence rather than amount.
Key terms
| Term | Meaning |
|---|---|
| Null hypothesis | Statement that there is no significant difference between the means. |
| Mean | The sum of all values divided by the number of values. |
| Standard deviation | Square root of the sum of squared deviations divided by n − 1. |
| Degrees of freedom | (n1 − 1) + (n2 − 1) for two samples. |
| Critical value | Table value of t at p = 0.05 used to judge significance. |
| Error bars | Bars on a graph showing the spread, e.g. one standard deviation, around a mean. |
Avoid these mistakes
1
Dividing the sum of squares by n instead of n − 1 — the standard deviation uses n − 1.
2
Calculating degrees of freedom as n1 + n2 — it is (n1 − 1) + (n2 − 1).
3
Rejecting the null hypothesis when t is below the critical value — it is rejected only when t is equal to or above it.
4
Forgetting to state the conclusion in terms of the investigation — say whether the means differ significantly.
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