5.3.3Tools
Processing Uncertainties in Biology — IB Biology SL Revision Notes & Topical Questions
5 min read 6 parts Lesson 9 of 10
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Part 1 of 6Uncertainty and Error
Uncertainty
- Uncertainty The range around a measurement within which the true value is expected to lie, written with a ± sign.
Error
- Error The difference between a measured value and the true value, caused by equipment or technique.
Analogue reading
- Analogue reading The uncertainty is normally half of the smallest scale division, for example ±0.05 cm³ on a 0.1 cm³ scale.
Precision
- Precision Processed values should not have more decimal places than the original measurements.
Part 2 of 6Error Bars and Fit
Error Bars and Fit
Error bars
- Error bars They are drawn above and below a point to show range, standard deviation or standard error, and the key must state which.
Overlap
- Overlap When error bars of standard deviation overlap, the difference between the means is probably not significant.
R²
- R² The coefficient of determination shows how well a trend line fits data;
- values near 1 mean a good fit and near 0 mean none.
Fit is not proof
- Fit is not proof A high R² does not prove that the model is correct or that one variable causes the other.
Part 3 of 6Correlation
1
Correlation is an association between two variables, and may be positive or negative.
2
The correlation coefficient r runs from −1 to +1, and values near the ends show a strong linear relationship.
3
A value near 0 shows little or no linear relationship between the variables.
4
A strong correlation does not show causation, because a third factor may influence both variables.
5
Causation needs evidence such as controlled experiments or a known mechanism.
Part 4 of 6Statistical Tests
Null hypothesis
- Null hypothesis States that there is no significant difference or association between the variables being tested.
t-test
- t-test Compares the means of two data sets to see whether they differ significantly.
Chi-squared test
- Chi-squared test Compares observed and expected frequencies, for example in a genetic cross or in the association between species.
Decision
- Decision If the calculated value is lower than the critical value at p = 0.05, the null hypothesis is not rejected,
- so any difference may be due to chance.
| Question | Suitable test |
|---|---|
| Do two means differ? | t-test |
| Are variables correlated? | Correlation coefficient |
| Do observed counts fit expected counts? | Chi-squared |
Part 5 of 6Worked Example
Question
- A cross between two heterozygous tall pea plants gave 290 tall and 110 dwarf offspring from 400.
- Test the fit with the expected 3:1 ratio.
- The critical value for one degree of freedom at p = 0.05 is 3.84.
- Expected valuestall 300 and dwarf 100.
- χ² = Σ (O − E)² ÷ E.
- Tall
- (290 − 300)² ÷ 300 = 100 ÷ 300 = 0.333;
- dwarf: (110 − 100)² ÷ 100 = 1.00.
- (290 − 300)² ÷ 300 = 100 ÷ 300 = 0.333;
- Total χ² = 1.33 with two categories, so 1 degree of freedom.
- 1.33 is less than 3.84.
Answer The difference is not significant, so the null hypothesis is not rejected and the data fit a 3:1 ratio.
Part 6 of 6Exam Checklist & Tips
5.3.3 – Key Points for the Exam
- Uncertainty Range around a measurement within which the true value is expected to lie.
- Error bar A bar on a graph showing uncertainty or variability.
- Correlation coefficient A value from −1 to +1 showing strength of linear association.
- Null hypothesis Statement of no significant difference or association.
- Degrees of freedom Number of categories minus one in a chi-squared test.
Common Mistakes
- Using the words error and uncertainty as if they meant the same.
- Assuming a strong correlation proves a causal link.
- Forgetting to state what the error bars represent.
- Saying the null hypothesis is proven true when it is not rejected.
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