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5.3.3Tools

Processing Uncertainties in Biology — IB Biology SL Revision Notes & Topical Questions

5 min read 6 parts Lesson 9 of 10

📚 IB Biology SL Hub / Topical Revision
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Part 1 of 6Uncertainty and Error

5.3.3 Processing Uncertainties in Biology
Uncertainty
  • The range around a measurement within which the true value is expected to lie, written with a ± sign.
Error
  • The difference between a measured value and the true value, caused by equipment or technique.
Analogue reading
  • The uncertainty is normally half of the smallest scale division, for example ±0.05 cm³ on a 0.1 cm³ scale.
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
  • They are drawn above and below a point to show range, standard deviation or standard error, and the key must state which.
Overlap
  • When error bars of standard deviation overlap, the difference between the means is probably not significant.
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
  • 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
  • States that there is no significant difference or association between the variables being tested.
t-test
  • Compares the means of two data sets to see whether they differ significantly.
Chi-squared test
  • Compares observed and expected frequencies, for example in a genetic cross or in the association between species.
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.
QuestionSuitable 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.

  1. Expected valuestall 300 and dwarf 100.
  2. χ² = Σ (O − E)² ÷ E.
  3. Tall
    • (290 − 300)² ÷ 300 = 100 ÷ 300 = 0.333;
      • dwarf: (110 − 100)² ÷ 100 = 1.00.
  4. Total χ² = 1.33 with two categories, so 1 degree of freedom.
  5. 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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