Data Analysis for A Level Biology

What does Standard Deviation (SD) measure?

• It measures the spread (or dispersion) of data around the mean.

Why is Standard Deviation considered a better measure of dispersion than the Range?

• SD uses all the data points, whereas the range only uses the highest and lowest values.

• SD is less affected by anomalies (outliers) than the range.

• SD reveals the spread around the mean, giving an indication of reliability.

When interpreting a graph, what conclusion should you draw if the error bars of two data sets overlap?

• There is no significant difference between the means.

• Any difference observed is likely due to chance.

• (Therefore, you cannot claim that the independent variable caused the change).

When interpreting a graph, what conclusion should you draw if the error bars do not overlap?

• There is a significant difference between the means.

• The difference is likely not due to chance.

• (You can likely claim the independent variable had an effect).

Which statistical test would you use to confirm if a difference between two means (with known SD) is significant?

• The Student's t-test (unpaired if separate groups, paired if same individuals before/after).

Question 1 (Evaluate - The "Overlap" Trap) A student investigated the effect of fertilizer on plant height. Group A (Fertilizer): Mean height = 45cm (± 5cm SD). Group B (No Fertilizer): Mean height = 38cm (± 4cm SD). The student concludes that the fertilizer significantly increased plant growth. Evaluate this conclusion.

• Calculation: Group A range is 40-50 (45 ± 5). Group B range is 34-42 (38 ± 4).

• Observation: The error bars (spread) overlap (between 40 and 42).

• Conclusion: The student is incorrect. Because the bars overlap, there is likely no significant difference between the means. The difference in height could be due to chance.

Question 2 (Explain) The standard deviation for the rate of reaction at 60°C is much larger than the standard deviation at 30°C. Explain what this indicates about the data at 60°C.

• The data at 60°C is more spread out / less consistent around the mean.

• This suggests the results at 60°C are less repeatable / less reliable.

• (This might be due to the difficulty of measuring fast rates or rapid denaturation).

Question 3 (Suggest) A researcher presents mean values for blood glucose levels but does not include standard deviation or range. Suggest why this makes it difficult to evaluate their results.

• We cannot see the spread of the data.

• We cannot identify if there were any anomalies (outliers).

• We cannot determine if the differences between the means are significant (cannot check for overlap).

Question 4 (Maths Skill) The formula for Standard Deviation is provided in the exam: see below . Explain what the term (n - 1) represents and why it is used

s = \sqrt{\frac{\sum(x - \bar{x})^2}{n - 1}}

• n represents the sample size (number of data points).

• (n - 1) represents the degrees of freedom.

• It is used to calculate the variance for a sample (rather than a whole population).

Question 5 (Application) You are designing an experiment to measure the effect of caffeine on heart rate. You plan to use the t-test to analyse your results. What condition must your data meet to use a t-test?

• The data must be continuous (heart rate is a continuous variable).

• The data should be normally distributed.

• You are comparing two means (e.g., Mean Heart Rate with Caffeine vs Mean Heart Rate without).