Introduction to Analysis of Experimental Results

Welcome to one of the most important parts of your Biology A Level! Once you have finished an experiment and collected your data, you are left with "raw data"—a collection of numbers or observations that don't tell a story yet. Analysis is the process of cleaning up that data, performing calculations, and drawing graphs so you can actually see what happened. Think of it as turning a pile of ingredients into a finished meal.

In this chapter, we focus on Module 1.1.3. We will look at how to handle significant figures, how to calculate biological values like rates and ratios, and how to present your findings so that anyone else can understand your hard work.

1. Handling Quantitative Data: The Basics

Most of your data will be quantitative (numerical). To make sense of it, we need to use some standard mathematical tools.

Significant Figures (M1.1)

One of the most common places students lose marks is by using too many or too few decimal places. The "golden rule" in OCR Biology is: Your processed data (the answer) should be given to the same number of significant figures as the raw data with the least number of significant figures.

Example: If you are calculating the mean of \( 2.1 \), \( 2.0 \), and \( 2.45 \), your answer should be to two significant figures (like the \( 2.1 \)) because that is your least precise measurement.

Standard Form (M0.1)

In biology, we deal with very big things (like populations) and very small things (like cells). Standard form makes these easier to write.
\( \text{Number} \times 10^n \)

Example: A red blood cell is approximately \( 0.000007 \text{ m} \) wide. In standard form, we write this as \( 7 \times 10^{-6} \text{ m} \).

Calculating Means and Percentages

The Arithmetic Mean (M1.2): Add all your repeats together and divide by the number of repeats. Don't forget to exclude any anomalies (results that clearly don't fit the pattern) before calculating the mean!

Percentage Change: This is vital for seeing how much a variable has increased or decreased relative to where it started.
\( \text{Percentage Change} = \frac{\text{new value} - \text{original value}}{\text{original value}} \times 100 \)

Quick Tip: If the answer is negative, it’s a percentage decrease. If positive, it’s a percentage increase!

2. The Biological "Recall" Formulas

According to your syllabus, there are several formulas you must be able to remember and use without being given them in the exam.

Magnification

\( \text{Magnification} = \frac{\text{image size}}{\text{actual size}} \)

Remember the "IAM" triangle! Always make sure your units for image size and actual size are the same (usually micrometres \( \mu\text{m} \)) before you divide.

Rates of Reaction

A "rate" tells you how fast something is happening.
\( \text{Rate} = \frac{1}{\text{time taken}} \) or \( \text{Rate} = \frac{\text{change in quantity}}{\text{time taken}} \)

Temperature Coefficient (\( Q_{10} \))

This shows how much the rate of a reaction increases when the temperature is raised by \( 10^\circ\text{C} \).
\( Q_{10} = \frac{\text{rate at } (T + 10)^\circ\text{C}}{\text{rate at } T^\circ\text{C}} \)

Cardiac Output

Used when studying the heart in Module 3.
\( \text{Cardiac Output} = \text{heart rate} \times \text{stroke volume} \)

Respiratory Quotient (\( RQ \))

Used to see which substrate (carbs, lipids, or proteins) an organism is respiring.
\( RQ = \frac{\text{CO}_2 \text{ produced}}{\text{O}_2 \text{ consumed}} \)

3. Plotting and Interpreting Graphs

Graphs are the best way to see a trend or correlation in your results. Here is what you need to master:

The "SLAP" Checklist for Graphs

When drawing a graph, remember:

  • S (Scale): It must fill at least half the provided grid.
  • L (Lines): Use a sharp pencil. For line graphs, join points with straight ruled lines or a smooth curve of best fit.
  • A (Axes): The Independent Variable (what you changed) goes on the x-axis. The Dependent Variable (what you measured) goes on the y-axis.
  • P (Points): Plot accurately with small "x" or a dot in a circle.

Interpreting the Slope (M3.5 & M3.6)

A straight line can be described by the equation \( y = mx + c \), where \( m \) is the gradient (the rate).
To find the gradient of a curve at a specific point, you must draw a tangent (a straight line that just touches the curve at that point) and calculate the gradient of that straight line using:
\( \text{Gradient} = \frac{\text{change in } y}{\text{change in } x} \)

Did you know? The steeper the gradient, the faster the rate of reaction at that specific moment.

4. Using Statistical Tests

In your exam, some complex formulas are provided for you (like Chi-squared and Spearman’s Rank). You don't need to memorize the formula, but you do need to know when to use which tool.

Which test should I use?
  • Chi-squared (\( \chi^2 \)): Use this when you have categorical data (counts of things) and you want to see if the "observed" results match the "expected" results (e.g., genetics crosses).
  • Student’s t-test: Use this when you want to compare the means of two sets of data to see if there is a significant difference between them.
    • Paired t-test: Comparing the same group before and after.
    • Unpaired t-test: Comparing two different groups.
  • Spearman’s Rank Correlation: Use this to see if there is a relationship/correlation between two variables (e.g., as light intensity increases, does the height of the plant increase?).
  • Simpson’s Index of Diversity (\( D \)): Used to measure the biodiversity of a habitat.

Analysis isn't just about math; it's about looking at the data critically.

Anomalies: These are data points that lie far outside the range of other repeats. When you find one, you should identify it and investigate why it happened. Don't just ignore it! In a calculation, you should usually leave it out of the mean.

Correlations:
- Positive correlation: As \( x \) increases, \( y \) increases.
- Negative correlation: As \( x \) increases, \( y \) decreases.
- No correlation: There is no clear relationship between the variables.

Note: Just because two things are correlated doesn't mean one caused the other! (Correlation does not equal causation).

Summary Checklist

Key Takeaways:
1. Always match your significant figures to the least precise raw data.
2. Use the Percentage Change formula to compare results of different starting sizes.
3. Practice drawing tangents to calculate the rate on a curved graph.
4. Be ready to use formulas like Magnification and RQ from memory.
5. Choose the right statistical test based on whether you are comparing means, looking for a correlation, or checking frequencies.

Don't worry if the math feels heavy at first. In Biology, the math is just a tool to help us understand the living world. Keep practicing the "recall" formulas, and the rest will follow!