Working Scientifically: Analysis and Evaluation
Welcome to one of the most exciting parts of science! Doing experiments and collecting numbers is only half the journey. The real magic happens when you look at your results, figure out what they mean, spot patterns, and decide how trustworthy your investigation was. This is called Analysis and Evaluation.
Don't worry if this sounds a bit technical at first — we will break down each step using simple rules, clear examples, and helpful tips!
1. Understanding Variables and Types of Data
Before you can organise your results, you need to understand what you measured.
Types of Variables
In any scientific experiment, you deal with different types of variables:
• Independent Variable: The factor that you deliberately change or choose to test. (Memory trick: I change the Independent variable!)
• Dependent Variable: The factor that you measure to see if it changes because of the independent variable. Its value depends on what you changed.
Types of Data
The type of data you collect determines how you display your findings:
• Categorical or Discrete Data: Data that falls into distinct categories, names, or whole counts. Examples include eye colour (brown, blue, green), blood type, or shoe size. This kind of data is best presented using a bar chart.
• Continuous Data: Numerical measurements that can take any value along a continuous scale. Examples include length, time, and temperature. This kind of data is best presented using a line graph or a scatter plot.
Key Takeaway: Always check your data type first! If it is made of separate categories, make a bar chart. If it is a continuous numerical measurement, make a line graph.
---2. Presenting Data: Tables and Standard Units
A good scientist always records measurements clearly so that anyone else can read and understand them immediately.
Rules for Great Tables
• Left Column: Always put the independent variable in the very first (left-hand) column.
• Right Columns: Put your dependent variable readings (including repeat trials and the calculated mean) in the columns to the right.
• Clear Headers: Every column header must state the name of the quantity and its unit, separated by a slash or brackets. For example: Time / \( \text{s} \) or Length (\( \text{cm} \)).
• No Units in Data Cells: Write units only in the top header, never next to each number inside the table grid.
• Consistent Precision: All raw numbers in the same column should be recorded to the same number of decimal places.
SI Units and Scientific Names
Scientists across the world use standardised units called SI units and standard chemical naming rules (IUPAC nomenclature) so everyone understands each other:
• Length: Metre (\( \text{m} \))
• Mass: Kilogram (\( \text{kg} \))
• Time: Second (\( \text{s} \))
• Electric Current: Ampere (\( \text{A} \))
• Temperature: Kelvin (\( \text{K} \))
Key Takeaway: Keep tables tidy, place the independent variable on the left, and always include units in the headers using SI standards.
---3. Mathematical Calculations and Statistics
Once you have gathered your raw data, you need to calculate statistical values to understand your results.
Measures of Central Tendency and Spread
• Mean (Average): The sum of your concordant (matching) values divided by the number of concordant values.
\( \text{Mean} = \frac{\text{Sum of concordant values}}{\text{Number of concordant values}} \)
Crucial Rule: Always identify and remove anomalies (outliers) before calculating the mean!
• Median: The middle number when all values are placed in order from smallest to largest.
• Mode: The number that appears most frequently in a dataset.
• Range: The spread of your data, calculated as the highest value minus the lowest value:
\( \text{Range} = \text{Maximum} - \text{Minimum} \)
Step-by-Step Example: Calculating the Mean
Imagine you timed how long it took a trolley to roll down a ramp over four trials:
Trial 1: \( 4.2\text{ s} \), Trial 2: \( 4.3\text{ s} \), Trial 3: \( 7.9\text{ s} \), Trial 4: \( 4.1\text{ s} \).
Step 1: Spot any anomalies. Notice that \( 7.9\text{ s} \) is much higher than the other values. It does not fit the pattern, so it is an anomaly.
Step 2: Cross out the anomaly. Ignore \( 7.9\text{ s} \).
Step 3: Calculate the mean of the remaining concordant values:
\( \text{Mean} = \frac{4.2 + 4.3 + 4.1}{3} = \frac{12.6}{3} = 4.2\text{ s} \)
Key Takeaway: Never include an anomaly when working out your mean! Strike it out first and divide only by the number of valid trials left.
---4. Drawing Accurate Graphs
Graphs provide a visual snapshot of your data, making patterns easy to see.
Graph Drawing Checklist
• Axes: Plot the independent variable on the horizontal x-axis and the dependent variable on the vertical y-axis. Label both axes clearly with quantity names and units.
• Scale: Choose a regular, linear scale that goes up in sensible steps (such as \( 1 \), \( 2 \), \( 5 \), or \( 10 \)). Your plotted points should take up more than \( 50\% \) of the graph grid.
• Plotting: Mark each data point precisely with a small, neat '\( \times \)' or a circled dot.
• Line of Best Fit: Draw a single, smooth line (straight with a ruler, or a smooth curve) that follows the general trend of your points, balancing an equal number of points above and below the line. Ignore any anomalies when drawing your line.
Common Mistake Alert!
Never join points dot-to-dot with a jagged line! In science, you must always draw a smooth line of best fit.
Key Takeaway: Independent on the x-axis, dependent on the y-axis, use at least half the page, and draw a smooth line of best fit.
---5. Interpreting Patterns and Drawing Conclusions
Drawing a conclusion means using your data and graph to answer your original question or test your hypothesis.
Describing Relationships
When describing a pattern from a graph, be specific about what happens to both variables:
• Positive Correlation: As the independent variable increases, the dependent variable also increases.
• Negative Correlation: As the independent variable increases, the dependent variable decreases.
• No Correlation: There is no clear pattern or relationship between the two variables.
Correlation vs. Causation
Did you know? Just because two things change together (correlation), it does not automatically prove that one causes the other (causation)!
For example, ice cream sales and sunburn rates both increase in the summer. Eating ice cream does not cause sunburn; both are caused by hot, sunny weather (a third, confounding factor).
Key Takeaway: A strong scientific conclusion describes the exact pattern shown by the data, explains how the results relate to the prediction, and considers whether one factor truly caused the change.
---6. Quality of Evidence: Accuracy, Precision, and Reliability
Scientists must judge how dependable their results are. Although people often mix up these terms in everyday conversation, in science they have very precise meanings!
Accuracy vs. Precision
• Accuracy: How close a measured value is to the true or accepted value.
• Precision: How close repeated measurements are to each other (having a very small range across repeats).
Analogy: Imagine throwing darts at a dartboard. If all your darts land tightly clustered together in the top-left corner far from the bullseye, your throws are precise but inaccurate. If your darts land in the bullseye, they are accurate.
Repeatability vs. Reproducibility
• Repeatable: An experiment is repeatable if the same investigator repeats the investigation using the same method and equipment and gets concordant (very close) results.
• Reproducible: An experiment is reproducible if a different investigator, or someone using different equipment or techniques, repeats the test and gets the same conclusions.
Key Takeaway: Precision means repeats are close together; accuracy means measurements are close to the true value. Repeatable means you can do it again; reproducible means others can do it too.
---7. Evaluating Errors and Suggesting Improvements
Evaluating an experiment means finding weaknesses in your method or equipment, explaining errors, and identifying new questions to investigate next.
Types of Experimental Errors
• Random Errors: Unpredictable variations that happen during an experiment. They can be caused by slight changes in room temperature, human reaction time with a stopwatch, or reading a scale from slightly different angles (parallax error).
How to reduce random errors: Take multiple repeat readings and calculate a mean value.
• Systematic Errors: Consistent, repeatable errors that shift every single reading in the same direction by the same amount. They are caused by faulty equipment or flawed experimental techniques.
Example: A zero error, which happens when a mass balance reads \( 0.2\text{ g} \) even when nothing is on it, making every measurement \( 0.2\text{ g} \) too heavy.
How to fix systematic errors: Recalibrate your equipment or adjust your experimental technique. (Taking a mean will not fix a systematic error!).
• Anomalous Results: A measurement that does not fit the general pattern of the rest of the dataset. Identify anomalies, circle them, and leave them out of your mean calculations.
How to Write a High-Scoring Evaluation
Avoid vague statements like "it was human error" or "I should measure more carefully". Instead, write specific, practical improvements:
• Instead of: "My timer was inaccurate."
• Write: "Using a manual stopwatch introduced random error due to human reaction time. To improve this, I could use light gates connected to a digital datalogger."
• Instead of: "Heat was lost."
• Write: "Heat was lost to the surroundings through the sides of the beaker. To improve accuracy, I could insulate the beaker with cotton wool and add a lid."
Key Takeaway: Name the specific error (random or systematic), explain how it affected your data, and describe an actionable, realistic equipment or method improvement.
---Quick Summary Checklist
✓ Data & Tables: Put the independent variable on the left, dependent on the right, and units only in headers.
✓ Calculations: Spot and remove anomalies before calculating the mean.
✓ Graphs: Use a regular scale covering \( >50\% \) of the grid, plot points with an '\( \times \)', and draw a smooth line of best fit.
✓ Accuracy vs. Precision: Accuracy is closeness to the true value; precision is closeness of repeats to one another.
✓ Errors: Random errors are reduced by repeats and means; systematic errors (like zero errors) require equipment calibration and method fixes.