IBPhysicsDPSLRevision NotesInquiry ProcessInquiry 2: Collecting and Processing Data in PhysicsInterpreting results in Physics

Interpreting results in Physics (DP IB Physics): Revision Note

Katie M

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Katie M

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DP Physics: SLDP Physics: HL

Interpreting results in Physics

  • This is the "sense-making" phase of your investigation, where you analyse your processed data to find patterns, trends, and relationships

  • The primary goal is to determine what your results are telling you so that you can answer your research question

  • This almost always involves creating a graph to visualise the relationship between your independent and dependent variables

Principles of interpretation

Interpret qualitative and quantitative data

  • Your qualitative observations are crucial evidence to help explain your quantitative results.

  • For example:

    • Your calculated value for the resistivity of a wire is higher than the accepted data booklet value

    • Your qualitative observation that "the wire felt warm to the touch after several measurements" is the perfect piece of evidence to explain why

    • The heating effect of the current increased the temperature of the wire, which in turn increased its resistance, leading to a higher calculated resistivity

Interpret diagrams, graphs and charts

  • Once a line of best fit is drawn, the following features of the graph may provide important information:

    • The gradient (slope):

      • This can represent a key physical quantity

      • For a graph of I vs. V for an ohmic resistor, the gradient is the reciprocal of the resistance 1 over R

    • The y-intercept:

      • This shows the value of the dependent variable when the independent variable is zero

      • It can often reveal systematic errors, like a zero error on a sensor

    • The area under the curve:

      • This can represent a total quantity, such as the displacement from a velocity-time graph or the work done from a force-distance graph

    • Error bars:

      • The size of your error bars gives a visual representation of the precision of your data

      • Large error bars suggest significant random error

      • If the line of best fit passes through the error bars of all points, it indicates a good fit

  • Once you have your graph, you must interpret it

  • This is a two-step process:

    1. Describe the trend:

      • State what the graph shows

      • Use key scientific terms like:

        • directly proportional

        • linear positive correlation

        • inversely proportional

        • exponential increase

    2. Explain the trend:

      • You must use your knowledge of physical principles and equations to explain why the data follows this trend

      • This is the most important part of the interpretation

Identify and justify anomalous results

  • An anomalous result, or outlier, is a data point that clearly does not fit the overall trend

  • You should highlight obvious anomalous results on your final graph

Graph showing a line of best fit with multiple points, and one point circled in red labelled as an anomaly.
Highlighting an anomalous result on a graph.

  • In your analysis, you must justify why it is an anomalous result

    • A good justification links the anomalous result to a likely experimental error

    • For example:

      • The result from trial 2 at 60°C was excluded from the average and the graph as it was significantly higher than the other two trials

      • This was likely caused by a random error, such as a delay in starting the stopwatch

Assess accuracy, precision, reliability and validity

  • These terms have very specific scientific meanings

    • Using them correctly in your interpretation shows a high level of understanding

  • Accuracy:

    • How close your final result is to the accepted or true value

    • You can only comment on accuracy if a literature value is available for comparison

    • Accuracy is affected by systematic errors

  • Precision:

    • How close your repeat measurements are to each other

    • A small spread in your data (e.g., concordant titres of 23.35, 23.40, and 23.40 cm3) indicates high precision

    • Precision is affected by random errors

Four targets show accuracy and precision: accurate and precise, accurate not precise, precise not accurate, neither accurate nor precise.
The difference between precise and accurate results.

  • Reliability:

    • This refers to the consistency of your results

    • If you collected several concordant repeat trials, your results can be described as reliable

  • Validity:

    • This relates to your experimental method

    • Your results are valid if your experiment was a fair test, meaning you successfully controlled all other significant variables

Worked Example

Research question:

  • "What is the relationship between the length of a simple pendulum and its period of oscillation?"

Graph:

  • After processing the data, a graph of square of the period T squared / s2 (y-axis) against length L / m (x-axis) is plotted

Graph of period squared (T²) versus pendulum length (L) showing a linear trend with red data points and a dashed best-fit line.

Interpretation:

  • Description of trend:

    • The graph of T squared vs. L shows a clear positive linear correlation

    • The line of best fit is a straight line that passes through the origin, which indicates that T squared is directly proportional to L

  • Explanation of trend:

    • This result is consistent with the theoretical pendulum equation, T space equals space 2 straight pi square root of L over g end root, which when rearranged, gives T squared space equals space open parentheses fraction numerator 4 straight pi squared over denominator g end fraction close parentheses L

    • This equation is in the form y space equals space m x, confirming the directly proportional relationship between T squared and L

  • Using the gradient:

    • The gradient of the graph was calculated to be 4.05 s2 m-1

    • Using the relationship gradient = fraction numerator 4 straight pi squared over denominator g end fraction , the experimental value for the acceleration due to gravity was found to be g space equals space fraction numerator 4 straight pi squared over denominator 4.05 end fraction = 9.76 m s-2

    • This is very close to the accepted value of 9.81 m s-2, with a percentage error of only 0.5%, suggesting the data is highly accurate

Worked Example

Research question:

  • "What is the relationship between the length of a constantan wire and its electrical resistance?"

Graph:

  • After processing the data, a graph of resistance R / Ω (y-axis) against length L / m (x-axis) is plotted

Graph showing the linear relationship between wire length in metres and resistance in ohms, plotted with data points and a red trend line.

Processed data:

  • The average diameter of the wire was calculated as 0.19 mm

Interpretation:

  • Precision and reliability:

    • The error bars for the resistance values are small, indicating that the measurements of voltage and current were precise

    • The data points all lie very close to the line of best fit, suggesting the relationship is strong and the results are reliable

  • Accuracy:

    • The y-intercept of the graph is +0.25 Ω

      • Theoretically, a wire of zero length should have zero resistance, so the line should pass through the origin

      • This non-zero intercept suggests the presence of a small systematic error, such as contact resistance from the crocodile clips, which adds a small amount of extra resistance to all measurements

    • The gradient of the graph is 15.54 Ω m-1

      • Using the relationship rho space equals space gradient space cross times space Awith A space equals space straight pi r squared = 2.84 × 10-8 m2, the experimental value for the resistivity of constantan wire was found to be rho = 4.41 × 10-7 Ω m

      • A literature search shows that the resistivity of constantan wire is 4.94 × 10-7 Ω m

      • The result is very close to the accepted value, suggesting that the result is accurate

Examiner Tips and Tricks

Explain the physics.

  • The most important part of your interpretation is linking the trend in your graph back to the relevant physical theory and equations.

  • This moves your analysis from a simple description to a scientific explanation.

Stay focused on your research question.

  • Remember: the ultimate goal of interpreting results is to test your hypothesis and answer your research question.

  • Keep circling back to this in your analysis.

Highlight anomalies transparently.

  • Never delete data without comment.

  • Mark and explain anomalous points, and use physics reasoning (not just “it looks odd”) to justify your decision.

Use the key vocabulary.

  • Explicitly use the terms accuracy, precision, and reliability in your interpretation.

  • This clearly demonstrates to the examiner that you understand the quality of your results.

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    Katie M

    Author: Katie M

    Expertise: Physics Content Creator

    Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.