Analysis

In this section, you will:

• Record the raw data gathered during your experiment
• Process the data as needed so you can use it to answer your research question
• Present and interpret the results of the processed data

An overview of the suggested structure of this section is shown in Table 1.
Details of what should be addressed in each subsection are presented after the table.

The ANALYSIS section of a report should include two subsections: 

• Data Collection
• Data Processing

Table 1 Suggested structure of Analysis section with the Rubric Criteria addressed in each part.

In the Analysis section, you are being assessed on how well you provide evidence that you have selected, recorded and processed data in your lab report.  You also need to interpret the data you have collected in ways that are relevant to the research question and can support your conclusion.

In Analysis your first goal is to clearly present the data you collected during your investigation. Then you must show any processing of the collected data, and finally, you must present your processed data in a way that clearly answers your research question.

Here are some examples of complete Analysis sections.

Detailed description of what should be included in the
Analysis Section

Subsection 1: Data Collection

In a scientific experiment, data is collected to answer the research question. The data which is collected may be qualitative, quantitative, or both.

• Qualitative data is descriptive data. Colors, behaviors, and comparisons are qualitative data.
• Quantitative data is numerical data, a measurement of a quantity.

Measured Data

All quantitative measurements in science are estimates. There is no such thing as an exact measurement. When we measure the length of an object, we might estimate the length to the nearest centimeter, the nearest millimeter, the nearest micrometer, but we always estimate to some level of precision. There is an uncertainty in our measurement due to the quality of the instrument. We call this instrumental uncertainty. When we make a measurement, we must report:

• the value of the measurement,
• the uncertainty in the measurement, due to the instrument used.

Here are some examples of how to report a measurement and its instrumental uncertainty appropriately.

The Meaning of Uncertainty

All measurements are estimates in science. There is no such thing as an exact measurement. When we say a table is exactly 85.0 cm tall, we are lying. It could obviously be 85.0000000001 cm tall, and we wouldn't know it. What we should say is that it is about 85.0 cm tall. If we say "about", that means the measurement is approximate, and there is some uncertainty as to the actual height of the table.

To communicate clearly, we must report the value and the uncertainty of any measurement we make in science.

The Reporting of Uncertainty

All data presented in your reports, both measurements and calculated results, have an associated uncertainty. It is important to report data and uncertainties appropriately. The value you report in a measurement is the value that you are confident in. It is the value that you trust to be correct. The uncertainty is the range around the reported measurement that the actual quantity might be.

For example, if you measured the height of your table with a meter stick, you could be sure to have a measurement you can trust to the nearest 1 mm. So when you report the height, you should say 85.0 ± 0.1 cm. If you report 85 cm, you are saying that you have no information about the tenths of a cm and have rounded to the nearest whole cm. This would be sloppy. If you report 85.000, you are claiming you are sure of the height to the nearest thousandth of a cm. This is a lie. The best way to report the height is 85.0 ± 0.1 cm.

All data in a scientific report must have an associated uncertainty and be represented in a graph, using uncertainty bars, if appropriate.

For lab reports the uncertainty is usually rounded to one significant figure, and the data value is rounded to match the uncertainty.

Exmple: A student measuring the rate of change of mass of a potato core in a salt solution should report the result as:

0.72 ± 0.03 g/s NOT AS
0.7254 ± 0.03 g/s, since you claim you know information about the thousandths place when the uncertainty is in the hundredths,
0.7254 ± 0.0317 g/s, since you should round uncertainty to one significant figure, and the data to match,
0.72 ± 0.031 g/s, since you should round uncertainty to one significant figure, or
0.7 ± 0.03 g/s, since if your uncertainty starts in the hundredths place, you should give the data value to the hundredths.

Determining Uncertainties in Measured Values

Uncertainties in measured values may be due to instrumental uncertainty or to procedural uncertainty.

Instrumental Uncertainty

Instrumental uncertainty is the uncertainty in the measurement due to the limit of precision in the instrument.

• For most glassware in chemistry, like graduated cylinders or beakers, the uncertainty is printed on the instrument.
• For most analogue scales, the uncertainty is estimated as half the smallest division, although for some thermometers with large markings, it is possible to estimate to the nearest third of the marking.
• For standard metersticks and rulers, the uncertainty is 1 mm.
• For digital instruments, the uncertainty is the smallest division. For example if your voltmeter reads 3.47 V, then the uncertainty would be 0.01 V.
• For computer probes, the most appropriate way to estimate the uncertainty is to take data for several seconds in an unchanging situation (for example place a temperature probe in a glass of water and take readings for several seconds). Then do a statistical analysis of the data and use the standard deviation as the instrument uncertainty.

Procedural uncertainty

Procedural uncertainty refers to the variation in results when repeating the same measurement several times. It is due to the inability to completely control all factors affecting an experiment.

This is why we take three trials and find the average whenever possible. The simplest way to get a rough estimate of the procedural uncertainty is to take half of the range of one set of trials. We usually use the largest, typical range of all your sets of three trials.

Repeated Measurements

In many experiments, you will be repeating measurements of the same quantity. For example, you might measure the acceleration of a ball rolling down a ramp three times. This is to increase our level of confidence in the results. In these cases, it is best to take an average of the three trials as our final result. As with all measurents, it is important to represent the level to which we estimated the measurement, and our level of uncertainty in the measurement. This is called the procedural or experimental uncertainty. When presenting the averages of a set of trials:

• The uncertainty is half the largest range of the set of trials rounded to 1 significant figure.
• The average value is rounded to the decimal place where the uncertainty starts.

Here is more detail on how to calculate and present the average of three trials and its uncertainty appropriately.

Data Presentation

Data may be presented using tables, diagrams, descriptions or photographs. It is important that all data be clearly labeled and easy to understand. Different types of data are presented differently.

• Quantitative data needs to be given in S.I. ("metric") units. Units and significant figures for each type of data must be consistent throughout the report.
• Diagrams need to be clear and large enough to see details. Biology drawings must be in pencil.
• Descriptions should be precise and informative. For example, was the solution after the test "blue" or was it "clear, deep, brilliant royal blue"? Or, maybe it was "cloudy, greenish blue"? Precisely describe how things felt, looked, smelled, or sounded

Your teachers will help you with the details of how to present different types of data for the laboratory investigations that you will be doing in your classes.

Data Tables

Many investigations generate a large amount of data, which is best presented in a table. Tables present the data in a way which allows the reader to quickly see trends and variations. A good data table has a number of characteristics.

Rules for Data Tables

• Data must be presented in a clear and organized manner.
• The reader should be able to understand tables without referring to the text.
• All tables need a heading ABOVE the table. For example: Table 1: The Acceleration of a Cart as Mass is Varied.
• Tables should have a key to explain symbols, abbreviations, or special methods, if necessary.
• Columns and rows should be headed with the quantity being measured, the units of measurement, and the uncertainty in the measurement, if appropriate.
• Units and uncertainties should be placed in column headings -- not in the individual cells of the table.
• Only tables that are referred to in the report should be included.
• NEVER split data tables over two pages. Titles must be on the same page as the table.
• Values in each column should be rounded appropriately to match the level of precision or uncertainty.

To summarize, a table needs a heading, quantity and units for each column, and clear organization and formatting.

Here are some examples of Data Tables.

Figures

Some types of data are more appropriately presented in a figure. This includes data and observations in the form of photographs, drawings, diagrams and graphs. Figures include photographs or diagrams of experimental set-ups; drawings of plants, cells, or microbes; photographs or diagrams of experimental results; and computer-generated graphs showing collected data.

Rules for Figures

• Figures must be clear and easy to understand.
• Figures must have numbered labels and captions which describe the figure and any important points, such as a legend (key) explaining any unusual symbols, abbreviations, or special methods used. Some examples of good labels and captions follow:
  • Figure 1: Bean Seedlings after 1 Week of Growth. Notice that the seedlings now have fully developed leaves and root systems.
  • Figure 2: Onion Epidermal Cells Stained with Iodine
  • Figure 3: Results of Sugar Tests on Unknown Samples. Notice that the result for the last sample is significantly lower than the rest.
  • Figure 4: The velocity-time graph for the ball thrown in the air in trial 1. The slope of the graph is the acceleration of the ball due to gravity.
• The label and caption always go BENEATH the figure.
• Only figures that will be discussed in the report should be included.
• All original drawings should be done in pencil.
• Drawings must be large enough to show clear detail.
• Stippling (drawing with short strokes or dots) of biological diagrams is better than shading.
• Drawings should be done on unlined paper.
• Drawings should be realistic.
• Composite diagrams are acceptable.

To summarize, a figure needs to be clear and easy to interpret, and must have a numbered label and descriptive caption.

Here are some examples of Figures.

 

Subsection 2: Data Processing

Once you have presented your collected data appropriately, you must process that data and present it in a way which clearly answers your research question. Sometimes, the measurements that you make during the experiment cannot directly provide an answer to your research question. You may need to perform some calculations using the collected data. The equations you use and the ways you rearrange the data will depend on the investigation. You will learn how to process data appropriately in lab investigations throughout the year. One example of all important calculations performed on the collected data should be shown in a sub-section entitled Sample Calculations, if appropriate.

Here is an example of what a good Sample Calculations section looks like.

You must then present this processed data in a way that clearly answers your research question. Your processed data can usually be presented in a line graph, table, or diagram. Bar graphs or pie charts are also sometimes appropriate. Knowing the most appropriate way to present your results is one of the things you will learn from your teacher. One of the most common ways of presenting the results of your investigation is a graph.

Graphs

We are now in the 21st century. We seldom draw graphs by hand. We usually use a computer to do it. It is easier, faster, and much more powerful. We will be using the Logger Pro graphing program for making graphs (some students may choose to use Microsoft or NUMBERS). A tutorial on Logger Pro has been included in this writing guide. Use it. 

A good graph has certain characteristics.

• You must have a title telling what the graph is showing. A good convention is to include the dependent and independent variables somewhere in the title.
• There should be a caption describing what is being shown on the graph, and discussing any important points that the reader should notice.
• Each axis of the graph should have a label and units, telling what is being measured and the units of measurement. In general, the independent variable should go on the x-axis, and the dependent variable on the y-axis, although there are some exceptions to this.
• When appropriate, there should be uncertainty bars on the data points.
• The axes should be scaled appropriately, so that the data fills most of the space in the graph. A good rule of thumb is that the data should take up approximately 75% of the space in the graph. For example, if your data ranges from 2.0 to 8.0, then a scale of 0 to 10 would be good for that axis. In most cases, it is best to scale each axis from 0.
• Finally, a best-fit line or curve should be fitted to the data when appropriate, rather than connecting the dots.

To summarize, a graph needs a title, caption, labels and units on the axes, appropriate scaling, and sometimes uncertainty bars and a best-fit line or curve.

Here is an example of what a good graph looks like.

 

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