Writing About Data - Descriptive Statistics
You will need to calculate some descriptive statistics to summarise and begin the investigation of your raw data. This section provides advice on how to present this information in your written report.
Presenting descriptive statistics
The descriptive statistics that you include are important because they introduce your variables to your readers.
NOTE: The use of p-values should be avoided in this section. Descriptive statistics are just that – they describe and summarise your data. P-values mean that a hypothesis has been tested.
If you have collected measurements (continuous variables), you should include:
- number of valid (non-missing) values.
- mean and standard deviation. If you have one or more groups of variables, you may wish to provide the number of data points, mean and standard deviation for each group.
- perhaps median.
- range.
- perhaps graphs – for example, if you have measured a variable over time, a line graph.
If you have categorical data with frequencies or counts:
- frequency of each category (including missing)
- perhaps graphs – for example, a bar chart or histogram to show the counts in each category or an X-Y scatter plot to show two linked variables.
Standard deviations can communicate the following information about your data:
- How spread the data points are around the mean value. If the SD is small, then the data points are clumped around the mean, but if the SD is larger, the data points are more variable (spread out) from the mean.
- The reliability of the mean value as a representative number for the data set. In other words, how accurately the mean value represents the data. If the SD is small, then the mean is more reliable, but if the SD is larger, then the mean is less reliable. It's important to note that just because you have a larger SD, it does not indicate your data is not valid. Biological measurements are notoriously variable.
- The likelihood of there being a significant difference between groups of data. A "significant difference" means that the results that are seen are most likely not due to chance or sampling error. In any experiment that involves sampling from a population, there is always the possibility that an observed effect occurred due to sampling error alone. But if your result is "significant", then the researcher may conclude that the observed effect actually reflects the characteristics of the population rather than just sampling error or chance.
Below is an example of how you can summarise your mean and standard deviation calculations into a table.
NOTE: Always right-align numbers in a table and keep the number of places after the decimal point consistent so the decimal points line up.
You should report the standard error alongside the mean to communicate the uncertainty around the mean.
For example: The mean height of a random sample of trees is 5.5m ± 1.8 (SE).
You can also present the same information as a graph using error bars. An error bar is a bar on a graph that shows how much error is built into the chart. The “error” here isn’t a mistake, but rather a range or spread of data that represents some kind of built in uncertainty.
In IB ESS, error bars usually represent the standard error of the mean, shown on top of the means of each data set.
In all cases the error bars only suggest whether data sets may or may not be statistically different. You should carry out appropriate statistical tests to confirm the difference, if any.
For tips on drawing error bar graphs in Excel, see our X-Y scatter graphs page OR this external website.