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More Than Numbers: Presenting Statistics In Your Writing

Writer(s): 
Tiffany Ip, The University of Hong Kong

Presenting statistics is no easy task. It is more than merely drawing fancy graphs and recording a few numbers. Statistics, when properly used, can serve as a powerful medium of information for your reader. In a world where data-oriented goals are valued, it is desirable to be capable of justifying your predictions and conclusions with statistics. While this article will not teach you technical skills regarding statistics, such as what analyses or models you may choose for a data set and how to interpret the results (you should either take a course or reference a textbook if you are unsure of these), this article will guide you in the fundamentals of effectively presenting statistics in writing. You will see how to achieve this primarily by following two principles, and hopefully in the process you will also acquire a sense of how to read others’ statistics as well. Put simply, you are now on the road to becoming both a good writer and reader of statistics.

Whether you intend to report the statistical outcome of your study, or use statistics gleaned from other sources in order to strengthen your own arguments, you need to bear in mind these two key principles: 1) Statistics should be presented in a readable and technically acceptable way. 2) Statistics should be explained to an appropriate extent; not inadequately explained (too little) or overly explained (too much).

Principle 1: Present Your Statistics in a Readable and Technically Acceptable Way

Communicating potentially difficult concepts does not mean that you have to use complicated language or structures. Research shows that those who use unnecessarily long words and complicated font styles in their writing are actually perceived as being less competent and confident than those who use more simple language (Oppenheimer, 2006). The best way to write statistics is to be direct and unambiguous. This can be done in two simple steps. First, provide definitions for the key technical terms and statistical concepts related to the statistics presented in your writing, and then translate your statistics into a form that will be easily understood by your readers. For example, the statement “The best predictor of students’ final exam grade is their language proficiency level (F(2, 13) = 832.14, p < 0.01), with an R2 of .993” is easier to understand than simply stating “Multiple regression analysis showed that the result was significant (F(2, 13) = 832.14, p < 0.01), with an R2 of .993”. Ultimately, the level of detail the definitions and explanations your statistics will need to have will depend on the readership and style of statistical writing of your particular field.

The second step to presenting statistics in a readable manner is to use visuals, especially when your data set contains a lot of information. Graphs, charts and tables, for example, can help simplify relationships in your statistics that may be difficult to comprehend for you and your readers. Graphical representations often act as visual shortcuts which can help make group comparisons easier as well. If you would like to have a look at some concrete examples and tips concerning reporting statistical results in figures, you may refer to the article Reporting statistical results in your paper located on Bates College’s website (see references). It provides some examples of summarizing statistical outcomes derived from t-tests, ANOVA, correlation, as well as regression analyses.

Just as academic writing prefers direct language, graphical representations should also be kept relatively simple. Avoid needless and obscure elements which can potentially distract the reader from the content of the paper. Consider this quote from the Purdue Online Writing Lab (2012):

Papers and articles are like faces. Graphics are like makeup. Makeup is always good in small doses, but don’t over apply, or you will end up looking worse than if you didn’t use any makeup at all. Use visuals, but be careful not to over use them.

Now, you may have a question concerning exactly what statistics you should present in your writing. What if your data set contains a lot of information, and even with the use of graphs or tables the information still seems difficult to reduce and present to the reader? Should you then go ahead and report all of the statistics that you have? The answer is most likely no; using statistics in writing is by and large a process of condensing the information that you have and making it relevant to your readers. If you present entire raw data sets in your writing, this defeats one of the primary purposes of your paper: making your statistics relevant to the reader. Instead, you can highlight statistics of interest and include the minimum amount of information (most likely the mean and the standard deviation) necessary for your reader to understand the essence of your arguments. Information remotely associated with your arguments and research aims can then be listed in detail in a separate appendix.

Principle 2: Explain the Statistics to an Appropriate Extent: Avoid Inadequate or Superfluous Explanations

Unless you are using the statistics in your writing as a minor support for your argument, it is usually necessary to explain the procedure you use to generate your statistics to your readers. This is particularly true if the statistics are the focal point of your argument. In this case your readers—some of whom may be unfamiliar with the procedures you used regarding your statistics—expect to have explained: who first used the procedures, why exactly they were used, and how they are applicable to the study they are reading.

Presenting as much information as is needed is crucial since it allows your readers to make critical interpretation of your data. Of course, you have the freedom to choose your own way of interpreting your statistics, but you also have to realize that readers may not blindly accept your interpretations and may be skeptical of the veracity of your data set. It is important to include sufficient information–for example, the mean, variability, sample size, and the p-values–before presenting conclusions to your readers, if you want to make a convincing argument. Also, if you are using statistics from others’ studies, make sure the sources are reliable and credible. Identifying the background of the data that you use, as well as letting your readers know where the sources are from, helps orient both them and yourself towards possible biases or weaknesses that could be present in the statistics being used.

Although you have the freedom in your writing to interpret the data in whichever way you prefer, be careful not to overly interpret the data to your reader. Do not simply state something is “important” when the data should instead be described as being “statistically significant”. Do not label something as being “not true” when no evidence can be generated from your data: this only means something may or may not be true. Be careful not to generalize your findings to everyone if your data are based on a specific population, gender, or age group. Take care not to confuse correlation with causation when exploring the associations between variables, or to assume that you can prove everything with statistics, even though they do provide empirical evidence for your arguments. Also, when presenting percentages or changes in percentages in your paper, aim to present them in their proper context. For example, if I simply state that you will become 74% more capable of presenting statistics in your writing after reading this article, you would still have no idea exactly how much better you would become. Meaningful conclusions about percentages cannot be made unless they are associated and explained in context.

One Final Thought

You may have come to the realization that statistics are a lot more than just numbers, and, if used carefully and effectively, they can strengthen your writing. Although these days we may tend to rely on computer programs (e.g. SPSS, a simple-to-use software package for statistical analysis that does not require the user to learn the programming language), we should avoid thinking of them as tools used for helping us interpret our data. The final thought to consider is that when writing statistics we should, above all else, write accurately, and we are only able to write accurately if we fully understand our statistics and how to interpret them. If we are able to do this, it will allow us to fulfill the two main principles discussed in this article, and to write our statistics in a way that will not bore, confuse, overwhelm, or mislead our readers.

References

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