## 5.5. Writing up your results

Substantial section titles are more attractive than structural ones. So instead of a title like ‘Hypothesis 1’ use a title stating what the hypothesis is about, like ‘The relationship between corruption and economic growth’. An alternative strategy is to state the question that the hypothesis is answering. In this case: “Do more corrupt countries show lower economic growth?” Personally, I like it even better when the basic finding is expressed in the title: “Lower growth in more corrupt countries”.

The same advice goes for the title of your paper. Especially when the main contribution of your piece is empirical, say what you found: summarize the main finding in the title. When the main contribution is in the data or the application of a new method, consider mentioning these in the subtitle.

One common pitfall I have encountered in theses using cross-sectional data, often from surveys, is that authors call associations between variables ‘effects’ or ‘influences’ of the predictor variable on the dependent variable. However, correlation is not causation; you cannot infer causality from an association between two variables. If you have non-experimental data, avoid the use of words that suggest causality such as ‘cause’, ‘effect’, ‘influence’, ‘result’, ‘determinant’, or ‘consequence’. Instead, talk about relations between variables, or better still: write about differences in Y between groups or categories X. For example: instead of ‘there is a positive relation between female and donation’ or ‘gender significantly affects giving’ write ‘men were found to give less frequently than females, but when they gave, they donated higher amounts’.

If you report results of regression analyses, do not merely state that a relationship between two variables is significant, but also give the reader an idea of the strength of the relationship. Remember that ‘effect size’ is a misleading term when you have non-experimental data. Only use "effect size" if you have random allocation to condition, as in an experiment.

Also remember that even a very weak relationship can be significant if the number of observations increases sufficiently (Goodman, 2008). The strength of relationships is often described using standardized coefficients such as the beta coefficients in an ordinary least squares regression. However, beta coefficients can be misleading if you have variables of different measurement levels in your analysis. Judging from the beta coefficients, dichotomous variables such as gender always seem to have less predictive value than the ordinal variables. This is an artifact of the distribution of the predictor variable: there are only two genders, while there may be many more values for the ordinal variables in your analysis, such as the level of education or household income. Therefore it is better to describe the strength of relationships by comparing the unstandardized coefficients relative to the reference group. Pick your reference group in a meaningful way - e.g. in the example of Table 5 above, the non-religious were the reference group, because they give the lowest amounts.

A general recipe for the description of the association between two variables is:

1. Describe the difference in y for a one unit difference in x.
2. Compare the difference in y for the extremes of x. How common are they?
   - If the extremes are rare, mention that few observations are at the extremes.
   - Are the y values for the extremes on the x in line with the almost extremes? Then the relationship between x and y is linear. If the y values for the extremes of x are not in line with the almost extremes, then you need to check what happens if you leave them out or winsorize them.
3. Compare the association or effect size of interest with another difference. This could be one from your model, e.g. the difference between men and women, or between the top and bottom 10% of the income distribution, or with another difference that readers will intuitively understand.

Another warning is against over precision. Numbers with three or more decimals suggest a very high level of precision. However, social science research typically has a large number of limitations as a result of choices in data collection and analysis – sampling procedures, measurement of concepts, coding of variables, model specifications and estimation algorithms. Any number you provide depends on a large number of factors that make the third or more decimal essentially meaningless. The choices you make – or others have made for you – are far from perfect and sometimes outright arbitrary. The proverb here – often attributed to John Keynes but formulated earlier by Carveth Read (Ratcliffe, 2012) – is “It is better to be vaguely right than exactly wrong.”

Be concise. Use graphs to illustrate your results. As DeVaux, Velleman & Brock (2012, p.19) say: the three rules of data analysis are: 1. Make a picture; 2. Make a picture; 3. Make a picture. A figure is often more appealing than a table. Be honest in your figures though: Figure 20 is misleading.

Avoid repetition. Say things only once. That is: do not repeat what you have said before.

In other words, do not write exactly the same sentence in two different sections such as the introduction, the results and the conclusion section. Do not describe the results from a table in the text by mentioning the numbers from the table. For example, if the coefficient for the log of income in a regression predicting the log of the amount donated to charity per year is .123, do not write “Model 1 of Table 1 shows that the income elasticity of charitable giving is .123” but write “Model 1 of Table 1 shows that a 10% increase in income is associated with an increase in the amount donated of 1.2%”. Finally – just in case I am your supervisor – it may be good to know that I am allergic to references to previous paragraphs like “As we have seen before in section 4.2.2.1” and “As explained above”.

Avoid footnotes. If you find yourself putting text in a footnote, decide whether it is an important detail. If it is, put it in the main text. Perhaps you need to rewrite it to make the text from the footnote fit. If the footnote text is not important enough to be in the main text, you may as well cut it. Or move it to an appendix.

When you think you are ready with your results section, copy the text to a new document and change the font (Dillard, 2018). Print a hard copy and read it on paper. You will find mistakes you have overlooked because you have become accustomed to the text by reading it over and over again. A wlel kown pehnmenon is taht pepole fial to regocinze seplling mitsakes aftr a whle. Evn txts wtht vwls r rdbl, espcly as lng as th frst and lst lttrs are in the rght plcs.

Next, give your text to a friend for proofreading. You will have seen your own text so many times by now, that you will not easily spot omissions, mistakes and bad writing.