First of all, let’s present the fictitious data we are going to work with. Let’s suppose that a pharmaceutical company is planning to launch a new vitamin that allegedly improves the employees’ resistance to effort. The vitamin is tested on a sample of 720 employees, divided into three groups: employees who take a placebo (the control group), employees who take the vitamin in low dose and employees who take the vitamin in high dose. Half of the employees are male, and half are female. Moreover, we have both blue collar employees and white collar employees in our sample. The resistance to effort is measured on a scale whatsoever, from 1 to 30 (30 being the highest resistance). Our goal is to determine whether the effort resistance is influenced by three factors: dose of vitamin (placebo, low dose, and high dose), gender (male, female) and type of employee (blue collar, white collar). You can find the experiment data in CSV format here. Third-order interaction effect First of all, let’s check whether the third-order interaction effect is significant. We are going to run the analysis using the aov function in the stats package (our data frame is called vitamin). aov1 <- aov(effort~dose*gender*type, data=vitamin) summary(aov1) In the formula above the interaction effect is, of course, dosegendertype. The ANOVA results can be seen below (we have only kept the line presenting the third-order interaction effect).
Df Sum Sq Mean Sq F value Pr(>F) dose:gender:type 2 187 93.4 22.367 3.81e-10The interaction effect is statistically significant: F(2)=22.367, p<0.01. In other words, we do have a third-order interaction effect. In this situation, it is not advisable to report and interpret the second-order interaction effects (they could be misleading). Therefore, we are going to compute the simple second-order interaction effects. Simple second-order interaction effects The simple second-order interaction effects are the effects of each pair of factors at each level of the third factor. Specifically, we have to compute the following effects:
- the interaction effect of dose and type of employee, for each gender category (male and female)
- the interaction effect of gender and type of employee, at each dose level (placebo, low and high)
- the interaction effect of dose and gender, for each type of employee (blue collar and white collar).
Df Sum Sq Mean Sq F value Pr(>F)
dose:type 2 249 124.7 28.42 3.57e-12
Df Sum Sq Mean Sq F value Pr(>F)
dose:type 2 137.2 68.6 17.31 6.74e-08
We can notice that both simple second-order interaction effects are significant (p<0.01). So we are dealing with a combined influence of the factors dose and type of employee in both male and female groups. In this situation, we have to examine the simple main effects for each factor. This is what we are going to do in the next section. Simple main effects Let’s compute the main effect for the factor dose of vitamin, which is the most important (after all, the company wants to demonstrate that the vitamin does affect the resistance to effort). You will be able to compute the other simple main effects yourself, using this as an example. Now we must create four separate data frames, for each combination of the factors gender and type of employee: male – blue collar, male – white collar, female – blue collar, female – white collar. [code lang=””r””] vitamin_male_blue <- filter(vitamin, gender=="male", type=="blue collar") vitamin_male_white <- filter(vitamin, gender=="male", type=="white collar") vitamin_female_blue <- filter(vitamin, gender=="female", type=="blue collar") vitamin_female_white <- filter(vitamin, gender=="female", type=="white collar") Next we perform a one-way ANOVA for each data frame. Let’s do it for the first group, male – blue collar. [code lang=””r””] aov1 <- aov(effort~dose, data=vitamin_male_blue) summary(aov1)
Df Sum Sq Mean Sq F value Pr(>F)
dose 2 2943.5 1471.8 349.9 <2e-16
The simple main effect for the factor dose on this group is statistically significant (p<0.01). In other words, there is a significant difference between placebo, low dose and high dose levels within the male – blue collar employees category, regarding the resistance to effort. To find out how big the differences are, we use the TuckeyHSD function to compute the test with the same name.
TukeyHSD(aov1) diff lwr upr p adj
low dose-high dose -2.528333 -3.413363 -1.643303 0
placebo-high dose -9.558333 -10.443363 -8.673303 0
placebo-low dose -7.030000 -7.915030 -6.144970 0
By inspection of the table we conclude that the differences in effort resistance between the dose groups are significant (p<0.01). The highest difference, in absolute values, is that between low dose and placebo levels: 9.5 points. So the employees who took a high dose present a higher resistance to effort than those who just took a placebo. One more example: the simple main effects of the variable dose of vitamin on the female – blue collar group. [code lang=””r””] aov1 <- aov(effort~dose, data=vitamin_female_blue) summary(aov1) Df Sum Sq Mean Sq F value Pr(>F)
dose 2 399.6 199.81 45.57 <2e-16
TukeyHSD(aov1) diff lwr upr p adjThe simple main effect is statistically significant, as it results from the first table. Furthermore, all the differences between dose levels are significant. The highest difference is the difference between low dose and placebo (3.5 points). To learn more on data analysis in R, check the free “Statistics with R” video course here.
low dose-high dose 1.083333 0.1797508 1.986916 0.0141485
placebo-high dose -2.476667 -3.3802492 -1.573084 0.0000000
placebo-low dose -3.560000 -4.4635826 -2.656417 0.0000000
SVM
Data visualization and charting are actively evolving as a more and more important field of web development. In fact, people perceive information much better when it is represented graphically rather than numerically as raw data. As a result, various business intelligence apps, reports, and so on widely implement graphs and charts to visualize and clarify data and, consequently, to speed up and facilitate its analysis for further decision making.
While there are many ways you can follow to handle data visualization in R, today let’s see how to create interactive charts with the help of popular JavaScript (HTML5) charting library 
For consistency purposes, I am including the code of 
Figure 1. Basic syntax of Markdown
This makes formatting as you write quick – no more buttons or keyboard shortcuts. Subsequently, the text file can be exported in multiple file formats, including PDF, html and even as a Word file to satisfy co-authors who prefer to use Word’s track-changes function.
R Markdown is a flavour of Markdown: it allows you to include R code either as a code chunk between paragraphs of text, or as code within the text. This code is executable. As such, you can do analyses, make figures and format results automatically.
One problem I’ve worked on previously is checking the accuracy of p-values in the literature. My colleagues and I found that p-values can be mistyped or miscalculated, leading to inaccurate reporting of results, however unintentionally, in half of all papers, and leading to potential changes in the conclusions in one out of eight papers (in psychology; Nuijten et al. 2015). Enabling researchers to insert p-values via direct computation instead of manually copying results from statistical programmes will resolve this issue, for a start.
R Markdown is simple and easy to learn and use. I will show just one exciting aspect here. More extensive 
Figure 2. Using R Markdown to write a document
However, in this text, we have a p-value that is calculated based on a t-value and the number of degrees of freedom. Let’s make this dynamic to ensure we have the rounding correct (Figure 3).
Figure 3. Using R Markdown to generate a document with dynamic results, to ensure accuracy of reporting and reproducibility of results
As we see, the original contained a mistake (p = 0.027 has become p = 0.028) – using R Markdown allowed us to catch that error by using R code to generate and properly round the p-value (i.e., round(pt(q = 1.95, df = 69, lower.tail = FALSE), 3) calculates the p-value and rounds the result to three decimal places). So, there are no more mistakes, and we can be confident in our reporting. Disclaimer: of course, you can still input wrong code – garbage in, garbage out.
Further, you can generate plots from your research data within your dynamic document. Figure 4 demonstrates using an example dataset pre-loaded in R (you can find more example datasets by typing data() into the console).
Figure 4. Using R Markdown to dynamically generate plots within a document
Finally, you can even use citations and alter the citation style throughout the whole document without any problem; my experience is that it’s easier with R Markdown than with EndNote or Mendeley.
These are just simple examples. You can write entire manuscripts in this way. That’s what I did for our Collabra manuscript: you can view the raw manuscript at 
We are pleased to announce the release of the ggedit package on 