inst/tutorial/ex2.md

In appRiori: Code and Obtain Customized Planned Comparisons with 'appRiori'

An example with a two-way interaction

For this example, we will use the stress database. It is contained in the appRiori package. This database, contains data referring to the level of stress perceived from 102 academics. NB: This data are fictional. (see ?stress for further information).

In our example we will consider the following variables:

• Stress, a numerical variable referring to the level of stress perceived at the moment of the assessment. It represents a score ranging from 0 (no stress) to 100 (maximum level of stress).
• Position, a categorical variable with three levels, referring to (A) PhD student, (B) Full-Time Researchers and (C) Professors (Associate or Full).
• Grant, a categorical variable describing if the individual is applying for a grant (YES), or not (NO).

Suppose now that a researcher is interested in understanding if the level of stress would change according to the following hypotheses:

1. The average level of stress of PhD students should be lower than the average level of stress of FT-Researchers. Finally, average level of stress of FT-Researchers should be lower than average level of stress of Professors.
2. This set of comparisons should be better detected considering the fact an individual is applying for a grant or not.

Let’s see how to set these planned contrasts with appRiori!

Step 1: After upolading the data and selected the “Interactions” Panel, we should select Two way from the first menu.

Step 2: We select the Position as the first variable and Grant as second.

Step 3: Then we select the appropriate contrasts for each variable. Sliding difference for the first variable and Scaled for the second (see the Type of contrasts section for further explanation of how such contrasts work).

Step 4: At that point, we ca see the default, new and hypotheses matrices related to our comparisons. Inside the New contrast matrix, we can see that the column 1,2 encodes the contrasts for the first main effect (i.e., Position). Columns 3 encodes the contrasts for the second main effect (i.e., Grant). The last two columns encode the contrasts for interaction.

Step 4.1: We can check the correlations among our contrasts.

Step 5: A final look at what we selected (just to be sure).

Step 6: Let’s obtain our Basic R code.

The following picture displays how to set and obtain the code corresponding to this example:

The end: Once we have the code, we can test the hypotheses through a linear regression.

Stress$Position=factor(Stress$Position)
Stress$Grant=factor(Stress$Grant)
contrasts(Stress$Position)=MASS::contr.sdif(3)
contrasts(Stress$Grant)=contr.sum(2)/2

summary(lm(Stress~Position*Grant,data=Stress))

## 
## Call:
## lm(formula = Stress ~ Position * Grant, data = Stress)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -9.0929 -2.2796 -0.1859  2.6179  7.7371 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         79.8214     0.3673 217.329   <2e-16 ***
## Position2-1         -1.3309     0.8997  -1.479   0.1423    
## Position3-2          1.5241     0.8997   1.694   0.0935 .  
## Grant1              -0.9067     0.7346  -1.234   0.2201    
## Position2-1:Grant1  -0.3971     1.7993  -0.221   0.8258    
## Position3-2:Grant1   0.9400     1.7993   0.522   0.6026    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.709 on 96 degrees of freedom
## Multiple R-squared:  0.0514, Adjusted R-squared:  0.001992 
## F-statistic:  1.04 on 5 and 96 DF,  p-value: 0.3986

Interpretation

What is the summary telling us? Let’s have a look at the Coefficients’ table:

1. The row referring to (Intercept) contains the estimated average values of stress of all the sample. It is quite high!

2. The row referring to Position2-1 contains the comparisons between the mean stress of Full-Time researchers (i.e., group B) compared to the mean temperature of PhD students (i.e., group A). Such difference is equal to  − 1.33 and it is not statistically significant (p = .14).

3. The row referring to Position3-2 contains the comparisons between the mean stress of Professors (i.e., group C) compared to the mean stress of Full-Time researchers (i.e., group B). Such difference is equal to 1.52 and it is not statistically significant (p = .09).

4. The row referring to Grant contains the comparisons between the mean stress observed in those who are not applying for a grant compared to those who are applying for a grant. Such difference is equal to  − 0.91 and it is not statistically significant (p = .22).

5. Now we can start with the interaction effect. The row referring to Position2-1:Grant1 contains the comparisons between the mean stress of Full-Time researchers (i.e., group B) compared to the mean temperature of PhD students (i.e., group A), across those who are not applying for a grant compared to those who are applying for a grant. Such a difference is equal to  − 0.40 and it is not statistically significant (p = .83).

6. The row referring to Position3-2:Grant1 contains the comparisons between the mean stress of Professors (i.e., group C) compared to the mean stress of Full-Time researchers (i.e., group B), across those who are not applying for a grant compared to those who are applying for a grant. Such a difference is equal to 0.94 and it is not statistically significant (p = .60).

It seems that:

If you work in academics, you are stressed.

Regardless of the position you have, or whether you are applying for a grant (or not).

Good job, researcher!

This is the last part of the tutorial.

Now is the moment to start using appRiori!

appRiori documentation built on April 4, 2025, 1:14 a.m.