Cognitive Behavioral Therapy

Section 7.2 Cognitive Behavioral Therapy

Those who study crime and criminals should pay great attention to the issue of rehabilitation. A significant portion of inmates eventually reintegrate into society, where they play crucial roles as members of our communities. A variety of rehabilitation programs have been developed to alter the belief systems and behaviors of offenders. Among the most prevalent programs implemented in correctional settings is CBT. CBT programs operate under the premise that holding antisocial attitudes correlates with increased engagement in antisocial behavior. Specifically, these programs posit that exposure to high-risk situations triggers antisocial thoughts and emotions, thereby heightening the probability of engaging in antisocial behavior (Vaske et al., 2011). CBT programs that target criminal activity have been used as popular interventions in correctional settings because many evaluation studies have shown that CBT reduces recidivism significantly (Landenberger & Lipsey, 2005; Lipsey et al., 2007; Zara, 2019).

🔗

Let’s consider a scenario where high-risk inmates were selected at random to participate in a CBT program. This program was conducted in a group setting within the prison, with trained facilitators leading individual sessions aimed at tackling the diverse challenges offenders encounter upon their return to the community. These challenges, spanning from addiction and employment to family obligations and victimization, frequently impede successful reintegration. The program consists of 10 sessions spread over a period of 10 weeks, totaling approximately 20 hours of engagement.

🔗

How do we assess the effectiveness of this CBT program? Initially, we must define the criteria by which we will evaluate its success. Those responsible for implementing the program must first clarify its objectives. For instance, the program might aim to modify the attitudes, behaviors, or both, of inmates. If our focus is on behavioral change, we could monitor participants’ recidivism rates, such as rearrest or reconviction. Alternatively, we could concentrate on shifts in participants’ attitudes.

🔗

Another critical consideration is the research design. We could compare participants in the program to those who did not participate, or within-group changes could be analyzed by comparing participants’ attitudes before and after the program.

🔗

Subsection 7.2.1 Independent-Samples T-Test

First, we will examine a scenario where high-risk inmates were randomly chosen to participate in a CBT program. In this context, we will compare the antisocial attitudes of those who were randomly selected for the program with those who were not. For our analysis, let’s assume that antisocial attitudes were assessed using a scale developed by Farrington and McGee (2017). This scale comprises a 24-item self-reported instrument with a 4-point response format, including statements like “If someone does the dirty on me, I always try to get my own back” or “I enjoy watching people getting beaten up on TV.” The higher antisocial attitudes score reflects higher levels of antisocial attitudes (e.g., aggressiveness).

🔗

We will use the fictitious dataset I constructed to contrast inmates who engaged in a CBT program with those who did not. In this hypothetical study, there were 100 high-risk inmates in the prison. Fifty inmates were randomly allocated to participate in a 10-week CBT program, while the other 50 were randomly assigned not to participate. If the program yielded an impact, we anticipate observing reduced levels of antisocial attitudes among those who participated compared to their counterparts.

🔗

Let’s first download the data from the shared Google Drive folder containing the CBT_dataset_independent.csv data. Then, load the data for this study using the syntax below. Each row in this data represents each inmate. The Group variable is a categorical variable where the category Participants refers to those who participated in a CBT program, whereas Non-Participants refers to those who did not. The AntiSocial variable represents inmates’ antisocial attitudes.

🔗

library(readr)
CBT_dataset_independent <- read_csv("CBT_dataset_independent.csv")
View(CBT_dataset_independent)

Executing library(readr) allows us to load the readr package into our R session. The readr package, part of the tidyverse collection, is specifically crafted to simplify importing flat-file data, such as CSVs and text files, into R. The read_csv function from the readr package is tailored for reading CSV files.

🔗

Subsection 7.2.2 NHST Steps for Independent-Samples T-Test

Following the NHST steps we covered in the previous chapter, we will conduct the independent-samples t-test because we are comparing the mean scores of two distinct groups of individuals (i.e., CBT participants and non-participants).

🔗

Subsubsection 7.2.2.1 Step 1: Formulate the Null and Alternative Hypotheses

\(H_0\text{:}\) There is no difference in mean antisocial attitudes between CBT participants and non-participants.
🔗

🔗
\(H_A\text{:}\) There is a difference in mean antisocial attitudes between CBT participants and non-participants.
🔗

🔗

🔗

Subsubsection 7.2.2.2 Step 2: Calculate the Test Statistic

The following code facilitates the execution of an independent-samples t-test. In R, a formula typically comprises a single variable on the left, denoted by a ~ (tilde), followed by one or more predictors on the right, which help predict the variable on the left. In statistical tests, the variable on the left of the formula represents the dependent variable (e.g., antisocial attitudes), while those on the right represent the independent variables (e.g., CBT program participation).

🔗

twosampt <- t.test(formula = CBT_dataset_independent$AntiSocial ~
                   CBT_dataset_independent$Group)
twosampt

The output should generate results from Welch’s t-test. Welch’s t-test differs slightly from the traditional t-test formula, primarily used when the data deviates from the assumption of equal variances. The t.test() output shows a t-statistic of 4.859. This t-value is well above a t-value of 1.96, which is the historical cut-off point for significance at the 95% confidence level.

🔗

Subsubsection 7.2.2.3 Step 3: Determine the Probability (P-Value) of Obtaining a Test Statistic at Least as Extreme as the Observed Value, Assuming No Relationship Exists

The p-value in this output was shown in scientific notation as 4.485e-06. You may be confused because you do not know how to convert this number. Here is the way to convert a p-value to a regular numeric format.

🔗

# Your p-value in scientific notation
p_value <- 4.485e-06
# Convert p-value to regular numeric format
formatted_p_value <- format(p_value, scientific = FALSE)
# Print the p-value
formatted_p_value

Now you know that the probability of obtaining a t-statistic of 4.859 is 0.000004485 if the null hypothesis is true, which is substantially smaller than .05, the conventionally used standard. R produces a regular numeric p-value, but when the p-value is very low, it may display scientific notation.

🔗

Subsubsection 7.2.2.4 Steps 4 and 5: Reject or Retain the Null Hypothesis

The t-statistic fell within the rejection region. The probability of this sample coming from a population where the mean antisocial attitudes for both CBT participants and non-participants are equal is exceedingly low. Therefore, it is probable that the sample is from a population where CBT participants and non-participants exhibit statistically significant different mean antisocial attitudes.

🔗

Subsection 7.2.3 Reporting the Results of an Independent-Samples T-Test

The results from our independent-samples t-test can be presented as follows:

🔗

An independent-sample t-test was conducted to compare the antisocial attitudes scores for CBT participants and non-participants. There was a significant difference in scores for participants (\(M = 46.46\)) and non-participants (\(M = 55.39\text{;}\) \(t(97.924) = 4.86\text{,}\) \(p < .05\text{,}\) two-tailed).

🔗

If you want to see how t-test results are reported in an academic peer-reviewed journal, please see Choi et al. (2020). My colleagues and I compared levels of fear of crime between women and men using independent-samples t-tests.

🔗

Subsection 7.2.4 Density Plot

You may wonder if there is a way to visualize the difference in antisocial attitudes between CBT participants and non-participants. A density plot is a useful tool that graphically represents a distribution of scores or values that take the form of a smooth curve. You can create a density plot using ggplot2 and tidyverse to visualize the distribution of antisocial attitudes between two groups (CBT participants and non-participants) from the dataset CBT_dataset_independent.

🔗

library(ggplot2)
library(tidyverse)
dens_cbt <- CBT_dataset_independent %>%
    ggplot(aes(x = AntiSocial,
               fill = Group)) +
    geom_density(alpha = .7) +
    theme_minimal() +
    labs(x = "Antisocial Attitudes", y = "Probability Density") +
    scale_fill_manual(values = c('gray', 'black'),
                      name = "Group")
dens_cbt

library(ggplot2) loads the ggplot2 package, which is used for creating data visualizations in R.
🔗

🔗
library(tidyverse) loads the tidyverse package, a collection of R packages including ggplot2 for data manipulation and visualization.
🔗

🔗
dens_cbt <- CBT_dataset_independent %>% creates a ggplot object called dens_cbt. It uses the pipe operator %>% to pass the CBT_dataset_independent data frame into the subsequent ggplot code.
🔗

🔗
ggplot(aes(x = AntiSocial, fill = Group)) begins the ggplot object and specifies the aesthetics (aes) mapping. It sets the x-axis to the AntiSocial variable and the fill color to the Group variable.
🔗

🔗
geom_density(alpha = .7) adds a density layer to the plot, displaying the distribution of antisocial attitudes for each group. The alpha parameter controls the transparency of the density curves.
🔗

🔗
theme_minimal() sets the plot theme to minimal, which removes gridlines and background elements for a cleaner appearance.
🔗

🔗
labs(x = "Antisocial Attitudes", y = "Probability Density") sets the x-axis and y-axis labels.
🔗

🔗
scale_fill_manual(values = c('gray', 'black'), name = "Group") manually sets the fill colors for the groups and provides a legend title.
🔗

🔗
dens_cbt displays the density plot.
🔗

🔗

🔗

You can also conduct an independent-samples t-test with directionality in R. Specifically, if we were curious about whether CBT participants have lower levels of antisocial attitudes compared to non-participants, you can perform this in R as well. When you specify the alternative hypothesis’s direction, it is called a one-tailed test. This is beyond the scope of this book, so we will move on to the next item in this chapter: paired-samples t-test.

🔗

Prev Top Next