Question

A large counseling center needs to evaluate several experimental programs. Write a paragraph summarizing the results of these tests. Did the new programs work? a. One program is designed for divorce counseling; the key feature of the program is its counselors, who are married couples working in teams. About half of all clients have been randomly assigned to this special program and half to the regular program, and the proportion of cases that eventually ended in divorce was recorded for both. The results for random samples of couples from both programs are reported here. In terms of preventing divorce, did the new program work? $$ \begin{array}{cc} \hline \hline \text { Sample 1 } & \text { Sample 2 } \\ \text { (Special Program) } & \text { (Regular Program) } \\ \hline P_{s 1}=0.53 & P_{s 2}=0.59 \\ N_{1}=78 & N_{2}=82 \\ \hline \end{array} $$ b. The agency is also experimenting with a program that includes peer counseling for depressed teenagers. About half of all clients were randomly assigned to the new program. After a year, a random sample of teens from the new program was compared with a random sample that received standard counseling. In terms of the percentage of children who were judged to be "much improved," did the new program work? $$ \begin{array}{cc} \hline \hline \begin{array}{c} \text { Sample 1 } \\ \text { (Peer Counseling) } \end{array} & \begin{array}{c} \text { Sample 2 } \\ \text { (Standard Program) } \end{array} \\ \hline P_{s 1}=0.10 & P_{s 2}=0.15 \\ N_{1}=52 & N_{2}=56 \\ \hline \end{array} $$

Short answer

The special divorce counseling program was effective in reducing divorces. The peer counseling program for teens was not as effective as the standard program.

Step-by-step solution

- Review Divorce Counseling Program Results

We have to compare the proportions of divorces in the special program and the regular program. For the special program, the proportion of cases that ended in divorce is \(P_{s1} = 0.53\) with a sample size of \(N_1 = 78\). For the regular program, the proportion of cases that ended in divorce is \(P_{s2} = 0.59\) with a sample size of \(N_2 = 82\).

- Analyze Divorce Rates

Comparing the proportions \(P_{s1} = 0.53\) for the special program and \(P_{s2} = 0.59\) for the regular program, observe that the special program has a lower proportion of divorces. Therefore, it appears the special program has a positive effect in reducing divorce rates.

- Review Teen Depression Counseling Results

We need to compare the proportions of children who were 'much improved' in the peer counseling program and the standard program. For the peer counseling program, the proportion of 'much improved' is \(P_{s1} = 0.10\) with a sample size of \(N_1 = 52\). For the standard program, the proportion is \(P_{s2} = 0.15\) with a sample size of \(N_2 = 56\).

- Analyze Improvement Rates

Comparing the proportions \(P_{s1} = 0.10\) for the peer counseling program and \(P_{s2} = 0.15\) for the standard program, observe that the peer counseling program has a lower proportion of 'much improved' cases. Therefore, the peer counseling program does not appear to be more effective than the standard program.

- Summarize Results

Based on the analysis, the special program for divorce counseling, where married couples work as counseling teams, was more effective in reducing divorce rates compared to the regular program. However, the peer counseling program for depressed teenagers was not as effective as the standard counseling program in significantly improving the condition of the teens.

Key concepts

Divorce Counseling

Divorce counseling is a specialized type of therapeutic service aimed at helping couples navigate the complexities of divorce. The goal is to provide support and practical strategies to reduce the emotional and mental health impact of this life-changing event.

In this specific counseling program, married couples work as counseling teams. This unique approach aims to bring both male and female perspectives into sessions, potentially offering more balanced support.

From the results provided, when comparing a special divorce counseling program (with married counselors) to a regular program:

• The special program had a divorce rate of 53%.
• The regular program had a divorce rate of 59%.

This suggests that the special program appears more effective, as fewer couples ended up divorcing.

Peer Counseling

Peer counseling involves individuals of similar age or status providing support to one another. This can be especially helpful among teenagers, who might find it easier to open up to peers rather than adults.

In the context of a program designed to help depressed teenagers, peer counseling was compared to standard counseling. The effectiveness was measured by the percentage of children deemed 'much improved' after a year.

Here's how it broke down:

• The peer counseling program had an improvement rate of 10%.
• The standard program had an improvement rate of 15%.

Unfortunately, the peer counseling program did not seem as effective as the standard approach in this case.

Experimental Design

Experimental design is a method used to test hypotheses by carefully planning and controlling the conditions. This ensures any changes in the dependent variables can be attributed to the manipulations of the independent variables.

In these counseling program evaluations, experimental design played a critical role:

• Random Assignment: For both programs, half of the clients were randomly assigned to the experimental program, and the other half to the control (or standard) program. This minimizes bias and ensures the groups are comparable.
• Control Groups: Having a regular (control) program allows for a comparison to see if any observed effects can be attributed to the new program.
• Sample Size: Ensuring an adequate sample size (78 couples for divorce counseling and over 50 teens for peer counseling) helps in achieving more reliable results.

This kind of structured, systematic approach allows for clear, objective comparisons between different interventions.

Statistical Analysis

Statistical analysis entails collecting, reviewing, and interpreting data to uncover patterns and trends. It's a crucial part of evaluating any experimental program.

For the counseling programs, the following steps were taken:

• Proportions: The researchers compared the proportions of outcomes (e.g., divorce rates or improvement rates) between the experimental and standard groups.
• Comparison: Evaluating whether one program had significantly different results than the other. For instance, the lower divorce rate in the special program suggests it might be more effective.

In the case of the divorce counseling program:

• The special counseling program had a divorce rate of 53%.
• The regular program had a higher divorce rate of 59%.

In the case of the peer counseling program:

• The peer counseling program had an improvement rate of only 10%.
• The standard program had a higher improvement rate of 15%.

Such statistical comparisons are vital to determine the effectiveness of new programs over existing ones.