Question

Problem 9.12 There are two parts of the problem a and b i was able to get the answer for the first part, but for the second part I wasn't able to finish it

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 percent- age of children who were judged to be “much improved,” did the new program work?

Sample 1 (Peer Counseling) Sample 2 (Standard Program)

ps1 5 0.10 ps2 5 0.15

N1 5 52 N2 5 56

Answer 1

As no data or response is provided with the question, so in this regard, I shall explain you how to proceed with this experiment.

This problem can be analysed with the help of One Factor Anova.

The One Factor Anova is generally used to analyse if there are any statistically significant differences between the means/averages of two or more independent or any such unrelated groups whic is applicable in your experiment.

In this case, say half of the clients were randomly assigned for the new program and after one year of the program, say a sample of size "n" was randomly selected from it and was analysed especially to check its improvement.

In this case, respective score or ratings can be given on a determined scale say 1 to 100 or 1 to 10 and all.

Say, for each and every teenager of the randomly selected sample (from the new program) a respective score is awarded after analysing their new condition. If there condition has improved then a better core of 7 to 10 can be assigned to it. Similarly on the other hand, for the standard program a random sample can be selected and then ratings can be assigned to it based on its improvement.

Later on, an One factor Anova will be performed in order to analyse if there is any significant difference observed in the average ratings of both the groups.

Hypothesis:

H₀ : U₁ = U₂ (U = average rating) (Null Hypothesis)

H_a : All the means are not equal (Alternate Hypothesis)

Here, if the null hypothesis is accepted, then it means that new program is not improving the condition of the depressed teenagers and on the other hand, if the alternate hypothesis is accepted then it means that there is a change in improvement among the two groups.

A sample collection of data is shown below just for reference purpose.

As no such observation is mentioned in the question, so I have considered a sample of 11 and gave them specific ratings out of 10 just for reference purpose in order to explain you the procedure of analysing the output of a One Factor Anova.

Let,

A = Standard Program

B = New Program

Sample rating for the members of each sample is given on a scale of 1-10.

Kindly note that this is a sample output where we are comparing the data of two different groups.

Here, you can see that the P value is 9.39 * 10^-7

If we take the confidence level as 95% (Alpha will 0.05)

Alpha = 1 - Confidence Level

= 1 - 0.95

= 0.05

Alpha level is the probability of rejecting the null hypothesis when the null hypothesis is true.

Here as the P value is smaller than 0.05, so we can state that the null hypothesis is not accepted. This is because there arises a significant difference in the means of the two groups.

Similarly for your case, if there is any significant difference observed than you can state that the average improvement is different in both the groups.

Later, you can perform a post hoc test to do the comparison and then determine how much the population in Sample B is improved in comparison to the population in group A.

End of the Solution...