Question

7. SPSS Interpretation Questions. The following SPSS output tables show the results from a new study of drug use in Boston. The study is based on a random sample of individuals (total N=250).  

A. The research team’s main research question was determining the effect of diversion program for drug offenders on their frequency of drug use. Participants in the program were not arrested for their crimes, but instead diverted for drug treatment. The researchers have information on a sample of 100 participants in the program and 150 non-participants in the program. They show the descriptive statistics for heroin usage for each group as well as the results of their difference-in-means hypothesis test in the tables below.

(Please note that the information about the equality of variances test has been removed from the table above. These are usually displayed in the first few boxes. They are not needed here.)

Group Statistics

N Mean Std. deviation Std. Error Mean

no 150 12.80 13.86609 1.13216

yes 100 8.1500 12.02302 1.20230

Independent Samples Test

t= 2.737, df=248, sig (2 tailed)=.007, mean difference 4.65000, std error difference= 1.69912, 95% CI of the Difference lower: 1.30345, upper: 7.99655

i Based on these tables above, please write a brief summary of the results. Support all conclusions about the substance of the difference and statistical significance with the relevant statistics. (Note: You only need about 3 sentences here.)

ii. Using the table above, what is the exact probability of falsely rejecting the null hypothesis? In other words, what is the probability of observing the difference between means reported in the table and the null hypothesis being true? The table provides this information as one of the reported statistics.

Answer 1

Result:

7. SPSS Interpretation Questions. The following SPSS output tables show the results from a new study of drug use in Boston. The study is based on a random sample of individuals (total N=250).  

A. The research team’s main research question was determining the effect of diversion program for drug offenders on their frequency of drug use. Participants in the program were not arrested for their crimes, but instead diverted for drug treatment. The researchers have information on a sample of 100 participants in the program and 150 non-participants in the program. They show the descriptive statistics for heroin usage for each group as well as the results of their difference-in-means hypothesis test in the tables below.

(Please note that the information about the equality of variances test has been removed from the table above. These are usually displayed in the first few boxes. They are not needed here.)

Group Statistics

N Mean Std. deviation Std. Error Mean

no 150 12.80 13.86609 1.13216

yes 100 8.1500 12.02302 1.20230

Independent Samples Test

t= 2.737, df=248, sig (2 tailed)=.007, mean difference 4.65000, std error difference= 1.69912, 95% CI of the Difference lower: 1.30345, upper: 7.99655

i Based on these tables above, please write a brief summary of the results. Support all conclusions about the substance of the difference and statistical significance with the relevant statistics. (Note: You only need about 3 sentences here.)

The 100 participants in the diversion program and 150 non-participants are studied for their heroin usage. The 100 participants in the program group (M = 8.15, SD = 12.02) and the 150 non participants group (M = 12.8, SD = 13.87), demonstrated a significant difference in heroin usage (t[248] = -2.737, p = .007).

ii. Using the table above, what is the exact probability of falsely rejecting the null hypothesis? In other words, what is the probability of observing the difference between means reported in the table and the null hypothesis being true? The table provides this information as one of the reported statistics.

Probability of observing the difference between means reported in the table and the null hypothesis being true = p value = 0.007.