# Stats Assignment

These data are from a random sample of students from schools in a southern state. Although not representative of the United States, it covers a variety of important delinquent behaviors and peer influences.

Data for Exercise

Data Set

Description

Youth.sav

These data are from a random sample of students from schools in a southern state. Although not representative of the United States, it covers a variety of important delinquent behaviors and peer influences.

Variables for Exercise

Variable Name

Description

D1

A binary variable based on the number of delinquent acts a respondent reported. A 0 indicates that the respondent reported 1 or fewer acts, whereas a 1 indicates 2 or more acts.

Lowcertain_bin

Binary indicator of whether respondents felt there was certainty that they’d be punished for delinquent behaviors. 1 = low certainty, 0 = high certainty.

Gender

The gender of the respondent where 1 = male and 0 = female.

V2

Age of the respondent in years.

Moral

A scale that measures whether respondents thought delinquency was morally wrong. High values indicate that delinquency is viewed as morally wrong.

Delinquency

A scale indicating the number of delinquent acts that an individual reports participating in.

Studyhard

Binary indicator of studying behavior of respondents where 0 = studies less than 8 hours per week and 1 = studies 8 or more hours per week.

1. Are delinquent teens more likely to be older than teens who don’t report delinquency? One way to look at this question is with a t test. In this case, we’ll compare the mean age for delinquent students with the mean age of non-delinquent students:

a. State research and null hypotheses for this topic.

b. What type of test should you use: an independent-samples t test or a matched-group test?

c. For this analysis, use an alpha of .001 for your significance level.

d. Conducting an independent-samples t test in SPSS: To run a t test in SPSS, select analyze->compare means-> independent-samples t-test. Put the variable “V2” (age) in the “test variable” box. Click “define groups” and enter 0 in one box and 1 in the other. Then, put our grouping variable, “D1,” in the “grouping variable” box. Select Ok:

i. The output for this needs some explanation. The first box that comes out tells you the number of cases in each group (n) and the mean and standard deviation for each group. The second box has two rows that correspond to t tests conducted with equal or unequal variances assumed. Levene’s test for equality of variances is an F test comparing group variances that will be addressed in a later question. You are interested in the columns labeled “T” and “sig. 2-tailed”; these are your test statistic and its exact p value. Also of interest is the “mean difference” box, which contains the value for the mean of group 1 minus the mean of group 2.

e. Assume that a difference of .15 in standard deviation is evidence that you have unequal variances. After looking at the standard deviations for either group, do you conclude that these groups have equal or unequal variances?

f. By using the appropriate variance assumptions, what do you conclude about the null hypothesis?

g. Write a sentence explaining what this result tells us about delinquency in substantive terms.

2. Are students who spend lots of time studying likely to also view delinquency as wrong? Some theorists would suggest this should be the case as high adherence to social roles (e.g., student, good kid) means that the penalties for delinquency will have a higher social cost. Let’s investigate with a t test:

a. State research and null hypotheses for this topic.

b. What type of test should you use: an independent-samples t test or a matched-group test?

c. For this analysis, use alphas of both of .05 and .001 for your significance level.

d. Conduct the independent-samples t test in SPSS (described earlier). In this case, use the variable “Moral” as the dependent variable and “Studyhard” as the independent variable.

Levene’s test for equality of variances: The easiest way to determine whether we should assume equal variances in our t test is to use an F test comparing the variances of both groups. The two columns for Levene’s test for equality of variances do just that. The output shows an F test and its associated p value. The null hypothesis in this case is that variances are equal, whereas the research hypothesis is that they are unequal. In other words, a significant test means we should use the “equal variances not assumed” test row:

e. What is your decision about the null hypothesis in Levene’s test? What assumptions should you use for your t test?

f. What is your conclusion regarding the null and research hypotheses?

g. Substantively, do these results support the theory described earlier, or do they contradict it? Use your data to explain why.

3. Do boys commit more delinquent acts, on average, than girls? Perform an independent-samples t test with the variables “Gender” and “Delinquency” to test this question. Use questions 1 and 2 to guide you through this process; be sure to check your F test in determining the appropriate test to use. After the test, provide a educational explanation for why you found what you did.

4. Just before being hauled off to jail, TV show villains often say, “I would have gotten away with it if it wasn’t for you meddling kids!” The underlying statement is that they committed the crime because they thought they could get away with it. We could ask, then, are individuals who think they won’t get punished more likely to commit delinquent acts? Conduct an independent hypothesis test between the variables “Lowcertain_bin” and “Delinquency.” Be sure to go through all steps of the hypothesis testing process. After the analysis, write a few sentences about the practical implications of this result.

5. “But I didn’t know it was wrong!” is a common statement made by children when they have been caught doing something bad. Perhaps the belief that their behaviors just aren’t so wrong might lead to more delinquency. To research this, conduct a t test of the variables “Moral” and “Delinquency.” You may notice that the variable “Moral” is not binary; when defining groups in the t test menu, use the value 16 as a cut point. This will compare individuals with scores that are greater than or equal to 16 against those who score less than 16. What do you conclude about the null hypothesis? What is the practical significance of this result?