**Reliability Statistics**

- A RELIABILITY procedure was performed on the 10 items of the AUDIT scale resulting in the attached output from SPSS. Please comment fully on the results of this procedure (shown below).

** Case Processing Summary**** **

N | % | ||

Cases | Valid | 98 | 92.5 |

Excluded(a) | 8 | 7.5 | |

Total | 106 | 100.0 |

a Listwise deletion based on all variables in the procedure.

** Reliability Statistics**** **

Cronbach’s Alpha | N of Items |

.855 | 10 |

** Item Statistics**** **

Mean | Std. Deviation | N | |

audit1 | 1.74 | 1.115 | 98 |

audit2 | 1.10 | 1.272 | 98 |

audit3 | 1.16 | 1.155 | 98 |

audit4 | .21 | .662 | 98 |

audit5 | .18 | .544 | 98 |

audit6 | .17 | .626 | 98 |

audit7 | .44 | .826 | 98 |

audit8 | .71 | 1.015 | 98 |

audit9 | .88 | 1.548 | 98 |

audit10 | .39 | 1.136 | 98 |

** Item-Total Statistics**** **

Scale Mean if Item Deleted | Scale Variance if Item Deleted | Corrected Item-Total Correlation | Cronbach’s Alpha if Item Deleted | |

audit1 | 5.26 | 36.110 | .678 | .830 |

audit2 | 5.90 | 33.804 | .744 | .822 |

audit3 | 5.84 | 34.550 | .777 | .819 |

audit4 | 6.79 | 42.954 | .351 | .856 |

audit5 | 6.82 | 43.286 | .398 | .854 |

audit6 | 6.83 | 41.629 | .546 | .846 |

audit7 | 6.56 | 40.620 | .488 | .847 |

audit8 | 6.29 | 36.722 | .705 | .828 |

audit9 | 6.12 | 35.016 | .492 | .857 |

audit10 | 6.61 | 37.498 | .549 | .842 |

** Scale Statistics**** **

Mean | Variance | Std. Deviation | N of Items |

7.00 | 46.433 | 6.814 | 10 |

- Self ratings of problem behaviour of 2 groups of adolescents were classified into the ranges ‘normal’ ‘borderline’ and ‘clinical’ (labelled 1,2 & 3 respectively) based on a standard clinical measure. An SPSS crosstabs procedure with a Pearson Chi-square statistical test was used to test whether there was an association between which school an adolescent belonged to and the assessment category allocated to them. Please fully interpret the output shown below.

** Case Processing Summary**** **

Cases | ||||||

Valid | Missing | Total | ||||

N | Percent | N | Percent | N | Percent | |

school * problembeh | 95 | 99.0% | 1 | 1.0% | 96 | 100.0% |

** school * problembehCrosstabulation**** **

problembeh | Total | |||||

1.00 | 2.00 | 3.00 | ||||

School | 1.00 | Count | 19 | 12 | 16 | 47 |

Expected Count | 31.2 | 7.4 | 8.4 | 47.0 | ||

Adjusted Residual | -5.3 | 2.6 | 4.1 | |||

2.00 | Count | 44 | 3 | 1 | 48 | |

Expected Count | 31.8 | 7.6 | 8.6 | 48.0 | ||

Adjusted Residual | 5.3 | -2.6 | -4.1 | |||

Total | Count | 63 | 15 | 17 | 95 | |

Expected Count | 63.0 | 15.0 | 17.0 | 95.0 |

** Chi-Square Tests**

Value | df | Asymp. Sig. (2-sided) | |

Pearson Chi-Square | 28.549(a) | 2 | .000 |

Likelihood Ratio | 31.931 | 2 | .000 |

Linear-by-Linear Association | 26.768 | 1 | .000 |

N of Valid Cases | 95 |

a 0 cells (.0%) have expected count less than 5. The minimum expected count is 7.42** **

- In the attached SPSS output a t-test has been performed to test the hypothesis that there are no differences in reported alcohol problems between two sets of adolescents. Please interpret the output information fully.

** Group Statistics**** **

school | N | Mean | Std. Deviation | Std. Error Mean | |

Audit | 1.00 | 48 | 10.7708 | 7.97400 | 1.15095 |

2.00 | 48 | 3.2500 | 3.27141 | .47219 |

**Independent Samples Test**** **

Levene’s Test for Equality of Variances | t-test for Equality of Means | |||||||||

F | Sig. | t | df | Sig. (2-tailed) | Mean Difference | Std. Error Difference | 95% Confidence Interval of the Difference | |||

Lower | Upper | |||||||||

audit | Equal variances assumed | 31.162 | .000 | 6.045 | 94 | .000 | 7.52083 | 1.24404 | 5.05076 | 9.99091 |

Equal variances not assumed | 6.045 | 62.386 | .000 | 7.52083 | 1.24404 | 5.03433 | 10.00733 |

**Solution**** **

- A RELIABILITY procedure was performed on the 10 items of the AUDIT scale resulting in the attached output from SPSS. Please comment fully on the results of this procedure (shown below).

** Case Processing Summary**

N | % | ||

Cases | Valid | 98 | 92.5 |

Excluded(a) | 8 | 7.5 | |

Total | 106 | 100.0 |

a Listwise deletion based on all variables in the procedure.

Case processing summary suggests that out of total 106 samples, 8 elements are excluded and only 98 elements are included. This means only 98 elements completed/responded sufficient items to be included in the analysis.

** Reliability Statistics**

Cronbach’s Alpha | N of Items |

.855 | 10 |

The reliability statistics table determineCronbach’s Alpha. The table indicates that Cronbach’s Alpha is 0.855. This indicates that there is high level of internal consistency for the considered scale. A Cronbach’s alpha of 0.7 or high consider as a metric for relatively higher degree of internal consistency. Further, number of items is only 10 which meansnumber of items in scale is 10.

** Item Statistics**

Mean | Std. Deviation | N | |

audit1 | 1.74 | 1.115 | 98 |

audit2 | 1.10 | 1.272 | 98 |

audit3 | 1.16 | 1.155 | 98 |

audit4 | .21 | .662 | 98 |

audit5 | .18 | .544 | 98 |

audit6 | .17 | .626 | 98 |

audit7 | .44 | .826 | 98 |

audit8 | .71 | 1.015 | 98 |

audit9 | .88 | 1.548 | 98 |

audit10 | .39 | 1.136 | 98 |

Above table gives means and standard deviations for each of your question items. Highest mean for audit 1 is 1.74 while highest standard deviation for audit 9 is 1.548.

** Item-Total Statistics**

Scale Mean if Item Deleted | Scale Variance if Item Deleted | Corrected Item-Total Correlation | Cronbach’s Alpha if Item Deleted | |

audit1 | 5.26 | 36.110 | .678 | .830 |

audit2 | 5.90 | 33.804 | .744 | .822 |

audit3 | 5.84 | 34.550 | .777 | .819 |

audit4 | 6.79 | 42.954 | .351 | .856 |

audit5 | 6.82 | 43.286 | .398 | .854 |

audit6 | 6.83 | 41.629 | .546 | .846 |

audit7 | 6.56 | 40.620 | .488 | .847 |

audit8 | 6.29 | 36.722 | .705 | .828 |

audit9 | 6.12 | 35.016 | .492 | .857 |

audit10 | 6.61 | 37.498 | .549 | .842 |

This table can really help you to decide whether any items need to be removed. The analysis is based on the fact that if any items gets removed, Cronbach’s alpha gets improved. Analysis suggests if ‘audit 4’ and ‘audit 9’ be removed, Cronbach’s Alpha gets improved. Hence ‘audit 4’ and ‘audit 9’ may be removed for improving reliability.

** Scale Statistics**** **

Mean | Variance | Std. Deviation | N of Items |

7.00 | 46.433 | 6.814 | 10 |

This final table in the output gives you the descriptive statistics for the questionnaire as a whole.

- Self ratings of problem behaviour of 2 groups of adolescents were classified into the ranges ‘normal’ ‘borderline’ and ‘clinical’ (labelled 1,2 & 3 respectively) based on a standard clinical measure. An SPSS crosstabs procedure with a Pearson Chi-square statistical test was used to test whether there was an association between which school an adolescent belonged to and the assessment category allocated to them. Please fully interpret the output shown below.

** Case Processing Summary**

Cases | ||||||

Valid | Missing | Total | ||||

N | Percent | N | Percent | N | Percent | |

school * problembeh | 95 | 99.0% | 1 | 1.0% | 96 | 100.0% |

Case processing summary suggests that out of total 96 samples, 1 element is excluded and only 95 elements are included. This means only 95 elements completed/responded sufficient items to be included in the analysis.

** school * problembehCrosstabulation**** **

problembeh | Total | |||||

1.00 | 2.00 | 3.00 | ||||

School | 1.00 | Count | 19 | 12 | 16 | 47 |

Expected Count | 31.2 | 7.4 | 8.4 | 47.0 | ||

Adjusted Residual | -5.3 | 2.6 | 4.1 | |||

2.00 | Count | 44 | 3 | 1 | 48 | |

Expected Count | 31.8 | 7.6 | 8.6 | 48.0 | ||

Adjusted Residual | 5.3 | -2.6 | -4.1 | |||

Total | Count | 63 | 15 | 17 | 95 | |

Expected Count | 63.0 | 15.0 | 17.0 | 95.0 |

This table helps in establishing the fact that maximum problem behaviour of both group classified into normal

** Chi-Square Tests**** **

Value | df | Asymp. Sig. (2-sided) | |

Pearson Chi-Square | 28.549(a) | 2 | .000 |

Likelihood Ratio | 31.931 | 2 | .000 |

Linear-by-Linear Association | 26.768 | 1 | .000 |

N of Valid Cases | 95 |

a 0 cells (.0%) have expected count less than 5. The minimum expected count is 7.42.

The table above is quite useful in inferring the results of Chi-Square Tests. “Pearson Chi-Square” row indicates that χ(2) = 28.549, p = .000. The degree of freedom may be consider as 2 [ (r-1) x (c-1)]. This indicates there are enough statistical evidence to reject the null hypothesis. Hence there is statistically significant association between groups and problem behaviourthat is, both groupsdo not associate similar to different category of problem behaviour namely ‘normal’ ‘borderline’ and ‘clinical’.

- In the attached SPSS output a t-test has been performed to test the hypothesis that there are no differences in reported alcohol problems between two sets of adolescents. Please interpret the output information fully.

The null and alternate hypothesis is described below:

H0: There are no differences in reported alcohol problems

Ha: There are significant statistical difference in reported alcohol problems** **

** Group Statistics**** **

school | N | Mean | Std. Deviation | Std. Error Mean | |

audit | 1.00 | 48 | 10.7708 | 7.97400 | 1.15095 |

2.00 | 48 | 3.2500 | 3.27141 | .47219 |

As a first step, descriptive statistics are estimated. The number of samples in both the groups is 48. The mean of first group is 10.7708 while mean of second group is 3.2500. The standard deviation of first group is 7.97400 while standard deviation of second group is 3.27141

** Independent Samples Test**** **

Levene’s Test for Equality of Variances | t-test for Equality of Means | |||||||||

F | Sig. | t | df | Sig. (2-tailed) | Mean Difference | Std. Error Difference | 95% Confidence Interval of the Difference | |||

Lower | Upper | |||||||||

audit | Equal variances assumed | 31.162 | .000 | 6.045 | 94 | .000 | 7.52083 | 1.24404 | 5.05076 | 9.99091 |

Equal variances not assumed | 6.045 | 62.386 | .000 | 7.52083 | 1.24404 | 5.03433 | 10.00733 |

The above table comprises of two important test. First, Levene’s Test for Equality of Variances and second, t-test for Equality of Means.Levene’s test is used to test if k samples have equal variances. Equal variances across samples is called homogeneity of variance. Some statistical tests, for example the analysis of variance, assume that variances are equal across groups or samples. The Levene test can be used to verify that assumption.

The null and alternate hypothesis for Levene’s Test for Equality of Variances is shown below:

H0: σ_{1}^{2 }=σ_{2}^{2 }

Ha: σ_{1}^{2 }≠σ_{2}^{2 }

Test Statistic: Given a variable Y with sample of size N divided into k subgroups, where N_{i} is the sample size of the ith subgroup, the Levene test statistic is defined as:

The p-value of test is less than 0.05 which is the level of significance of test. Hence there are sufficient statistical evidence to reject the null hypothesis. Hence, it can be inferred that variances of two groups are unequal.

Post that t-test is conducted for independent samples having un-equal variances. The null and alternate hypothesis of the test is already defined above. Degree of freedom for the tests is n1 + n2 -2 = 48 + 48 -2 = 96.The t- static is defined as follows:

Where symbols have standard meanings

The p-value of the tests is 0.00 which means there is sufficient statistical evidence to reject null hypothesis which means there are significant statistical difference in reported alcohol problems of the two samples.