EXERCISE 31

Exercise 31 Responses 

  1. Given the data in this study, it meets all the basic assumptions for an independent sample t-test; the dependent variable was measured on an ordinal or continuous scale; the data was drawn from a random sample; based on the Levene’s test there as homogeneity of variances; and the dependent variable is normally distributed. All these assumptions are met for an independent t-test for the data given. 

Levene’s Test for homogeneity of variance

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  1. The shape of wage, the dependent variable is normally distributed as seen in the below distribution curve. Also, based on the Shapiro-Wilk test the p-value is given as 0.194 which is greater than 0.05 indicating that the distribution is normally curved. 

Normal distribution of wage

Shapiro-wilk Test for normality 

Tests of Normality
GroupKolmogorov-SmirnovaShapiro-Wilk
StatisticdfSig.StatisticdfSig.
wagesTreatment.14710.200*.90110.223
control.19310.200*.91410.311
*. This is a lower bound of the true significance.
a. Lilliefors Significance Correction
  1. The mean wages for the treatment group was $232.7 (SD = 65.3249) while that of the control group was $128.4000 (SD = 43.0251). 

Group mean wages 

Group Statistics
GroupNMeanStd. DeviationStd. Error Mean
wagesTreatment10232.700065.3249120.65755
control10128.400043.0250613.60572
  1. Based on the independent t-test analysis the t-value was 4.127 with 18 degrees of freedom 

Independent T-test output

Independent Samples Test
Levene’s Test for Equality of Variancest-test for Equality of Means
FSig.tdfSig. (2-tailed)Mean DifferenceStd. Error Difference95% Confidence Interval of the Difference
LowerUpper
wagesEqual variances assumed2.477.1334.21718.001104.3000024.7356052.33243156.26757
Equal variances not assumed4.21715.572.001104.3000024.7356051.74540156.85460
  1. Using the table above showing the independent t-test, the t-value is given as 4.127 and is significant at 0.05. Ideally, it is clear that the P-value is 0.001 which is less than alpha (0.05), hence the null hypothesis is rejected indicating that there was significant difference in the group mean wages. 
  2. Based on the p-value in the above table in part 4, the chances of making type 1 error is 0.001 or 0.1% which is the p-value realized in the SPSS analysis. In other words, there is a 0.1% chance of obtaining a t-test value that is extreme, given that the null hypothesis is true.  
  3. The treatment group earned higher money after the intervention (treatment) than the control group. This can be explained by the a greater mean wages of the treatment group ($232.70) comparing with that of the control group ($128.40)

Mean wages for the two groups 

Group Statistics
GroupNMeanStd. DeviationStd. Error Mean
wagesTreatment10232.700065.3249120.65755
control10128.400043.0250613.60572
  1. Considering the above study results, if they were to appear in APA-formatted journal, they would appear as follows; 

Disabled veterans (n = 10) participating in a work-assistance program earned significantly more money (Mean = $232.70, SD = 65.32) than the veterans (n = 10) who never received this type of work-assistance program (M = $128.40, SD = 43.0206); tdf = 4.217, P < 0.05). 

  1. Based on the results, it is clear that there is a significant difference between the wages earned by participants who received the intervention programme than the group that never received it. Therefore, the employment vocational rehab programme has a positive impact on the wages earned by the participants (the disabled veterans). 
  2. I don’t think that the sample size was adequate to reveal the differences in income between these two groups. Ideally, a sample of 10 participants does not adequately or statistically represent the whole population; hence it is not advisable to generalize the findings. Further studies with larger sample sizes can investigate this phenomenon. 

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