1. Do the example data meet the assumptions for the independent samples t -test? Provide a rationale for your answer.
Yes, the example data meets the criteria for independent sample t-test
The assumptions include; the means of the samples from the population are distributed normally. The two samples exhibit like variance. The dependent is computed at the ratio/interval levels. The observations in every sample are independent. All of these assumptions are met since, the members of the first group are not the same as those in the second sample. This will result to the two data from the clusters to be statistically different.
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2. If calculating by hand, draw the frequency distributions of the dependent variable, wages earned. What is the shape of the distribution? If using SPSS, what is the result of the Shapiro-Wilk test of normality for the dependent variable?
| Tests of Normality | ||||||
| Kolmogorov-Smirnov a | Shapiro-Wilk | |||||
| Statistic | df | Sig. | Statistic | df | Sig. | |
| Weekly Wages Eaned (Treatment group) | .147 | 10 | .200 * | .901 | 10 | .223 |
| *. This is a lower bound of the true significance. | ||||||
| a. Lilliefors Significance Correction | ||||||
The Shapiro-Wilk p-value is 0.223 for the weekly Wages. This value shoes that the frequency distribution didn’t deviate from the normal in a significant way.
3. What are the means for two group's wages earned?
Group Statistics | |||||
| Participant | N | Mean | Std. Deviation | Std. Error Mean | |
| Weekly Wages Earned | Treatment Group | 10 | 232.70 | 65.325 | 20.658 |
| Control Group | 10 | 128.40 | 43.025 | 13.606 | |
The mean of the weekly wages earned for the treatment group was 232.70, while that of the mean of weekly wages earned for the control group was 128.40. The joint mean for both groups is (232.70+128.40)/2=180.55
4. What is the independent samples t -test value?
| Independent Samples Test | ||||
| Levene's Test for Equality of Variances | t-test for Equality of Means | |||
| F | Sig. | t | ||
| Weekly Wages Earned | Equal variances assumed | 2.477 | .133 | 4.217 |
| Equal variances not assumed | 4.217 | |||
| Independent Samples Test | ||||
| t-test for Equality of Means | ||||
| df | Sig. (2-tailed) | Mean Difference | ||
| Weekly Wages Earned | Equal variances assumed | 18 | .001 | 104.300 |
| Equal variances not assumed | 15.572 | .001 | 104.300 | |
| Independent Samples Test | ||||
| t-test for Equality of Means | ||||
| Std. Error Difference | 95% Confidence Interval of the Difference | |||
| Lower | Upper | |||
| Weekly Wages Earned | Equal variances assumed | 24.736 | 52.332 | 156.268 |
| Equal variances not assumed | 24.736 | 51.745 | 156.855 | |
The t-test for the independent samples for weekly wages earned computed using SPSS is t=4.217
5. Is the t -test significant at a = 0.05? Specify how you arrived at your answer.
The t-value is statistically significant at α=0.05. We obtained this solution by contrasting the t-value of 4.217 with the limits of 52.33(lower limit) and 156.27(upper limit). The value does not falls inside of the two boundaries.
6. If using SPSS, what is the exact likelihood of obtaining a t -test value at least as extreme or as close to the one that was actually observed, assuming that the null hypothesis is true?
From the output obtained from SPSS, we observe that there is a 90% likelihood of getting a t-test value that is at least as extreme or near the observed value.
7. Which group earned the most money post-treatment?
The treatment group had a total of $2,327 weekly wages earned, while the control group had a total of $1,284. This means that the treatment earned the most money post treatment.
8. Write your interpretation of the results as you would in an APA-formatted journal.
Given the sample for the treatment group as n=20, and α=0.05>t=4.217, the outcome showed statistical significance for the test. This means that there is no difference between the number of a participant and the weekly wages earned.
9. What do the results indicate regarding the impact of the supported employment vocational rehabilitation on wages earned?
The findings show that the vocational rehabilitation has sufficiently effect on the wages earned by both the control and the treatment groups.
10. Was the sample size adequate to detect significant differences between the two groups in this example? Provide a rationale for your answer.
The size of the sample was sufficient to find the difference between the groups, since the results produced a significance level at α=0.05
