Statistics Paper Example with Questions on T-Test

EXERCISE 31

1. Do the example data meet the assumptions for the independent samples t-test? Provide a rationale for your answer.

In reflection to the data, the answer is a yes, the sample means from the population are usually distributed, through intervals and ratio level the dependent variable is measured with the two examples having equal variance ( that is the non-significant Levene's test since p > 0.05), will all observations recorded within each sample being independent.

Test of Homogeneity of Variances

wages

Levene Statistic df1 df2 Sig.

2.477 1 18 .133

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-Smirnova Shapiro-Wilk

Statistic df Sig. Statistic df Sig.

wages .155 20 .200* .935 20 .194

*. This is a lower bound of the real significance.

a. Lilliefors Significance Correction

The value Shapiro-Wilk value of 0.935 is not significant just because the amount of p 0.194 is more significant than 0.05.

3. What are the means for two group's wages earned?

Descriptives

Group Statistic Std. Error

wages 1 Mean 232.7000 20.65755

2 Mean 128.4000 13.60572

Mean group 1 (treatment group) is $232.70

Mean group 2 (control group) is $128.40

4. What are 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 Df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference

Lower Upper

wages Equal variances assumed 2.477 .133 4.217 18 .001 104.30000 24.73560 52.33243 156.26757

Equal variances not assumed 4.217 15.572 .001 104.30000 24.73560 51.74540 156.85460

The independent samples t vale = 4.217.

5. Is the t-test significant at a = 0.05? Specify how you arrived at your answer.

It is essential to conduct the t-test. With the p-value for this t-test being 0.001, which is considered to be smaller than an alpha of 0.05 and hence viewed to be statistically meaningful.

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 observed, assuming that the null hypothesis is correct?

The exact expectation of achieving a t-test value at least as close as or as extreme to the one that was observed at first which is 0.001.

7. Which group earned the most money post-treatment?

The treatment group or, the Post-treatment group 1 earned the most money. The earning was viewed as an average of $232.70 per week versus the control group getting an average of $128.40 per week.

8. Write your interpretation of the results as you would in an APA-formatted journal.

When a paired samples t-test computed on weekly wages, it demonstrated that those who were participating, those who gained supported employment treatment had essentially more weekly wages post-treatment than participants in the control group, t (18) = 4.217, p = 0.001; x = $232.70 versus $128.40, respectively. Hence, the supported employment treatment adopted to enlarge weekly wages of those participating was efficient as demonstrated by enlargement in weekly wages earned post-treatment by participants in the control group verses the treatment group

9. What do the results indicate regarding the impact of the supported employment vocational rehabilitation on wages earned?

The results about the impact of the supported employment vocational rehabilitation on wages gained indicate that the appeared treatment to have a substantial effect on enlarging weekly wages, as evidenced by the wages of the supported employment treatment group increased weekly wages of $232.70 versus the control group only earning $128.40 weekly

10. Was the sample size adequate to detect significant differences between the two groups in this example? Provide a rationale for your answer.

It's a yes; the sample size was enough in detecting essential differences that exist between the two groups as demonstrated. The value of P was identified to be 0.001, which is considered to be less than an alpha of 0.05, and hence statistically significant.

EXERCISE 32

1. Do the example data meet the assumptions for the paired samples t-test? Provide a rationale for your answer.

The example data meet the assumptions for the paired sample t-test with the dependent variable being approximately distributed. From a rational example, the data are measured at interval level with a repeated measure from one subject group in which they are serving as their matching and control of groups on the selected variable. The difference that is existing between the paired scores is identified to be independent.

2. If calculating by hand, draw the frequency distributions of the two variables. What are the shapes of the distributions? If using SPSS, what are the results of the Shapiro-Wilk tests of normality for the two variables?

Tests of Normality

Kolmogorov-Smirnova Shapiro-Wilk

Statistic df Sig. Statistic df Sig.

Baselineaffectivedistressscore .134 10 .200* .953 10 .705

posttxaffectivedistress .235 10 .124 .912 10 .292

*. This is a lower bound of the real significance.

a. Lilliefors Significance Correction

Post-treatment affective distress scores - Shapiro-Wilk is 0.912

Baseline affective distress scores - Shapiro-Wilk is 0.953

The Shapiro-Wilk is identified not to be statistically crucial with a p-value being recorded at 0.292 for post-treatment scores and 0.705 for baseline scores. The p-value for both scores is much more significant than 0.05 and hence its viewed not to be significant.

3. What are the means for the baseline and posttreatment affective distress scores, respectively?

Statistic Std. Error

baselineaffectivedistressscore Mean 3.030 .5262

95% Confidence Interval for Mean Lower Bound 1.840 Upper Bound 4.220 5% Trimmed Mean 3.061 Median 3.300 posttxaffectivedistress Mean 2.040 .3110

95% Confidence Interval for Mean Lower Bound 1.337 Upper Bound 2.743 Baseline mean = 3.030

Post treatment mean = 2.040

4. What is the paired samples t-test value?

Paired Samples Test

Paired Differences t Df Sig. (2-tailed)

Mean Std. Deviation Std. Error Mean 95% Confidence Interval of the Difference Lower Upper Pair 1 baseline - posttx .9900 1.0929 .3456 .2082 1.7718 2.865 9 .019

The paired samples t-test value is 2.865.

5. Is the t-test significant at a = 0.05? Specify how you arrived at your answer.

The t-test is considered to be significant, with the p-value for the paired t-test is considered to be 0.019, which is far much lesser than 0.05 and therefore it is considered to be statistically significant.

6. If using SPSS, what is the exact likelihood of obtaining a t-test value at least as extreme as or as close to the one that was observed, assuming that the null hypothesis is correct?

The likelihood of coming up with a t-test value at close and extreme to the one that was observed is 0.019.

7. On average, did the affective distress scores improve or deteriorate over time? Provide a rationale for your answer.

Paired Samples Statistics

Mean N Std. Deviation Std. Error Mean

Pair 1 baseline 3.030 10 1.6640 .5262

posttx 2.040 10 .9834 .3110

The effective distress scores improved over time. This happened by considering a greater scores in the presented data and more emotional distress that resulted in pain. According to the chart above, the mean decreased from 3.030 at baseline affective scores to 2.040 at post-treatment scores. This ends up decreasing in the means indicating great improvement in affective scores for a period.

8. Write your interpretation of the results as you would in an APA-formatted journal.

Paired samples t-test that is computed on impacting distress scores showed that the patients who were subjected to rehabilitation for facing emotional distress had lower efficient distress scores importantly from post-treatment to baseline, t(9) = 2.865, p = 0.019; x = 3.030 versus 2.040, respectively. Hence, the specific type of rehabilitation method adopted on improving the affective distress levels of patients was impacted as represented by decreases in affective distress scores.

9. What do the results indicate regarding the impact of the rehabilitation on emotional distress levels?

The results demonstrated that rehabilitation seems to have been efficient when it comes to reducing the emotional distress through lowering the affective distress scores. Baseline affective ratings achieved a mean of 3.030 and post-treatment scores gained a way of 2.040, showing a general decrease in emotional distress after the process of treatment.

10. What are the weaknesses of the design in this example?

Concerning weaknesses, one significant fault of the design showed that one sample design was achieved without a comparison group. Hence, there do exist various alternatives that explain some of the changes over them. On the other hand, among them are testing effects, statistical regression, maturation, and history. Additionally, the sample size that was achieved is also viewed to be too small with only ten participants.