10 Statistics questions

Grove and Cipher Amanda Barnett-McLean 21 July 2020

Ex: 16

1. In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary. The number of independent ways by which a dynamic system can move, without violating any constraint imposed on it.

2. .

3. For age, the t-value is -1.498 and the p value is 0.136. The p-value being more than 0.05 means that it is not statistically significant and the t value being

Ex: 17

1. Assumptions are in a paired t-test study that The distribution of scores is normal or approximately normal, the dependent variable is/are measured at interval or ratio levels, repeated measures data are collected from one group of subjects, resulting in paired scores, and the differences between the paired scores are independent. The assumptions made are that the variables were measured on a scale that is continuous. The independent variable also consisted of two marched pairs that were categorical. Significance outliers were not experienced with the data. The distribution was considered to be standard. The Lindseth study was also observed to have met the mentioned criteria, whereby the independent variables were harmonized pairs, variables being continuous, and the distribution being normal.

2. The “2 weeks without diets” is important to make sure that the patient's system returns to a normal baseline. This is important to make sure that the results are not being skewed in anyway.

3. The t-test value for mood is 3.4. This is statistically significant because a t-test with a p-value of 0.002 is less than p = 0.05 and therefore statistically significant.

4. When consuming a high aspartame diet (25mg/kg body weight/day) for 8 days versus a low aspartame diet (10mg/kg body/weight/day) for 8 days, there will be no effect on mood. This null hypothesis was rejected as there was an effect noted on mood and irritability between the two diet regimens that were viewed as statistically significant. The null hypothesis, which was indicated to be aspartame did not indicate any significant effect on the mood, thereby illustrating irritability. Thus, such hypothesis was excluded. The t-test statistic was 3.4 as the p-value was 0.002. These values also indicated that the values of the means of such neurobehavioral tallies were substantially diverse.

5. The t-value is 3.8 for the Depression category. It is statistically significant because p is 0.001 or <0.01 and that is less that a = 0.05. The depression’s t-value represented one of the utmost relative differences between the dies of low-aspartame and high-aspartame. The t-value was also significant 3.8, including p-value of 0.001. In that case, the p-value was way below the value of alpha level, which was at 0.05. Thus, indicating that the result was weighty. The greatest relative difference was also witnessed since t-value was one of the greatest from measured values.

6. The t-value was used to quantity the size of the variance relative to the sample population variation. When t-value is large, the change between the sample populations also becomes greater.

7. The findings of the research study indicate that a diet of high-aspartame has negative impacts on depression. Such findings are clinical important since aspartame is a mutual ingredient in many diets, including sodas. This might be one of the reasons why some individuals succumb to depression. Therefore, a change in diet might help with the alleviation of such problems.

8. The processes of the working memory indicate the smallest t-value, which was 1.5. This was also an indication that the variance between the groups relative to the sample variation was not good enough to result into statistical connotation.

9. Such kinds of investigation are clinically essential since aspartame is widespread in food diets of many individuals. Artificial inducement has neurobehavioral effects and the issue is alarming. For that reason, further study should be warranted, including the investigation of the negative effect it might have. From the helthlin.com, aspartame is considered to be dangerous to individuals who have phenylketonuria because it can cause diseases such as cancer, diabetes, and tardive dyskinesia.

10. The results of the study were not ready for enactment as far as health practice is concerned. Even though they are good studies, which provide auspicious evidence, studies should be meticulous and exhibit large population sample for broader conclusions as per the findings.

Ex: 18

1. The degree of freedom is usually obtained by deducting k, whereby the number of the groups within the study is taken to be 3. The number of the participants is also represented by N. For that reason, df = 255 – 3 = 252. The error experienced by df is expressed as follows k-1 = 3-1=2.

2. The results obtained as F = 38.1 when p=<0.0001 implies that there is a substantial dissimilarity between one of the groups that is matched to other two groups in the research study. Also, post-hoc analysis is essential for determining, where the significance of the study lies.

3. The outcomes of the investigation indicate that the post-hoc result for the hospital facilities when comparing the hospital without LCP versus the one with LCP is p=0.85. The alpha value of the connotation also implies that there is no variance when using the means for comparison. According to my opinion, this was an expected fining because the hospital facilities were expected to have standard of care, thereby implying that the facilities are also similar.

4. Assumptions that can be made while using ANOVA include the following:

1. The groups were conjointly exclusive.

1. The observations made were independent.

1. The same used was of normal distributions.

1. The groups had equal variance.

1. The hooked on variable was in the form of ratio or interval.

5. What variable on Table 3 has the result F = 10.6, p < 0.0001? What does the result mean?

Symptom management was witnessed in the obtained result. The result also indicated that one of the measured groups was significantly or substantially different than the others. Consequently, meaning that one group had a substantially better symptom management at the end of the life cycle. There was also the possibility of the worse symptom management.

6. Even though t-tests can be used in analyzing the data, they might not be appropriate because in the experiment, several groups were compared to one another. Furthermore, t-tests can only be used in comparing two means and for that reason, multiple t-tests ought to have been done. The comparison might also raise the possibility of Type I error, whereby significant results are obtained even though they are not really significant.

7. The Tukey’s HSD was performed like the post-hoc test. Also it was observed that Scheffe test was more conservative than when compared to the Tukey’s HSD. The comparison might have prevented type 1 error and detection of the true differences from the mentioned tests.

8. The null hypothesis implies that care is quantified to be equal across the given three study groups. However, the null hypothesis might be rejected because p=<0.0001 and F=35.9.

9. For the care experiment, the post-hoc results indicate that Hospice was significantly or substantially higher care than the Hospital having LCP, including the Hospital without LCP. Furthermore, Hospital without LCP has lower statistically significant care than the Hospital with LCP.

10. The findings of the study presented in table 2 and table 3 indicate that Hospice has significantly higher scores for facilities, communication, care, and environment during the end of a life care. However, there were no differences in the management or control of symptom while comparing the hospice to the hospitals that have LCP. Differences were also observed when comparing the same with the hospitals without the LCP protocol. The findings also indicate that hospice facilities are better suited when compared to hospitals. They can handle end of life care for patients having critical conditions.

Ex: 31

1. No. there are 2 independent categorical groups. The dependent variable looks to be normally distributed the variance of the dependent variables are not equal in the first table.

2. The first histogram on the left is positively skewed with a gap at 100 the second histogram on the right Is a U-shaped histogram or concave. The normality for both histograms is 10 being greater than 0.05 Thus meaning it is normal.

3. The control mean is 128.4000 and the mean for treatment group is 232.7000.

4. -4.217

5. On the t-test, the sig. dif was p=0.001 but the sample size was small. So,while it is statistically significant, it may not be accurate or reliable information.

6. This is based on the Levene’s test, otherwise known as the probability of obtaining a statistical value at least as extreme or as close to the other one as actually observed, assuming that the null hypothesis is true. Levene’s test = t-test value of 4.022, p value of .001.

7. Group 5 and 7 earned the most weekly during treatment.

8. An independent samples t-test computed on Post-Treatment Weekly Wages Earned by Treatment Group revealed that median wages were significantly higher than the control group. While the control group was positively skewed, the treatment group showed concave-convex partitioning but was still higher overall with ranges from 150-350 versus 75-200 in the control. The t-test also revealed the mean and standard deviation being much high in treatment group.

9. The results indicate that the impact was significant, and wages earned were much higher than the control group.

10. The sample size is what hurts this study. The sample size was only 10 people which is relatively small and therefore seems to provide room for to much doubt and error in this study. It should be done with a much larger sample size for better accuracy.

Ex: 32

1. There are four main assumptions: The dependent variable must be continuous , the observations are independent of one another , the dependent variable should be approximately normally distributed , and the dependent variable should not contain any outliers.

2. The Histogram on the left is a convex histogram and the histogram on the right is a positively skewed histogram. The results for the Shapiro-Wilk test for normality shows that at baseline the significance was less than 0.05 and therefore statistically significant. However, the follow up and difference scores at 0.149 and 0.524 respectively are well above 0.05 and therefore not significant.

3. Baseline mean is 1.8850. Follow up mean is 3.2917. difference mean is 1.4058.

4. t-test value is = -3.956

5. At 11df and 0.05 on two tailed appendix a, the significance is 2.201. This makes it not significant.

6. This is based on the Levene’s test, otherwise known as the probability of obtaining a statistical value at least as extreme or as close to the other one as actually observed, assuming that the null hypothesis is true. Levene’s test = t-test value of -3.956, p value of 0.001.

7. The scores initially rose showing worsening symptoms for a while and then fell off again creating a convex shaped histogram on follow up. This was quite a spike however from the positively skewed histogram from baseline.

8. A paired sample t-test computed on Esophageal Symptom Scores at Baseline and 2-Week Follow-up revealed that the patients with GERD undergoing the removal of proton pump inhibitor treatment for their symptoms experienced and increase in GERD treatment compared to their baseline with treatment. The study included N=12, p = 0.05, and t= -3.956. The removal of the proton pump inhibitors appeared to play a role in the deterioration of the esophageal mucosal integrity.

9. The results indicate that the removal of PPI’s cause worsening symptoms to patients with GERD as well as physical internal damage possibly in the long term.

10. The major noted weakness in this study is again the size of participants used for the study. Only having included 12 participants makes this a study that could have large room for error.

Ex:33

1. The data does not meet the criteria for homogeneity of variance because the degrees of freedom in group 1 and the degrees of freedom in group 2 are a distance apart from each other. With homogeneity it is assumed that the spread of the two groups being compared is similar.

2. The histogram is minorly positively skewed but also convex in nature with a peek between 15 and 20 hours worked. The results of a Shapiro-Wilk test of normality is 0.284. This reveals that the data would be classified as normal.

3. Mean hours worked per group were: Supported = 14.80, TAU/Observational = 15.20, and TAU/randomized 26.60. The total was 18.87.

4. The F value for the group is 5.795 and the df for this set of data is 2 between groups, 12 within groups, and 14 total.

5. The critical F value being at 5.795 means that it is not significant. A large F value of 6.93 shows significance whereas a small P value shows significance. 2 and 12 in appendix C equal the F value shown.

6. The exact likelihood of obtaining an F value at least as extreme as or as close to the one that was actually observed, assuming the null hypothesis is true, was 0.017 x100 =1.7%?

7. While participant 13 worked the most, there is no difference between among the Supported Employment Treatment, Treatment as Usual Randomized, and Treatment as Usual Observational groups in post-treatment number of hours worked among veterans with spinal cord injuries.

8. A one-way ANOVA performed on months to program completion revealed no significant differences among three groups being compared in a Post-Treatment Hours Worked by Treatment Group study. F (2,12) = 5.795, p =0.017, N=15. The mean differences showed no variance at all. No difference between the Supported Employment Treatment group, the Treatment as Usual Randomized group, and Treatment as Usual Observational group in post-treatment number of hours worked among veterans with spinal cord injuries was noted.

9. There are only differences noted in the lower and upper bounds and the significance levels. The mean differences and Std. Error are identical from group to group.

10. The appropriate statistic would be to use paired samples and t-tests. This would result is a two tailed histogram to read for data.