Research Question : Does activity level prior to surgery impact the number of da

ID: 3226651 • Letter: R

Question

Research Question: Does activity level prior to surgery impact the number of days of physical therapy required before release from care after surgery?

3. Carry out an ANOVA to test whether Use alpha=0.05. Your answer should include the following. For full credit, please show your work:

· The null and alternative hypotheses.

· Verification of the ANOVA assumptions.

· The calculated test statistic and the p-value for the test.

· Your conclusions. (Do you reject your null hypothesis? Why or why not?)

4. Conduct the appropriate post-hoc tests to determine which means differ. Use an overall (i.e. family-wise) Type I error rate of alpha=0.05. Your answer should include the following. For full credit, please show your work, including:

· The t-statistics and the associated p-values for each of the tests – which are statistically significant?

· Give 95% confidence intervals that control for the family-wise Type I error rate for each of the differences between group means.

· Do your answers for the post-hoc hypothesis tests and the confidence intervals agree?

· Fully describe your conclusions in the context of the scientific problem.

activity

Surgery to correct a tear of the meniscus in the knee requires undergoing a regimen of physical therapy after the surgery until the joint is again strong enough so that the participant can be released from care. A physical rehabilitation clinic wished to assess the impact of level of activity prior to corrective knee surgery on days to successful completion of post-surgical physical therapy. Data were obtained on 24 male participants aged 18-30 years who had undergone similar surgeries in the prior year. Their level of physical activity prior to injury and surgery was assessed as “Below Average”, “Average” or “Above Average”. The number of days spent in physical therapy care after surgery was also recorded. The data are available on the Moodle page in the file knee.csv. Research Question: Does activity level prior to surgery impact the number of days of physical therapy required before release from care after surgery? 4. Carry out an ANOVA to test whether Use alpha=0.05. Your answer should include the following. For full credit, please show your work: • The null and alternative hypotheses. • Verification of the ANOVA assumptions. • The calculated test statistic and the p-value for the test. • Your conclusions. (Do you reject your null hypothesis? Why or why not?) 5. Conduct the appropriate post-hoc tests to determine which means differ. Use an overall (i.e. family-wise) Type I error rate of alpha=0.05. Your answer should include the following. For full credit, please show your work, including: • The t¬-statistics and the associated p-values for each of the tests – which are statistically significant? • Give 95% confidence intervals that control for the family-wise Type I error rate for each of the differences between group means. • Do your answers for the post-hoc hypothesis tests and the confidence intervals agree? • Fully describe your conclusions in the context of the scientific problem.

Research Question: Does activity level prior to surgery impact the number of days of physical therapy required before release from care after surgery?

3. Carry out an ANOVA to test whether Use alpha=0.05. Your answer should include the following. For full credit, please show your work:

· The null and alternative hypotheses.

· Verification of the ANOVA assumptions.

· The calculated test statistic and the p-value for the test.

· Your conclusions. (Do you reject your null hypothesis? Why or why not?)

· The t-statistics and the associated p-values for each of the tests – which are statistically significant?

· Give 95% confidence intervals that control for the family-wise Type I error rate for each of the differences between group means.

· Do your answers for the post-hoc hypothesis tests and the confidence intervals agree?

· Fully describe your conclusions in the context of the scientific problem.

activity

group days Below Avg 1 29 Below Avg 1 42 Below Avg 1 38 Below Avg 1 40 Below Avg 1 43 Below Avg 1 40 Below Avg 1 30 Below Avg 1 42 Average 2 30 Average 2 35 Average 2 39 Average 2 28 Average 2 31 Average 2 31 Average 2 29 Average 2 35 Average 2 29 Average 2 33 Above Avg 3 26 Above Avg 3 32 Above Avg 3 21 Above Avg 3 20 Above Avg 3 23 Above Avg 3 22

Explanation / Answer

Solution

Let xij = The number of days spent in physical therapy care after surgery by the jth patient whose level of physical activity prior to injury was i, i = 1, 2, 3 representing respectively, “Below Average”, “Average” and “Above Average”.

Back-up Theory

The model assumed for ANOVA is: xij = µ + i + ij, where µ = common effect, i = effect of ith pre-surgery activity level and ij = error which is assumed to be Normal with mean 0 and constant variance, say 2.

Now, to work out solution,

ANOVA Table is given below Part (d)

Part (a)

The null and alternative hypotheses

H0: 1 = 2 = 3. Vs HA: H0 is false. ANSWER

Part (b)

The calculated test statistic, F = 16.961 ANSWER

Part (c)

The p-value for the test.

Under H0, F ~ F2,21 and hence p-value of the test statistic = P(F2,21 > 16.961) = 4.1E-05 ANSWER

Part (d)

Conclusions. Reject null hypothesis. Because p-value < 0.05 (given ) ANSWER

ANOVA

Source

Fcrit

p-value

Activity

672

336

16.96154

3.4668

4.1E-05

Error

416

19.80952

Total

1088

47.30435