One hundred patients with moderate‑to‑severe knee osteoarthritis who were eligible for a total knee replacement were enrolled in a randomized controlled study. Fifty patients were assigned to receive a total knee replacement with a 12-week12-week follow‑up of nonsurgical treatment consisting of exercise, education, dietary advice, use of insoles, and pain medication. The other 5050 patients received only the 1212 weeks of nonsurgical treatment. One purpose of the randomization is for the two groups to have similar levels of knee osteoarthritis before undergoing the treatments. After the random assignment, we can compare the two treatment groups to see how well the randomization worked. The Kellgren‑Lawrence score, which can take the values 0,0, 1,1, 2,2, 3,3, or 4,4, is based on a standard X‑ray and assesses the severity of knee osteoarthritis, with 00 indicating no osteoarthritis and 44 indicating the most severe symptoms. If the randomization worked, then both treatment groups should have similar levels of osteoarthritis before undergoing the two treatments. The initial Kellgren‑Lawrence scores for the two treatment groups are given in the table. Kellgren‑Lawrence Score Treatment Group 22 33 44 Nonsurgical treatment group 55 2121 2424 Total‑knee‑replacement group 77 2121 2222 Do a chi‑square test to see if there is a significant difference in the initial distribution of Kellgren‑Lawrence scores for the two treatments. What did you find? Find the test statistic ?2.. Give your answer to two decimal places. ?2= Find the ?-value�-value for these data. Give your answer to two decimal places. ?-value:�-value:
One hundred patients with moderate‑to‑severe knee osteoarthritis who were eligible for a total knee replacement were enrolled in a randomized controlled study. Fifty patients were assigned to receive a total knee replacement with a 12-week12-week follow‑up of nonsurgical treatment consisting of exercise, education, dietary advice, use of insoles, and pain medication. The other 5050 patients received only the 1212 weeks of nonsurgical treatment. One purpose of the randomization is for the two groups to have similar levels of knee osteoarthritis before undergoing the treatments. After the random assignment, we can compare the two treatment groups to see how well the randomization worked.
The Kellgren‑Lawrence score, which can take the values 0,0, 1,1, 2,2, 3,3, or 4,4, is based on a standard X‑ray and assesses the severity of knee osteoarthritis, with 00 indicating no osteoarthritis and 44 indicating the most severe symptoms. If the randomization worked, then both treatment groups should have similar levels of osteoarthritis before undergoing the two treatments. The initial Kellgren‑Lawrence scores for the two treatment groups are given in the table.
| Kellgren‑Lawrence Score | |||
| Treatment Group | 22 | 33 | 44 |
| Nonsurgical treatment group | 55 | 2121 | 2424 |
| Total‑knee‑replacement group | 77 | 2121 | 2222 |
Do a chi‑square test to see if there is a significant difference in the initial distribution of Kellgren‑Lawrence scores for the two treatments. What did you find?
Find the test statistic ?2.. Give your answer to two decimal places.
Find the ?-value�-value for these data. Give your answer to two decimal places.
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