Question

A clinical trial evaluates a new compound designed to improve wound healing in trauma patients. The new compound is compared against a placebo. After treatment for 5 days with the new compound or placebo, the extent of wound healing is measured and the data are shown in table 7-51. Is there a difference in the extent of wound healing by treatment? Run the appropriate test at a 5% level of significance. (Hint : Are treatment and the percent of wound healing independent?

Answer 1

The Chi-Square test of independence is used to determine if there is a significant relationship between two factors.

For variables % Wound Healing and Treatment ,

The Chi-Square test of independence is performed in following steps,

Step 1: The hypothesis is defined as,

Null hypothesis, Ho:There is no association between two variables.

Alternative hypothesis, Ha There is an association present between the two variables.

Step 2: The significance level for the test is,

Step 3: The Chi-Square test statistic is obtained as follow,

The observed values are,

Obsserved values
	% Wound Healing
	0-25%	26-50%	51-75%	76-100%	Total
New Compound	15	37	32	41	125
Placebo	36	45	34	10	125
Total	51	82	66	51	250

Step 4: The expected values are obtained using the formula,

The expected values are,

Expected values
	% Wound Healing
	0-25%	26-50%	51-75%	76-100%	Total
New Compound	25.5	41	33	25.5	125
Placebo	25.5	41	33	25.5	125
Total	51	82	66	51	250

Step 5: Now the Chi-Square Value is obtained using the formula,

Step 4: The P-value for Chi-Square statistic is obtained using the chi square distribution table,

Step 5:

The null hypothesis is rejected. It can be stated now, the two variables are dependent. There is a statistically significant association between two variables % Wound Healing and Treatment.