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. See chart below: Wound Healing by Treatment

Percent of Wound Healing

Treatment 0-25 26-50 51-75 76-100 New Compound (n=125) 15 37 32 41 Placebo (n=125) 36 45 34 10 Is there a difference in the extent of wound healing by treatment? Run the appropriate test at a 5% level of significance. Are treatment and the percent of wound healing independent?

Answer 1

The null and alternative hypothesis

H0: Treatment and wound healing are independent .

Ha: Treatment and wound healing are not independent.

Test statistic is

where Oi : observed frequency

Ei : expected frequency

The contingency table

	0-25	26-50	51-75	76-100	total
New	15	37	32	41	125
placebo	36	45	34	10	125
total	51	82	66	51	250

Expected frequency calculation

E(15) = 125*51/250=25.5 , E(36)= 51-25.5=25.5 , etc

The contingency table

	0-25	26-50	51-75	76-100	total
New	15(25.5)	37(41)	32(33)	41(25.5)	125
placebo	36(25.5)	45(41)	34(33)	10(25.5)	125
total	51	82	66	51	250

The expected frequencies are in the parenthesis

Calculation of Chi square

	Oi	Ei	(Oi-Ei)^2/Ei
	15	25.2	4.128571429
	37	41	0.390243902
	32	33	0.03030303
	41	25.5	9.421568627
	36	25.5	4.323529412
	45	41	0.390243902
	34	33	0.03030303
	10	25.5	9.421568627
total			28.13633196

Thus

28.14

degrees of freedom = (2-1)*(4-1) = 3

Note : degrees of freedom = ( number of rows -1) *( number of columns-1)

Critical value of chi square at 0.05 with 3 df

7.815 (from chi square table)

Since calculated value of > 7.815  

We reject H0

There is sufficient evidence to conclude that there is a significant difference in wound healing by treatment . That is treatment and wound healing are not independent.