Question

A study of randomized controlled trial of animals facilitated therapy with dolphins in the treatment of (mild and moderate) depression collected the data as follows:

Depression Improved
Treatment	Yes	No	Total
Dolphin	10	5	15
Control	3	12	15
Total	13	17	30

Is the distribution of patients' depression significantly different between dolphin treatment and control treatment? Is there a treatment effect or could such a difference be explained by chance? Use the 8 step procedure to answer this question.

Answer 1

Solution:

Here, we have to use chi square test for independence of two categorical variables.

Null hypothesis: H₀: The distribution of patients' depression is significantly different between dolphin treatment and control treatment.

Alternative hypothesis: H_a: The distribution of patients' depression is significantly different between dolphin treatment and control treatment.

We assume/given level of significance = α = 0.05

Test statistic formula is given as below:

Chi square = ∑[(O – E)^2/E]

Where, O is observed frequencies and E is expected frequencies.

E = row total * column total / Grand total

We are given

Number of rows = r = 2

Number of columns = c = 2

Degrees of freedom = df = (r – 1)*(c – 1) = 1*1 = 1

α = 0.05

Critical value = 3.841459

(by using Chi square table or excel)

Calculation tables for test statistic are given as below:

Observed Frequencies
	Depression Improved
Treatment	Yes	No	Total
Dolphin	10	5	15
Control	3	12	15
Total	13	17	30

Expected Frequencies
	Depression Improved
Treatment	Yes	No	Total
Dolphin	6.5	8.5	15
Control	6.5	8.5	15
Total	13	17	30

Calculations
(O - E)
3.5	-3.5
-3.5	3.5

(fo-fe)^2/fe
1.884615	1.441176
1.884615	1.441176

Test Statistic = Chi square = ∑[(O – E)^2/E] = 6.651584

χ² statistic = 6.651584

P-value = 0.009907

(By using Chi square table or excel)

P-value < α = 0.05

So, we reject the null hypothesis

There is not sufficient evidence to conclude that the distribution of patients' depression is significantly different between dolphin treatment and control treatment.