Question

Suppose that strong claims, with weak evidence, have been made about the efficacy of an herbal treatment for attention deficit disorder (ADD). You are a research assistant for a professor who decides to empirically test the validity of these claims. You locate 10 fifthgrade students, in 10 different classrooms, who have been diagnosed with ADD. Sitting unobtrusively at the back of each classroom with stopwatch in hand, you record the number of seconds that the child with ADD is out of seat during a 20-minute period of silent reading. Each of the 10 children is then given daily doses of the herbal treatment for one month, after which you return to the classrooms to again record out-of-seat behavior during silent reading. Thus you end up with 10 pairs of observations: a pretreatment score and a posttreatment score for each student. The data collected are given below:

Pre-score 13 7 24 9 18 3 20 10 8 12 Post-score 8 5 15 7 11 0 9 4 13 3

a. Describe the independent variable and its levels.

b. Describe the dependent variable and its scale of measurement (N.O.I.R.)

c. What does the null hypothesis predict for the problem described above. (Be sure to use the variables given in the description.)

d. Conduct the appropriate statistical test of the null hypothesis using p = .05.

e. Provide an interpretation of your statistical conclusion to part D.

f. Obtain the 95% confidence interval for the sample statistic.

g. Provide an interpretation for the interval obtained in part F.

h. How does the confidence interval obtained in part F compare to your statistical conclusion in part D?

Answer 1

As we have paired observations, we conduct a paired t test.

The paired sample t-test, sometimes called the dependent sample t-test, is a statistical procedure used to determine whether the mean difference between two sets of observations is zero. In a paired sample t-test, each subject or entity is measured twice, resulting in pairs of observations.

1. The independent variable is the herbal treatment for attention deficit disorder (ADD) with two levels :

i) herbal treatement is done, ii) herbal treatement is not done

2. The dependent variable is the out-of-seat behavior during silent reading i.e the score(pre and post treatment)  and it is measured on ratio scale.

3. As strong claim have been made about the efficacy of an herbal treatment for attention deficit disorder (ADD), the alternative  hypothesis (H1) is of less than type i.e it states that the post treatment scores are less than pre treatment scores i.e the students used to have more out of seat behavior before treatment.

The null hypothesis (H0) assumes that the true mean difference of scores(μd) between two groups is equal to zero.

The lower-tailed alternative hypothesis (H1) assumes that μd is less than zero. (after<before)

H0: μd = 0 vs  H1: μd < 0    (lower-tailed)

4. at p=0.05 appropriate statistical test is the paired t test with test statistic :

t = $\bar{d}$ /SE( $\bar{d}$ ) where, SE( $\bar{d}$ ) = sd / $\sqrt{n}$ , sd= standard deviation of the differences and $\bar{d}$ = mean difference

Calculation :

$\bar{d}$ = -4.90, sd= 4.653553, n=10

So, test statistic t equals -3.329748

Critical value of t : t_c = -1.833

5. As observed value of t =-3.329748 < critical value of t =-1.833 then we reject the null hypothesis and conclude that the post treatment scores are less than pre treatment scores i.e the students used to have more out of seat behavior before treatment i.e the treatement was effective.

6. 95% confidence interval is :

for test statistic is the CI is [-1.8331 : ∞].

For true mean difference the CI is [-2.7000 : ∞].

7. Interpretation : If the true mean difference lies in the above confidence interval then we should accept H0.

8. Conclusion and comparioson : As the true mean difference $\bar{d}$ =-4.90 does not lie in the confidence interval at 0.05 significance level i.e if we perform the test 100 times, 95 of the times the true mean difference will fall outside the above CI. Hence we reject H0 and conclude post treatment scores are less than pre treatment scores i.e the students used to have more out of seat behavior before treatment i.e the treatement was effective.