Question

Twenty children participated in a study of the effectiveness of augmentative communication therapy. The children were matched for expressive language scores, intelligence scores, and age at the beginning of the study. One member of each matched pair was a child with autism and the other member of the matched pairs was a child with Down syndrome. Researchers hypothesized that children with Down Syndrome (D) would have more success with the therapy than children with Autism (A).  Success was measured at the end of the 3 month study by the number of spontaneous communication attempts the children made using the augmentative communication device in a 4 hour afternoon session. The data are given below. Using SPSS software to do the appropriate type of data analysis. Make sure you label the variables so that the output is clear.

Based on the output you got using SPSS what conclusion can the researchers draw? Write a summary sentence of the results. (write both parts of step 5 of the hypothesis test).

Down	20	30	50	40	25	15	12	15	22	41	33	21	52	12	17	14	3	16	25
Autism	6	5	10	20	4	8	12	5	6	8	14	12	19	6	5	3	0	5	8

Answer 1

Paired t - test: It is used to test the mean of two dependent variables

(1) Null and Alternative Hypothesis:

H0: Children with Down Syndrome (D) would have not more success with the therapy than children with Autism (A)

H1; Children with Down Syndrome (D) would have more success with the therapy than children with Autism (A)

(2) From the given data

S.NO.	Down	Autism	Difference (d)	d^2
1	20	6	14	196
2	30	5	25	625
3	50	10	40	1600
4	40	20	20	400
5	25	4	21	441
6	15	8	7	49
7	12	12	0	0
8	15	5	10	100
9	22	6	16	256
10	41	8	33	1089
11	33	14	19	361
12	21	12	9	81
13	52	19	33	1089
14	12	6	6	36
15	17	5	12	144
16	14	3	11	121
17	3	0	3	9
18	16	5	11	121
19	25	8	17	289
	Total :		307	7007

4) Critical value of : 1.7341
P-Value: 0.0000

since t - value > t critical value and P-value <0.05 so we reject H0

5) Thus we conclude that Children with Down Syndrome (D) would have more success with the therapy than children with Autism (A)

SPSS output:

Mean = 16.158

SD = 10.663

Test Statistic = t = 6.605

P-value = 0.000 for two tail so P-value = 0.00005 for one tail

since t - value > t critical value and P-value <0.05 so we reject H0

Thus we conclude that Children with Down Syndrome (D) would have more success with the therapy than children with Autism (A)