Question

In a study of mother-infant interaction, mothers are rated by trained observers on the quality of their interactions with their infants. Mothers were classified on the basis of whether this was their first child or not and whether the infant was low-birth weight (LBW) or full-term (FT). The data represent a score on a 12-point scale, on which a higher score represents better mother-infant interaction. Use alpha = .05.

           

	First Born (X)	(X)2	Not First Born (X)	(X)2
Low Birth weight	6		7
	5		8
	5		8
	4		9
	9		8
Sums
Full Term	8		9
	7		8
	7		9
	6		9
	7		3
Sums

a. What are your df (you should identify 5 df’s)? What are your critical F’s (there should be 3)?

b. What are the values of your observed F’s (there should be 3)?

c. Based on the above information, would you reject H₀, or fail to reject it? Why? What would your conclusions be?

Answer 1

Result:

	First Born (X)	(X)2	Not First Born (X)	(X)2		Total
Low Birth weight	6	36	7	49		13
	5	25	8	64		13
	5	25	8	64		13
	4	16	9	81		13
	9	81	8	64		17
Sums	29	183	40	322
Full Term	8	64	9	81		17
	7	49	8	64		15
	7	49	9	81		16
	6	36	9	81		15
	7	49	3	9		10
Sums	35	247	38	316
Total	64	430	78	638

a. What are your df (you should identify 5 df’s)? What are your critical F’s (there should be 3)?

Total Df = 19

Df for Birth weight = 1

Df for first born = 1

Df for interaction   = 1

Df for error = 1

F critical for Birth weight = 4.494

F critical for first born = 4.494

F critical for interaction = 4.494

b. What are the values of your observed F’s (there should be 3)?

F observed for Birth weight = 0.2783

F observed for first born = 3.4087

F observed for interaction = 1.1130

c. Based on the above information, would you reject H₀, or fail to reject it? Why? What would your conclusions be?

To test for Birth weight, calculated F=0.2783 < critical F =4.494, Ho is not rejected. We conclude that birth weight is not significantly related.

To test for first born, calculated F=3.4087 < critical F =4.494, Ho is not rejected. We conclude that first born is not significantly related.

To test for interaction, calculated F=1.113 < critical F =4.494, Ho is not rejected. We conclude that interaction is not significant.

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	0.8000	1	0.8000	0.2783	0.6051	4.4940
Columns	9.8000	1	9.8000	3.4087	0.0834	4.4940
Interaction	3.2000	1	3.2000	1.1130	0.3071	4.4940
Within	46.0000	16	2.8750
Total	59.8000	19