Question

ANOVA BY HAND (DF BETWEEN AND WITHIN)

Does a woman’s chance of suffering from postpartum depression vary depending on the number of children she already has? To find out, a researcher collected random samples form four groups of women: the first group having just given birth to their first child, the second group having just given birth to their second child, and so on. He then rated their amount of postpartum depression on a scale from 1 to 5. Test the null hypothesis that the chances of developing postpartum depression do not differ with the number of children to which a woman has previously given birth. Test at .05 LOS. Please give an extensive interpretation. Please provide summary table.

First                            Second                        Third                           Fourth

Child                           Child                           Child                           Child

3                                  3                                  5                                  4

2                                  5                                  5                                  3

4                                  1                                  3                                  2

3                                  3                                  5                                  1

2                                  4                                  2                                  5

Answer 1

From the given data,the following statistics are calculated :

	First Child	Secondchild	Third child	Fourth child	Total
N	5	5	5	5	20
	14	16	20	15	65
Mean	14/5=2.8	16/5=3.2	0/5=4	15/5=3	65/20=3.25
	42	60	88	55	245
Std. Dev.	0.8367	1.4832	1.4142	1.5811	1.3328

ANOVA Table is formed from the above Table as follows:

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Sum of Squares	F
Btween Treatments	4.15	3	4.15/3=1.3833	F=1.3833/1.85=0.74775
Within Treatments	29.6	16	29.6/16=1.85
Total	33.75	19

The F - Ratio value = 1.3833/1.85 = 0.74775.

= 0.05

Degrees of Freedom for Numerator = 3

Degres ofFreedom for Denominator = 16

By Technology, the p-value = 0.5394.

Since p-value = 0.5394 is grater than = 0.05, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data support the claim that the chances of developing postpartum depression do not differ with the number of children to which a woman has previously given birth.