Question

male	1st Systolic	1st Diastolic	2nd Systolic	2nd Diastolic
1	132	74	132	82
2	108	70	108	74
3	124	78	134	78
4	116	42	116	48
5	118	76	116	70
6	128	80	128	80
7	132	90	130	92
8	106	64	110	64
female
1	168	46	156	52
2	198	82	192	84
3	110	74	110	76
4	170	94	168	100
5	142	58	140	52
6	168	52	172	54
7	90	32	82	0

Above are two readings of systolic and diastolic blood pressures taken from 15 individuals. Test the hypothesis that there is a significant difference between the first and second readings for systolic blood pressure (both sexes combined), with an α of 0.05. What test would be most appropriate and why? Is the result significant? State your conclusions.

Answer 1

Here, we have to use two way ANOVA (Analysis of variance) because here we have to find the SIgnificant difference of interaction effects between both sex (male-female) & first and second readings for systolic blood pressure. It is possible to interpret that there is any significant difference between the two factors using Two way ANOVA .

Hypothesis:-

  H₀: There is no interaction between the individual Sex and which first and second readings for systolic blood pressure.
H₁: There is interaction between the individual Sex and which first and second readings for systolic blood pressure.

ANOVA Table:- By using Minitab software,

Source	DF	Seq SS	Contribution	Adj SS	Adj MS	F value	p Value
Sex	1	5222.3	21.60%	5222.3	5222.29	7.44	0.011
Stage	1	8.5	0.04%	8.5	8.53	0.01	0.913
Error	27	18944.6	78.36%	18944.6	701.65	~	~
Lack-of-Fit (Interaction)	1	46.0	0.19%	46.0	46.00	0.06	0.803
Pure	Error	26	18898.6	78.17%	18898.6	726.87	~
Total	29	24175.5	100.00%	~	~	~	~

Conclusion:-

Here p value of interaction effects of both factor is greater than the given level of significance α=0.05. Hence, we accept the null hypothesis.

Interpretation:-  

There is a significant difference between the first and second readings for systolic blood pressure (both sexes combined), with an α of 0.05.