Question

For a research project, a SACAP student is interested in determining the difference of three types of drinks on the concentration span of medical professionals working longs shifts. The following table indicates scores from three groups of medical professionals who were measured on the same night. Using manual computation, perform the appropriate hypothesis test at ? = 0.05. Show all calculations and decision making steps. Also calculate size of the treatment effect using Tukey’s Honestly Significance.

High Caffene Content Soda	Expresso shot	Water
3	7	4
2	9	3
3	6	2
5	4	4
2	5	4
6	4	2
7	2	9
4	3	3

  

Answer 1

here null hypothesis H0:all three drink means are same

alternate hypothesis H1: atleast one drink mean differ from other

since p-value=0.5205 is more than alpha=0.05, so we accept (or fail to reject)null hypothesis and conclude that all three drinks have same scores at 5% level of significance.

effect size of the treatment : since we fail to reject the null hypothesis so there is no need of calculating this effect size.

grand sum=G=103, n=24

total sum of square=3*3+2*2+....+9*9+3*3-103*103/24=100.96

Between sum of square=32*32/8+40*40/8+31*31/8-103*103/24=6.0833

following anova has been generated from above information

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	6.0833	2.0000	3.0417	0.6733	0.5207	3.4668
Within Groups	94.8750	21.0000	4.5179
Total	100.9583	23

	High Caffene Content Soda	Expresso shot	Water
	3	7	4
	2	9	3
	3	6	2
	5	4	4
	2	5	4
	6	4	2
	7	2	9
	4	3	3
sum=	32	40	31