Question

To determine the effect of various cooling devices during exercise, a researcher assigns 10 people to each of the following four groups: No Cooling Device, Only Head Cooling Device, Only Vest Cooling Device, Both Head and Vest Cooling Device. The researcher takes the body temperature of each individual after exercise and runs an ANOVA to test the null hypothesis that .

Here is the R input:

> NoCool=c(102,104,101,102,103,101,99,102,100,100)> HeadCool=c(102,102,100,101,103,101,99,101,101,100)
> VestCool=c(101,102,100,100,102,100,99,101,100,100)> HeadVestCool=c(100,99,99,100,100,99,98,100,99,99)
> Device = c(rep("None",10),rep("Head Only",10),rep("Vest Only",10),rep("Head and Vest",10))
> Temperature=c(NoCool,HeadCool,VestCool,HeadVestCool)> Temp = data.frame(Device,Temperature)
> Temp.mod=aov(Temperature~Device,data=Temp)
> anova(Temp.mod)

Here is the output:

The researcher concludes that at least one of the means is different and, as a result, runs a Tukey Test.

Here is the R input:

> TukeyHSD(Temp.mod)

Here is the output:

Question:  Which means should the researcher conclude to be different from each other at the significance level of 0.05?

		Head Only Head & Vest
		None Head & Vest
		Vest Only Head & Vest
		None Head Only
		Vest Only Head Only
		Vest Only None

Answer 1

Solution

> NoCool=c(102,104,101,102,103,101,99,102,100,100)
> HeadCool=c(102,102,100,101,103,101,99,101,101,100)
> VestCool=c(101,102,100,100,102,100,99,101,100,100)
> HeadVestCool=c(100,99,99,100,100,99,98,100,99,99)
> Device = c(rep("None",10),rep("Head Only",10),rep("Vest Only",10),rep("Head and Vest",10))
> Temperature=c(NoCool,HeadCool,VestCool,HeadVestCool)
> Temp = data.frame(Device,Temperature)
> Temp.mod=aov(Temperature~Device,data=Temp)
> anova(Temp.mod)
Analysis of Variance Table

Response: Temperature
Df Sum Sq Mean Sq F value Pr(>F)   
Device 3 24.9 8.30 6.64 0.0011 **
Residuals 36 45.0 1.25
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> # Since the p-value = 0.0011< 0.05 so we conclude that The researcher concludes that at least one of the means is different and, as a result
> #runs a Tukey Test.

> TukeyHSD(Temp.mod)
Tukey multiple comparisons of means
95% family-wise confidence level

Fit: aov(formula = Temperature ~ Device, data = Temp)

$Device

	diff	lwr	upr	p adj
Head Only-Head and Vest	1.7	0.353386	3.046614	0.00863
None-Head and Vest	2.1	0.753386	3.446614	0.000925
Vest Only-Head and Vest	1.2	-0.14661	2.546614	0.0952
None-Head Only	0.4	-0.94661	1.746614	0.853944
Vest Only-Head Only	-0.5	-1.84661	0.846614	0.750344
Vest Only-None	-0.9	-2.24661	0.446614	0.289976

Which means should the researcher conclude to be different from each other at the significance level of 0.05?

We will use P-value Criteria

If P-value < 0.05 level of significance then we say that means should different from each other at the significance level of 0.05

So

1. Head Only-Head and Vest

2. None-Head and Vest

So these pair of means different from each other at the significance level of 0.05.