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# Chapter 13. Slightly More Complicated Testing

In This Chapter

• Working with two variables

• Working with replications

• Understanding interactions

In Chapter 11, I show you how to test hypotheses with two samples. In Chapter 12, I show you how to test hypotheses when you have more than two samples. The common thread through both chapters is that one independent variable (also called a factor) is involved.

Many times, you have to test the effects of more than one factor. In this Chapter, I show how to analyze two factors within the same set of data. Several types of situations are possible, and I describe Excel data analysis tools that deal with each one.

# Cracking the Combinations

FarKlempt Robotics, Inc., manufactures battery-powered robots. They want to test three rechargeable batteries for these robots on a set of three tasks — climbing, walking, and assembling. Which combination of battery and task results in the longest battery life?

They test a sample of nine robots. They randomly assign each robot one battery and one type of task. FarKlempt tracks the number of days each robot works before recharging. The data are in Table 13-1.

Table 13.1. FarKlempt Robots: Number of Days before Recharging in Three Tasks with Three Batteries

Battery 1

Battery 2

Battery 3

Average

Climbing

12

15

20

15.67

Walking

14

16

19

16.33

Assembling

11

14

18

14.33

Average

12.33

15.00

19.00

15.44

This calls for two hypothesis tests:

H0: μBattery1 = μBattery2 = μBattery3

H1: Not H0

and

H0: μClimbing = μWalking = μAssembling

H1: Not H0

In both tests, ...

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