A laboratory technician measures the breaking strength of each of 5 kinds of lin

Question

A laboratory technician measures the breaking strength of each of 5 kinds of linen thread by means of 4 different instruments, obtains the following result (in ounces): Is there a difference in instrument performance or thread performance? Show your work and provide a complete answer. What is the name of the statistical test you performed? What would the experimental design be? What if you wanted to determine if there was an interaction? What would you have to add? What statistical test would you perform to determine whether there is a difference in instrument performance or thread performance? What would the experimental design be? How should you select the thread to be tested? How should you decide which instrument to use? List the types of things you think would need to keep "the same", your control variables.

Explanation / Answer

a. Yes, there is significant difference between the Thread performance.

But, there is no significant difference between the Instrument performance.

We used 2 -way ANOVA using excel add-in (without replication):

b. We performed the 2-way ANOVA test without replication.

H0: no difference between performance

Ha: H0 is not true

so, in case of thread performance we reject H0 at 5% level.

c. There has to be replications under each experiment as in we have to consider at least 2 readings under each combination of thread & instrument. Again, we will perform 2-way ANOVA with Replication. This will result interaction and main effect both.

d. Since there is no difference in instruments' performance so all instruments are fine. However, for pair wise comparison we can use Tuckey's HSD test. However, by reading the mean data, we can say that thread-2 has strongest breaking strength.

e.

1) The instrument,

2) the type of cloth with which experiment is performed

3) The tailor/experimenter

4) Conditions of experiment

5) time/duration

To avoid any block effect.

Anova: Two-Factor Without Replication SUMMARY Count Sum Average Variance Thread-1 4 82.7 20.675 0.329167 Thread-2 4 102.6 25.65 1.85 Thread-3 4 94.1 23.525 2.2225 Thread-4 4 94.8 23.7 2.58 Thread-5 4 83.6 20.9 1.566667 I-1 5 114.3 22.86 7.333 I-2 5 113.6 22.72 5.452 I-3 5 114.5 22.9 7.18 I-4 5 115.4 23.08 3.907 ANOVA Source of Variation SS df MS F P-value F crit Rows 70.173 4 17.54325 8.315979 0.001878 3.259167 Columns 0.33 3 0.11 0.052143 0.983526 3.490295 Error 25.315 12 2.109583 Total 95.818 19

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