Anova (Two-Way) - Casio fx-9860G Series User Manual

k ANOVA (Two-Way)
Description
The nearby table shows measurement results for a metal product produced by a heat
treatment process based on two treatment levels: time (A) and temperature (B). The
experiments were repeated twice each under identical conditions.
B (Heat Treatment Temperature) B (Heat Treatment Temperature)
A (Time) A (Time)
A1 A1
A2 A2
Perform analysis of variance on the following null hypothesis, using a signifi cance level of
5%.
H : No change in strength due to time
o
H : No change in strength due to heat treatment temperature
o
H : No change in strength due to interaction of time and heat treatment temperature
o
Solution
Use two-way ANOVA to test the above hypothesis.
Input the above data as shown below.
List1={1,1,1,1,2,2,2,2}
List2={1,1,2,2,1,1,2,2}
List3={113,116,139,132,133,131,126,122}
Defi ne List 3 (the data for each group) as Dependent. Defi ne List 1 and List 2 (the factor
numbers for each data item in List 3) as Factor A and Factor B respectively.
Executing the test produces the following results.
• Time differential (A) level of signifi cance P = 0.2458019517
The level of signifi cance (p = 0.2458019517) is greater than the signifi cance level (0.05),
so the hypothesis is not rejected.
• Temperature differential (B) level of signifi cance P = 0.04222398836
The level of signifi cance (p = 0.04222398836) is less than the signifi cance level (0.05), so
the hypothesis is rejected.
• Interaction (A × B) level of signifi cance P = 2.78169946e-3
The level of signifi cance (p = 2.78169946e-3) is less than the signifi cance level (0.05), so
the hypothesis is rejected.
The above test indicates that the time differential is not signifi cant, the temperature
differential is signifi cant, and interaction is highly signifi cant.
6-5-24
Tests
B1 B1
113 , 113 , 116 116 139 , 139 ,
133 , 133 , 131 131 126 , 126 ,
20070201
B2 B2
132 132
122 122