The researcher has done the research on Statistical Methods Quantitative Techniques in Business and Industry.Statistical methods means analyzing, collecting and overall summarization and interpretation of numerical data. Statistical techniques can be
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42
CHAPTER 1. ST STATISTICAL DESCRIPTION OF EXPERIMENTAL DATA At 95% confidence t = 2.31 (for 8 degrees of freedom, i.e., (6 tspooled
− 1 ) + ( 4 − 1) = 8). Then
N 1 + N 2 6+4 = (2. (2.31)(0. 31)(0.0744%) = 0.111% 111%. N 1 N 2 6 4
·
Since x1 x2 = 12 12..61 12 12..53 = 0.08% 08% we conclude that at the 95% confidence level there is no difference in the alcohol content of the two wine bottles.
−
1.7.2 1.7.2
−
Comp Compari aring ng Var Varian iance cess - The F -test
Sometimes Sometimes you need to compare compare two measured variances variances.. For example, is one method of analysis is more precise than another? Or, are the differences between the variances for the two methods of analysis statistically significant? To answer these types of questions we use the F -test. F -test. F is the ratio of the variance of sampling A with ν A = N A 1 degrees of freedom and sampling B with ν B = N B 1 degrees of freedom, that is 2 sA F exp = (1.72) exp 2 . sB
−
In the limit of ν A
−
→ ∞ and ν B → ∞ then 2 σA F = 2 . σB
(1.73)
0.8 (νΑ = 10,νΒ = 12)
0.7 0.6
(νΑ = 3,νΒ = 5)
0.5 0.4 p (F)
0.3 0.2 0.1 0.0 0
1
2
3
4
5
6
7
8
9 10
F
Figure Figure 1.21: F distribution for ν A = 3 and ν B = 5. P. J. Grandinetti, January 20, 2000
