Chapter 4, Problem 4.17P

Interpretation Introduction

Interpretation:

Whether the given standard deviations and given means of two methods are significantly different or not has to be given.

Concept Introduction:

Comparison of Standard Deviation with F Test:

For the comparison of mean values of two sets of measurements, we decide whether the standard deviations of the two sets are “statistically different”. This is done by F test.

The F test with quotient F is given as:

${\text{F}}_{\text{calculated}}=\frac{s_1^2}{s_2^2}$

Where, $s_1$ and $s_2$ are standard deviations for the set of measurements using original instrument and substitute instrument.

If ${\text{F}}_{\text{calculated}}>{\text{F}}_{\text{table}}$ , then the difference is significant.

Degrees of Freedom:

For a n set of measurement, the degrees of freedom will be $(n-1)$

Comparing Means of replicate measurements:

When the two standard deviations are not significantly different from each other, the equation used is:

$\begin{array}{l}t\text{ test for comparison of means: }\\ t=\frac{\left|\overline{x_1}-\overline{x_2}\right|}{\sqrt{(s_{\text{pooled}})}}\sqrt{\frac{n_1{n}_2}{n_1+n_2}}(\text{since }{s}_{\text{pooled}}=\sqrt{\frac{s_1^2(n_1-1)+s_2^2(n_2-1)}{n_1+n_2-2}})\end{array}$

To Give: Whether the given standard deviations and given means of two methods are significantly different or not.