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or computer packages (Table 1.9). If the calculated value ofFis less than the table

value, the null hypothesis is proved and the two standard deviations are considered to

be similar. If the two variances are of the same order, then equations 1.16 and 1.17 are

used to calculatetcalcfor the two data sets. If not, equations 1.18 and 1.19 are used.

tcalc¼x^1 x^2

spooled

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

n 1 n 2

n 1 þn 2

r

ð 1 : 16 Þ

spooled¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

s^21 ðn 1  1 Þþs^22 ðn 2  1 Þ

n 1 þn 2  2

s

ð 1 : 17 Þ

tcalc¼

x 1 x 2

p

ðs^21 =n 1 þs^22 =n 2 Þ

ð 1 : 18 Þ

degrees of freedom¼ s

ðÞ 12 =n 1 þs 22 =n 22

ðÞs^21 =n 12 =ðÞþn 1 þ 1 ðÞs^22 =n 22 =ðÞn 2 þ 1

()

 2 ð 1 : 19 Þ

wherex 1 andx 2 are the calculated means of the two methods,s^21 ands^22 are the

calculated standard deviations of the two methods andn 1 andn 2 are the number of

measurements in the two methods.

At first sight these four equations may appear daunting, but closer inspection reveals

that they are simply based on variance (s^2 ), mean (x) and number of analytical meas-

urements (n) and that the mathematical manipulation of the data is relatively easy.

Table 1.9Critical values ofFat the 95% confidence level

Degrees of

freedom forS 2

Degrees of freedom forS 1

23461015301

2 19.0 19.2 19.2 19.3 19.4 19.4 19.5 19.5

3 9.55 9.28 9.12 8.94 8.79 8.70 8.62 8.53

4 6.94 6.59 6.39 6.16 5.96 5.86 5.75 5.63

5 5.79 5.41 5.19 4.95 4.74 4.62 4.50 4.36

6 5.14 4.76 4.53 4.28 4.06 3.94 3.81 3.67

7 4.74 4.35 4.12 3.87 3.64 3.51 3.38 3.23

8 4.46 4.07 3.84 3.58 3.35 3.22 3.08 2.93

9 4.26 3.86 3.63 3.37 3.14 3.01 2.86 2.71

10 4.10 3.71 3.48 3.22 2.98 2.84 2.70 2.54

15 3.68 3.29 3.06 2.79 2.54 2.40 2.25 2.07

20 3.49 2.10 2.87 2.60 2.35 2.20 2.04 1.84

30 3.32 2.92 2.69 2.42 2.16 2.01 1.84 1.62

1 3.00 2.60 2.37 2.10 1.83 1.67 1.46 1.00

30 Basic principles