Student t factor

We calculate the confidence limits as shown above and translate onr Nnll hypothesis into a mathematical formnla resulting in a formnla for an observed Student-t-factor tobseived- We can now compare this observed valne with the critical value for 95% confidence and the degrees of freedom for onr nnmber... 

The limit of determination depends on the precision of the measurement sdv(R), on the sensitivity of the measurement (the slope of the calibration curve), on the number of data used for calibration nc and analysis na, on the choice of calibration points (moal) and on the statistical probability influencing students t-factor. Proceeding from nc = 4 calibration data on a straight line to nc = 8 the limit of determination is lowered by a factor of four. In analysis a threefold determination is sufficient98). 

The standard deviations of the slope and intercept are given by similar formulas without the Student t factor ... 

The Student t-factor depends on the statistical reliability P and the number of degrees of freedom /= m — 1. Because a certain statistical reliability P must be chosen for the calculation of T, which has to be taken into account when interpreting the result, the result is given in %P. 

Table 1.3. Critical Student s t-Factors for the One- and Two-Sided Cases for Three Values of the Error Probability p and 7 Degrees of Freedom f...

Figure 4.47. Drug assay using HPLC respectively UV Spectroscopy. Correlation of HPLC and UV results obtained on four batches of a cream. The vertical error bars each give the mean + standard deviation of 6 HPLC determinations because the Student s t-factor for five d.f. is nearly equal to /6 (see Section 1.3.2), the bars can also be interpreted as 95% confidence limits. The circles connected by a line indicate the corresponding duplicate UV determinations. The proportionality line passes through the origin and the center of mass for the four coordinates. The drug is slightly overdosed (= 103-104% the traditional UV assay apparently is not as selective as it should be an interference adds about 4% to the result.

Using the correlation coefficients, calculate the Student s t factors, and display these (the larger this value, the more probable the correlation values below about 2 are insignificant). 

Using the Student s t factors and the number of degrees of freedom, calculate the probabilities p that correlations are due to chance alone (error probabilities) these are interpreted as follows ... 

Here, the uncertainty intervals are standard deviations multiplied by Student s t factor for 95% probability and 5 degrees of freedom (t = 2.571) [48]. 

Based on these estimates and literature values for the fugacity, Oldani and Bor obtained equation 14.31, from which they derived the reaction enthalpy and entropy at the mean temperature of the experimental temperature range (T = 272 K) Ar//2°72 = 58.6 2.6 kJ mol-1 and ATS 72 = 304 10 J K-1 mol-1. The uncertainty intervals are standard deviations multiplied by Student s t factor for 95% probability and 18 degrees of freedom (t = 2.101) [48]. 

Table 2.34 is formed for the two separated factors with two inlets. Effects of factors X2 and X5 are quantitatively determined from the table. Then, a significance check of obtained effects is done by the Students t-criterion. 

Factors X4 and X7 with their respective effects EXi=13.0, EX4=14.5 and EX7=19.5 are also screened out visually from the scatter diagram. A statistical significance check of these effects is done by quantitative calculation of their values through a table with three inputs and a check with the Students t-test. An auxiliary table with three inputs is shown in Table 2.41. 

Accordingly we should conclude that D and N interact, and we should inspect the data broken down into one factor experiments. We can compare Dj with D, at each level of N, using the Student t test to compare the two means for D. We find that the difference between Dj and is not significant for N, but is quite considerable for Nj. Similarly we can compare the difference between Ni and N, for each level of D, when we find that the difference between the two levels of N is greater for Dj than for Dj. 

QREDJrBL.dat Table 1.7 Reduced critical -values (division of -values for p = 0.05 by the appropriate Student s t-factor and SQR(2)), as used with the multiple range test in MULTI. 

The expanded uncertainty can then be estimated after the calculation of the effective number of degrees of freedom, df (Eq. 7). Therefore the coverage factor used was the Student t defined for that number and a 95% significance level (/(df, 95%). The estimated confidence interval is defined by... 

Number of Degrees of Freedom V Maximum Value of Student s t Factor for the Significance Levels Indicated ... 

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