Significance Tests. In order to decide whether the difference between the measured and standard amounts can be accounted for by random error, a statistical test known as a significance test can be employed Significance tests are widely used in the evaluation of experimental results.
u, arises solely as a result of random errors.
differs significantly from zero.
d2, of the duplicates are
shown in the Table.
25.06 25.18 24.87 25.51 25.34 25.41
Test for positive bias in these results.
mean = 25.228 ml, standard deviation = 0.238 ml
A proposed method for the determination of the chemical oxygen
demand of wastewater was compared with the standard (mercury
salt) method. The following results were obtained for a sewage
In order to use Grubbs' test for an outlier, that is to test Ho : all measurements come from the same population, the statistic G is calculated:G = I suspect value - I /swhere and s are calculated with the suspect value included.The test assumes that the population is normal.
The critical values of Q for P = 0.05 for a two-sided test are given in Table A.6.
If the calculated value of Q exceeds the critical value, the suspect value is rejected.
The critical value of Q (P= 0.05) for a sample size 7 is 0.570. The suspect value 0.380 is rejected (as it was using Grubbs' test).
It is important to appreciate that for a significance level of 5% there is still a chance of 5%, or 1 in 20, of incorrectly rejecting the suspect value.
When the two suspect values are at opposite ends of the data set. This results in a large value for the range, As a result Q is small and so not significant.
Extensions of Grubbs' test give tests for pairs of outliers. Further details for dealing with multiple outliers can be found from the bibliography at the end of this chapter.
This suggests that there is little difference between conditions A and B but that conditions C and D differ both from A and B and from each other.
In this case the number of degrees of freedom is 3 and the mean square is 62, so the sum of the squared terms is 3x62=186.
F = 62/3 = 20.7
and dividing by the # degrees of freedom = 12-1 =11
This method of estimating o2 is not used in the analysis because the estimate depends on both the within- and between-sample variations.
This additive property holds for ANOVA calculations described here
cantly from those which would be expected on this null
Suppose that the ratio of male to female students in the College of
Sciences is exactly 1:1, but in the Pharmacy class over the pas
ten years there have been 80 females and 40 males. Is this
significant departure from expectation?
numbers of males and females in the College of Sciences, so we might
expect that there will be equal numbers of males and females in
Pharmacy. So we divide our total number of Pharmacy students (120) in
a 1:1 ratio to get our ‘expected’ values.
109, 89, 99, 99, 107, 111, 86, 74, 115, 107, 134, 113, 110, 88, 104
%cumulative frequency = 100 x cumulative frequency/(n + 1)
where n is the total number of measurements.
with the cumulative distribution function of the hypothesized distribution.
25.13, 25.02, 25.11, 25.07, 25.03, 24.97, 25.14 and 25.09 ml.
Could such results have come from a normal population?
z = (x - 25.07)/0.059
1.01, -0.84, 0.67, 0, -0.67, -1.69, 1.18 and 0.34.