Statistik

Testing a Hypothesis Carry out measurements on an accurately known standard. Experimental value is different from the true value. Is the difference due to a systematic error (bias) in the method - or simply to random error?

SIGNIFICANCE TEST

Figure shows (A) the curve for the true value (mA = mt) and (B) the experimental curve (mB)

NULL HYPOTHESIS : Ho Ho: to imply that there is no difference between the observed and known values apart from that due to random variation. Ho : x = μ

If ItI < certain critical value  then the null hypothesis is retained If ItI > certain critical value  then the null hypothesis is rejected

The critical value of t for a given significance level can be found from Table A-2 Miller (ex P: 0.05 (5%) or 0.01 (1%)).

Example 1 :

Answer 1 :

Example 2.

Answer 2. Ho : the two methods give same result Ho : μ1 = μ2

If s1 and s2 are not significantly different, use pooled s :

Example 3 :

Answer 3 :

If the standard deviation is not equal :

t = - 8.48

critical value t 5 = 4.03

t > critical value t, Ho is rejected There is evidence that the mean concentration of the thiol differs between the group.

Paired t-test Two methods of analysis are compared by applying both of them to the same set of test materials, which contain different amounts of analyte.

Paracetamol concentration in tablets by two different methods. Tablets from ten different batches.

In addition to random measurement error, differences between the tablets and the differences between the methods may also contribute to the variation between measurement. d (difference between each pair of the results given by the methods

Where d and sd are the mean and standard deviation respectively of d values, the differences between the paired values.

Rerata d = 0.159, sd = 0.570 t = 0.88

critical value t9 = 2.26 (P = 0.05)

t < t9, Ho is retained the methods do not give significantly different results for the paracetamol concentration.

One-sided and two-sided test (One-tailed and two-tailed test) The methods described so far have been concerned with testing for a difference between two means in either direction.

Two-sided or two- tailed One-sided or one- tailed

Not concern positive or negative trend concern to decrease or increase trend

F-test for the comparison of standard deviations The significance tests described so far are used for comparing means

Detect systematic errors

OUTLIERS Titration result : 12.12, 12.15, 12.13, 13.14, 12.112 ml

Outlier? Grubbs` test

Ho presumes that there are no outliers, and the population has a normal distribution.

DIXON`S TEST (Q-Test)