APMDA D'O'Hare Stats

• Describes reproducibility of results
• Describes how well a series of measurements agree with each other
• Related to random error.
• Precise data are clustered but not necesarily about the true result

• How close a result is to the true or accepted value
• Related to systematic error.

• Random error: Results in a scatter of results centred on the true value for repeated measurements on a single sample. Can improve with repeated measurements
• Systematic error: Results in all measurements exhibiting a definite difference from the true value. Can't improve with repeated measurement.

Occur occasionally, are often large and may cause a result to be high or low. May be caused by human error.

An estimate attached to a test result which characterises the range of values within which the true value is asserted to lie.

Slope of calibration curves

3 x standard deviation of y-intercept.

• The true positive, the rate at which the test correctly classifies sick people as sick
• TPR = TP    = TP      
•           P         TP+FN

The true negative rate, the rate at which it identifies healthy people as healthy

• TNR = TN =      TN        
•            P       (TN + FP)

• 1. Analysis of standard samples:
• especially certified reference materials for the whole analytical process and standard solutions for the measurement step (to test for losses, poor recovery or matrix effects
• 2. Independent analysis: The method should differ as much as possible from the test method, ideally being based on a different physical or chemical principle
• The method can be taken as valid if the confidence limits of the results include the true or accepted value, where the confidence limit is given by 
• +ts   
• - √n

3. Blank determinations: A blank consists of the entire matrix but no analyte. All the steps of the analysis should be applied to the blank material to reveal errors arising from the reagents, glassware etc. 

4.Variation in sample size: Consant error can be revealed by this process

• Instrumental errors: caused by non-ideal instrument behaviour, faulty calibrations or inappropriate conditions. 
• eg Volumetric glassware at temperature that differs from the calibration temp, pH meter outside range, 50Hz noise

• Method errors: Arise from non-ideal chemical or physical behaviour of the analytical system. 
• - eg unstable enzyme solutions
• - Most difficult errors to detect

Personal errors: result from carelessness or peronal limitations of the analyst.

eg estimating position of pointer between scale divisions, colour blindness, prejedice etc.

• Increasing the number of measurements.
• standard deviation decreases with n/2.

• 
• You assume that the samples are drawn from populations with equal standard deviations.

Use two tailed t-test to test for differences and one tailed t to test if one mean is larger than another.

• Plot instrument response on (ordinate) y axis and the standard solutions (with known conc and moles) on the abscissa (x axis). 
• Assume that variances arise soley from instrument response and that the standards are precise
• Ensure calibration range brackets expected range for unknown sample
• Range MUST be centred on expected result
• Data should be evenly spaced over whole range

• Equal volumes of standard solution are taken
• All but one are SPIKED with different amounts of a known conc of standard soln analyte
• Extrapolation to the x-intercept allows calculation of analyte in original sample

• Benefits:
• Any matrix interferences will affect all samples identically
• Can also check if method is used within linear working range.

• Use standards and plot least precise(y) against most precise (x)
• Plot method A versus method B
• If its in perfect agreement r=1 slope = 1 and intercept =0
• Non zero intercepts could show background offsets in one method
• Systematic error could yield a slope of more than or less than 1.

• Can detect outliers by plotting y residuals versus actual values
• Check for curvlinear relationships of this with sign test

Only use for paired data (band altman)

• Plot differences between pairs on the y-axis 
• Plot the means of the pairs on the x axis

• Pro
• Low variance
• Quicker and cheaper for large sample size

• Cons: Concentration range must include the unknown concentration
• Range must be centred at expected concentration

• Pros:
• Overcomes interferents present in original sample
• Better for smaller sample numbers
• Can be used to check if method is being used in linear working range

• Cons
• Comes at cost of increased variance

• (i) Relative merits of a calibration working curve and the method of standard additions 
• Calibration curve has lower variance, is quicker and therefore cheaper than for large numbers of samples.
• Standard addition overcomes interferents present in the original sample but at the cost of increased variance. Standard addition is more economical for smaller sample numbers.

• (ii) For calibration working curves
• The concentration range must include the expected value of the unknown and should be centred on the expected value.
• For standard additions, multiple standard additions should be used to ensure that the linear range is not exceeded.

• (iii) Use standard solutions for calibration.
• The analyte should be traceable to a primary standard.
• The composition of the standard solution should resemble the unknown in terms of matrix and concentration range.
• Solutions should be freshly prepared and chemically stable.

(i)Re-examine the data to see if a gross error could have been made- check your lab book!

(ii) If possible, repeat the measurement.  Agreement with the bulk of the data lends weight to rejecting the dubious data point.  If retention is still indicated, the effect of the outlier will be reduced.

(iii) If possible, estimate the expected precision of the method.

(iv) Apply a statistical test to see if you can reject the data on statistical grounds.  The most widely used are Dixon’s Q and Grubbs’ test.

• 1. Electromagnetic pickup: 50Hz and harmonics from mains electricity
• 2. Capacitive coupling from mains

• To alleviate:
• Use a well-grounded faraday cage (to ground/cold water tap)
• Reduce reference electrode impedance using a luggin probe or inserting a Pt wire short in the Luggin
• Screedn cables to aoid ground loops
• Driven shields and guard inputs
• Filters as a last resort since they cause offset