Pharmaceutical Calculations

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  • Created by: LBCW0502
  • Created on: 03-04-18 20:39
12.5 is to how many significant figures?
3 significant figures
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The result of any calculation involving an approximate number should be rounded off to contain how many uncertain figures?
1
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Accuracy of measurements will depend on what?
Instrument sensitivity/calibration e.g. balance measures to 2.d.p, pipette calibrated in tenths of a mL
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How do you calculate measurement accuracy?
(100 x maximum potential error)/(permissible percentage error)
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What is accuracy?
The closeness of a measured value to the true value
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What is precision?
The dispersion or variability of a set of measurements
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What is absolute error?
Observed value - expected value (or sample mean - expected mean)
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Why can absolute error be misleading?
Because it is affected by the magnitude of the measurement (lowest absolute error indicates the most accurate measurement)
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What is relative error?
Absolute error/expected value (% relative error = (100 x absolute error) / expected value) - greater numerical values indicate decreased accuracy
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Does precision give any indication of the closeness of the measured values to a given (true/expected) value?
No (low variability about a central value/low standard deviation corresponds to high precision)
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How do you calculate the coefficient of variation (CV)?
Standard deviation / mean (higher value - less precise)
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What are random errors?
Non-reproducible for each measurement. Use statistics to eliminate effects - replicate measurements
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What are determinate errors?
They affect each measurement in the same way and to the same extent
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What are constant errors?
Reproducible in magnitude (use blank to eliminate effects)
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What are systematic errors?
Same direction for all measurements by indeterminate magnitude (minimised by instrument calibration)
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What are proportional errors?
Constant relative errors (avoid with use of appropriate controls)
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Describe features of propagation of errors
y = A + B (formulae), y = A.B (formulae)
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How do you calculate density?
Mass / volume (volume = mass / density)
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Convert 1 cm to Angstrom
1 x 10^8 Angstrom
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Convert 1 cm cubed to Angstrom
1 x 10^24 Angstrom cubed
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How do you calculate the volume of one molecule given the volume of one mole?
Volume of one mole / Avogadro's number
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What are the units of density?
g/cm^-3
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How do you calculate the unknown volumes of two functional groups?
Use simultaneous equations
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What is the common logarithm (to the base 10) of a number?
The power to which we raise (the base) 10, to get that number
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What is the natural logarithm (to the base e) of a number?
The power to which we raise (the base) e to get that number (also use ln) - remember the number 2.303
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Describe features of a logarithmic graph plot
2 cycle semi-log graph, y-axis is logarithmic, scale increases in powers of 10, x-axis is linear (widely used for pharmacokinetics)
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What is nominal (or categorical) data?
Data classifiable into groups, no ranking possible
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What is ordinal data?
Data classified into groups, ranking possible
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What is interval data?
Data that can be ranked and can be precisely defined in measured units
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What is ratio data?
Interval data whose ratios convey precise quantitative information
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What are discrete variables?
Only certain values are permissible
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What are continuous variables?
Any value within the measured range is allowable/possible
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What is chi-squared?
A test for categorical data association (goodness of fit test)
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How do you calculate expected data given the observed data?
E.g. sample of 100 people where 80 are vaccinated and 20 of those have a very severe attack (0.8 x 0.2 = 0.16) - 16 people vaccinated/had a very severe attack
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Outline the method needed to analyse the data using chi-squared?
Sum of (O - E)^2 divided by E, determine the number of degrees of freedom, (n rows -1) x ( columns -1 ), compare chi-squared value with critical value (use a confidence limit)
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What conclusion can you make if the chi-squared value >> critical value?
Reject the null hypothesis
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What conclusion can you make if the chi-squared value
Accept the null hypothesis
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Describe features of contingency tables?
Apply Yates' correction if table is only 2 x 2 (if O < E, add 0.5 to O and if O > E, subtract 0.5 from O), if total sample size is
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How do you calculate standard error?
Standard deviation of sample / square root of number of samples taken
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How do you calculate population average?
sample average +/- t(standard error)
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What are student's t-tests used for?
To compare the different between observed and expected means (accept of reject null hypothesis)
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How do you calculate the number of degrees of freedom?
n - 1
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Are paired samples more reliable?
Yes
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Describe features of type I errors
The probability that the test results in the rejection of the null hypothesis when it is actually true. Alpha error, related to chosen significance level for test (alpha = 0.05)
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Describe features of type II errors
The probability that the test results in acceptance of the null hypothesis but it is actually false. The greater the power, the more sensitive the test. Power = 1 - beta (beta is the type II error resulting from accepting H0 when H0 is false)
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How do you estimate standard deviation and means prior to the experiment?
N = (s/delta)^2 (t alpha (df) + t beta (df))^2 (compare value with critical value)
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What is the y-axis also known as?
Ordinate (DV)
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What is the x-axis also known as?
Abscissa (IV)
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What is the formula for the line of best fit?
Sum of XY = (a x sum of x^2) + (b x sum of x^2) where a and b are the slope and intercept
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What does a regression coefficient close to 1 indicate?
A strong correlation (positive)
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What does a regression coefficient away from 1 indicate?
A weak correlation (negative)
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Describe features of differentiation
Provides gradient/slope (rate of change of y with change of x). Essential for: optimisation (drug design/formulation), chemical kinetics (optimisation of syntheses), enzyme kinetics (drug design) and pharmacokinetics (medicine stability in vitro/vivo
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What is the general rule for differentiation?
Multiply by the power, decrease the power by 1
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What is the multiplication rule?
dy/dx = u(dv/dx) + v(du/dx)
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What is the quotient rule?
dy/dx = v(du/dx) - u(dv/dx) / v^2
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What are the rules for logs?
If y = log e (x) (y = ln x) then dy/dx = x^-1
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What are the rules of exponentials?
If y = e^x then dy/dx = e^x. If y = e^ax then dy/dx = a.e^ax
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Describe the application to the Lennard Jones potential function
Derivation to get r = 2^1/6 x sigma (maximum negative, minimum positive)
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What is the general rule for integration?
Increase the power by 1, divide by the power (used to work out area under a curve also e.g. between limits)
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What are the standard integrals?
a.x^n gives a.x^n+1/n+1, e^x gives e^x, x^-1 gives ln(x)
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What is an infinite integral?
A definite integral in which the upper limit of integration equal infinity and/or the lower limit of integration equals infinity
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