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\f43\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\fs32\ul Statistics for AKT
\par }{Everything I knew for the AKT (must admit some of the more obscure equations like pre and post test probability were not well remembered!).  Based mainly on Nick Collier\rquote s teaching and passmedicine answers.
\par }{\fs28\ul Data
\par }{Data can be continuous, discrete, or categorical (which may in turn be ordinal or nominal).
\par Continuous data concerns a continuous variable (e.g. height or weight)
\par Discrete data must be a whole number (e.g. number of children)
\par Categorical data concerns categories (e.g. blue or brown eyes) 
\par Categorical data may be ordinal data where it is possible to rank the categories (e.g. small, medium and large) or nominal when ordering is not possible (e.g. eye colour)
\par Continuo
us data from a biological population will usually form a bell shaped curve when plotted.  If the curve is symmetrical it is called a Normal distribution (a type of parametric distribution and so parametric statistical techniques are required). If it is no
t symmetrical it is a Skewed distribution (a type of non \endash  parametrical distribution and non-parametric statistical techniques are required)
\par }{\fs28 Normal Distribution (a type of parametric distribution)
\par }{\field{\*\fldinst { HYPERLINK "http://academic.kellogg.edu/mckayg/buad112/web/pres/normal curve 2" }{{\*\datafield 
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\par Mean=mode (most frequently occurring number)=median (middle number when the numbers are ranked )
\par Distribution is described using the mean and the standard deviation or variance
\par Standard Deviation = the average distance each data point is from the mean (i.e. how spread out the data is).  66% of the data points will be within 1SD of the mean, 95% within 1.96SD, 99% within 3SD
\par Variance = SD}{\super 2
\par }{Standard error of the mean \endash  this concept is quite confusing, so imagine the population of the UK.  The heights of everyone will be normally distribute
d and will have a mean.  If you want to find out the mean height of the UK population you could measure everyone but that would take too long.  An alternative would be to take a sample of the population e.g. the population of Northallerton, and assume tha
t
 it is representative of the whole of the UK.  You can then measure everyone in Northallerton and calculate the mean and standard deviation for Northallerton.  However, how likely is it that the mean for Northallerton matches the mean for the UK?  The way
 to work this out is the Standard Error of the Mean \endash 
 basically this gives a range of figures measured from the sample mean (i.e. the Northallerton mean) that the population mean is likely to be within.  There is a 95% chance that the population mean will l
ie within 1.96SEM of the sample mean (i.e. take the Northallerton mean and add and subtract 1.96SEM from it and this will give you a range within which there is 95% chance that the UK mean will be)  This is how confidence intervals are arrived at.  The bi
gger the sample size is the smaller the SEM becomes.  This makes sense, if you measure the heights of half the population you are likely to be more accurate than if you measure the height of only 10 people.
\par SEM = SD/}{\field{\*\fldinst { QUOTE }{\lang1024\langfe1024\noproof {\*\shppict{\pict{\*\picprop\shplid1026{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fRotateText}{\sv 1}}{\sp{\sn pictureTransparent}{\sv 16777215}}
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\par }{\fs28 Skewed Distributions (a type of non parametric distribution)
\par }{Described using median and range (distance between smallest and largest number)
\par Positive is skewed to the right (i.e. the longer tail sticks out to the right).  Mean>median>mode.
\par Negative is skewed to the left (i.e. the longer tail sticks out to the left).  Mean <median<mode.
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\par (To remember the order of mean, median and mode write them out in that order, which is alphabetical, then put in the arrows pointing to the direction of the skew)
\par }{\fs28\ul Statistical Tests
\par }{When doing a study, what is being looked at is whether there is a difference between two sets of data.  For example, does treatment with an ACE inhibitor change the blood pressure in the treatment group compared to the non-treatment group?
\par Before starting a study several values have to be decided on:
\par The null hypothesis (i.e. the assumption which needs proving or disproving) is that there is no difference between the two groups of data (i.e. that the two samples were drawn from the same population).
\par p value (level of statistical significance) = the probability that the two samples have come from the same popul
ation (i.e. no difference between the two groups) = the probability of obtaining our result or something more extreme if the null hypothesis is true.
\par P<0.05 = probability of the two samples being from the same population is <1/20
\par Once the level of statistical significance to be shown has been chosen then the power of the study is used to calculate the sample size needed.
\par Power = probability of the study rejecting the null hypothesis when it is false (ideally should be >95%).  This is affected by the sample size, treatment effect size and the p value to be demonstrated.  You want to make sure you have a large enough sample
 to give a meaningful result that wouldn\rquote t be achieved by chance alone.
\par Even if the study has a power of 95% there is still a 1/20 chance that it will not reject the null hypothesis when it is false (i.e. will say there is no difference between the two samp}{\f406 
le groups even if there is).  If this happens it is a Type 2 error (i.e. a false negative \endash  the null hypothesis is accepted when it is actually false).  The rate of a type 2 error occurring is signified as \'e2 and 1-\'e2
 = power.  The other type of error that can occur is a type 1 error where the null hypothesis is falsely rejected when it is true (i.e. a false positive).  If p= 0.05 then this type of error will happen with a 1/20 chance.  A type 1 error is signified as 
\'e1.
\par }{Therefore if there is no difference bet
ween the two samples then if the study has a p value of 0.05 then there is a 1/20 chance of it showing a difference between the two samples ( a type 1 error).  If there is actually a difference between the two samples then a study with a power of 95% has 
a 1/20 chance of showing no difference (a type 2 error).  
\par There are various ways of deciding if there is a difference between the two groups of data.  The significance of this difference is determined by the p value.  Depending on the distribution of the data different tests need to be used.  We don\rquote 
t really need to know how these tests are done so it is just a case of learning which should be used when.
\par Numerical data:
\par }\pard \ql \li720\ri0\sa200\sl276\slmult1\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin720\itap0 {Normal/parametric distribution \endash  Student\rquote s T test (\lquote paired\rquote  if it is the same people in 
each sample, i.e. a before and after study, \lquote unpaired\rquote  is used if the two groups contain different people)
\par Skewed/non-parametric distribution \endash  Paired \endash  Wilcoxon, Unpaired - Mann Whitney U (these    rank the data before analysis)
\par }\pard \ql \li0\ri0\sa200\sl276\slmult1\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {Categorical data (binomial = two possible outcomes expressed as percentage or proportion) \endash  Fishers\rquote 
s test or Chi squared for large samples 
\par }{\fs28\ul Correlation and Regression
\par }{As well as looking for differences between two sets of data you might want to see if two sets of data correlate (e.g. does blood pressure reduce as ACE inhibitor dose is increased).  You again use different tests depending on the data distribution.

\par Numerical data:
\par \tab Normal/parametric \endash  Pearson\rquote s correlation coefficient (N.B. }{\b P}{arametric = }{\b P}{earson\rquote s)
\par \tab Skewed/non-parametric \endash  Spearman\rquote s rank correlation coefficient (N.B. }{\b S}{pearman\rquote s = }{\b S}{kewed)
\par Correlation exists when there is a linear relationship between two variables (N.B .there may be a non-linear relationship between two variables but this would give a low correlation coefficient)
\par Correlation coefficient = r, this is the strength of the relationship i.e. how closely points lie to a line drawn through plotted data.  If the points are very scattered then the two variables are not very well correlated, however if all the poi
nts lie on the line of best fit then the two variables are well correlated.  r can vary from -1 (negative correlation) to +1 (positive correlation) and 0 is no correlation
\par Correlation does not give any information on how much a variable will change based on the other variable.  It also does not show cause and effect.
\par Linear regression is used to predict how one variable changes when a second variable is altered i.e. it quantifies the relationship between two variables.  It describes the line of best fit in 
mathematical terms.  The regression coefficient gives the slope of the line (i.e. the change in one value per unit change in the other).  Regression is measured using the method of least squares.  Regression is useful if we want to use one measure as a pr
oxy for the other e.g. fasting glucose for HbA1c.
\par }{\fs28\ul Survival Time
\par }{Cumulative survival over time in a cohort of patients if shown in a Kaplan Meier survival curve and it is possible to compare survival in different groups of patients using the curves. Regressi
on models can be used to calculate the relative hazard ratio for events occurring in each (i.e. you can find out the impact on survival that individual events have and give them a figure = the relative hazard ratio).
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