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Introduction Introduction to Medical to Medical StatisticsStatistics
Why Do Statistics?Why Do Statistics? Extrapolate from data collected to make Extrapolate from data collected to make
general conclusions about larger general conclusions about larger population from which data sample was population from which data sample was derivedderived
Allows general conclusions to be made Allows general conclusions to be made from limited amounts of datafrom limited amounts of data
To do this we must assume that all data is To do this we must assume that all data is randomly sampled from an infinitely large randomly sampled from an infinitely large population, then analyse this sample and population, then analyse this sample and useuse results to make inferences about the results to make inferences about the population population
DataData Categorical data:Categorical data: values belong to categories values belong to categories
Nominal dataNominal data:: there is no natural order to the categories there is no natural order to the categoriese.g. blood groupse.g. blood groups
Ordinal dataOrdinal data:: there is natural order e.g. Adverse Events there is natural order e.g. Adverse Events (Mild/Moderate/Severe/Life Threatening)(Mild/Moderate/Severe/Life Threatening)
Binary dataBinary data:: there are only two possible categories there are only two possible categoriese.g. alive/deade.g. alive/dead
Numerical data:Numerical data: the value is a number the value is a number(either measured or counted)(either measured or counted) Continuous dataContinuous data:: measurement is on a continuum measurement is on a continuum
e.g. height, age, haemoglobine.g. height, age, haemoglobin Discrete dataDiscrete data:: a “count” of events e.g. number of a “count” of events e.g. number of
pregnanciespregnancies
Descriptive StatisticsDescriptive Statistics:: concerned with summarising or concerned with summarising or describing a sample eg. mean, describing a sample eg. mean, medianmedian
Inferential StatisticsInferential Statistics:: concerned with generalising from a concerned with generalising from a sample, to make estimates and sample, to make estimates and inferences about a wider population inferences about a wider population eg. T-Test, Chi Square testeg. T-Test, Chi Square test
Statistical TermsStatistical Terms MeanMean:: the average of the data the average of the data
sensitive to outlying data sensitive to outlying data MedianMedian:: the middle of the data the middle of the data
not sensitive to outlying data not sensitive to outlying data ModeMode:: most commonly occurring value most commonly occurring value RangeRange:: the spread of the data the spread of the data IQ rangeIQ range:: the spread of the data the spread of the data
commonly used for skewed data commonly used for skewed data Standard deviationStandard deviation:: a single number which a single number which
measures how much measures how much the observations vary the observations vary around the meanaround the mean
Symmetrical dataSymmetrical data:: data that follows normal data that follows normal distribution distribution (mean=median=mode) (mean=median=mode)
report mean & standard deviation report mean & standard deviation & & nn
Skewed dataSkewed data:: not normally distributed not normally distributed (mean (meanmedian median mode) mode) report median & IQ Range report median & IQ Range
Standard Normal Standard Normal DistributionDistribution
Standard Normal Standard Normal DistributionDistribution
Mean +/- 1 SD encompasses 68% of observations
Mean +/- 2 SD encompasses 95% of observations
Mean +/- 3SD encompasses 99.7% of observations
Steps in Statistical Steps in Statistical TestingTesting Null hypothesisNull hypothesis
Ho: there is no difference between the Ho: there is no difference between the groupsgroups
Alternative hypothesisAlternative hypothesisH1: there is a difference between the groupsH1: there is a difference between the groups
Collect dataCollect data Perform test statistic eg T test, Chi squarePerform test statistic eg T test, Chi square Interpret P value and confidence intervalsInterpret P value and confidence intervals
P value P value 0.05 Reject Ho 0.05 Reject Ho
P value > 0.05 Accept HoP value > 0.05 Accept Ho Draw conclusionsDraw conclusions
Meaning of PMeaning of P P Value: the probability of P Value: the probability of
observing a result as extreme or observing a result as extreme or more extreme than the one actually more extreme than the one actually observed from chance aloneobserved from chance alone
Lets us decide whether to reject or Lets us decide whether to reject or accept the null hypothesisaccept the null hypothesis
P > 0.05P > 0.05 Not significantNot significant P = 0.01 to 0.05P = 0.01 to 0.05 SignificantSignificant P = 0.001 to 0.01P = 0.001 to 0.01 Very significantVery significant P < 0.001P < 0.001 Extremely significantExtremely significant
T TestT Test T test checks whether T test checks whether twotwo samples are likely to have come samples are likely to have come
from the same or different populationsfrom the same or different populations Used on continuous variablesUsed on continuous variables Example: Age of patients in the APC study (APC/placebo)Example: Age of patients in the APC study (APC/placebo)
PLACEBO: PLACEBO: APC: APC: mean age 60.6 yearsmean age 60.6 years mean age 60.5 yearsmean age 60.5 years
SD+/- 16.5SD+/- 16.5 SD +/- 17.2SD +/- 17.2 n= 840n= 840 n= 850n= 850 95% CI 59.5-61.795% CI 59.5-61.7 95% CI 59.3-61.795% CI 59.3-61.7
What is the P value?What is the P value? 0.010.01 0.050.05 0.100.10 0.900.90 0.990.99
P = 0.903 P = 0.903 not significant not significant patients from the same patients from the same populationpopulation(groups designed to be matched by randomisation so no (groups designed to be matched by randomisation so no surprise!!)surprise!!)
T Test: SAFE “Serum T Test: SAFE “Serum Albumin”Albumin”
Q: Are these albumin levels different?Q: Are these albumin levels different?Ho = Levels are the same (any difference is there Ho = Levels are the same (any difference is there by chance)by chance)H1 =Levels are too different to have occurred H1 =Levels are too different to have occurred purely by chancepurely by chanceStatistical test:Statistical test: T test T test P < 0.0001 (extremely P < 0.0001 (extremely significant)significant)Reject null hypothesis (Ho) and accept alternate Reject null hypothesis (Ho) and accept alternate hypothesis (H1) hypothesis (H1) ie. 1 in 10 000 chance that these samples are both ie. 1 in 10 000 chance that these samples are both from the same overall group therefore we can say from the same overall group therefore we can say they are very likely to be differentthey are very likely to be different
PLACEBOPLACEBO ALBUMIN ALBUMINnn 35003500 3500 3500meanmean 2828 30 30SDSD 1010 10 1095% CI95% CI 27.7-28.327.7-28.3 29.7-30.3 29.7-30.3
RANDOMIZED CONTROLLED TRIALS
Reducing Sample SizeReducing Sample Size Same results but using much smaller sample size (one tenth)Same results but using much smaller sample size (one tenth)
ALIVEALIVE DEAD TOTAL % DEAD DEAD TOTAL % DEAD
PLACEBO 58 (69.2%) 26 (30.8%) 84 (100%)PLACEBO 58 (69.2%) 26 (30.8%) 84 (100%) 30.8 30.8
DEADDEAD 64 (75.3%) 64 (75.3%) 21 (24.7%) 85 (100%) 21 (24.7%) 85 (100%) 24.7 24.7
TOTALTOTAL 122 (72.2%) 122 (72.2%) 47 (27.8%) 169 (100%) 47 (27.8%) 169 (100%)
Reduction in death rate = 6.1% (still the same)Reduction in death rate = 6.1% (still the same) Perform Chi Square test Perform Chi Square test P = 0.39 P = 0.39 39 in 100 times this difference in mortality could have 39 in 100 times this difference in mortality could have happened by chance therefore results not significant happened by chance therefore results not significant Again, power of a study to find a difference depends a lot Again, power of a study to find a difference depends a lot on sample size for binary data as well as continuous data on sample size for binary data as well as continuous data
SummarySummary
Size matters=BIGGER IS BETTERSize matters=BIGGER IS BETTER Spread matters=SMALLER IS Spread matters=SMALLER IS
BETTERBETTER Bigger difference=EASIER TO FINDBigger difference=EASIER TO FIND Smaller difference=MORE Smaller difference=MORE
DIFFICULT TO FINDDIFFICULT TO FIND To find a small difference you need To find a small difference you need
a big studya big study
