Statistics Flashcards
Parametric tests
ANOVA
require distribution
P value
More powerful than non para - show a diff that really exists
Analysis of variance - test multiple groups of parametrics
Req distribution to be normal
Incidence of of hypertension analysed w/
Categorical (or qualitative) data thus requiring a non-parametric test (that is, chi square test).
Mean
average of a group of values “average” - when add all numbers & divide
the central tendency of a group of measurements
most sensitive measurement, because its value always reflects the contributions of each of the data values in the group
Median
mid-point of a group of values. / middle value in the list of numbers.
find - list numerical smallest to largest, so you may have to rewrite your list before you can find the median.
data set contains a small number of outliers at one extreme, the median may be a better measure of the central tendency of the data than the mean
Mode
mode is the value that appears most frequently in the group of measurements.
Qualititve data -
Not numerical -> names/labels
ASA grade, type op, hair colour, pain scolour
Nominal - Mutually exclusive - no logical order hair colour type op
Ordinal - instrincs order - pain score asa grade
Quantitative
Numeral in value - vary represent contin scale
HR BP Height
Discrete - vary by set amount
number childer cant have 2.4
Contionous - take any number height bp age
Interval - zero point another point - not no measurement
Celsiues
How dispaly qual data in graphical form
qual data - not murical - vary has lavel =
Freq table - before depiected bar chart / pie chart
each freq can be given %
How describe quantitative
Quote central tendency - scatter of data from central point
Normally dsitrubted - mean dexc cenral tend
vary / sd - describ ebarration
Non normal distrub - median
IQ range - scatter
Normal distribution
non normal distribution
Distrub curve - created plotting observed values on X
freq y
Normally distrib - curve symettrical & bell shaped
Normal distrub mean mode median all same
‘parametric’
nON NORMAL / non para - ditrsub curve not symetric bell
Skewed either direction / bimodal
tail skewed right - right / pos skew
Data skew - mean mode median no longer same
Mod - most freq occuring - always peak
median - vlaue where equal numbers below & above - moves towards tail skew
mean also pulled same direction tail - erronues
How calculate variance
Spread data around central point
First calculate mean X~
Subract each idnvidual result from mean - find defrence X~-X
Square all result - make sure all positive
Add together
Divide number of degrees of freedom - obs minus 1 or N-1
What is SD
Central tendency prametic - described mean
vary around mean described variance
Calculated by swuare root of variance - used freqenty - dexvrib coventiontly
68% pop - 1SD either side
96% 2SD
99%3SD
What is the standard error of the mean
SEM used wheter mean reflects mean of true populaton
Show how mean small sample size repreents whole pop
Larger sample - more likely refeclt true pop
If SD small- vraiamce around mean small - more confident closs mean true pop
Calculated dividing standard dev by square root of degrees of freedom
Though of standrad dev mean - 68% sample mean - lie withone one standrard
Confidence limits
Related to SEM
Sample Mean will only lie outside 1.96 standrad errors 5% of time
Confident 95% sample mean rfelcts population mean
Range between two standard errors below the mean and two standard arror above = Condifence itnerval
Either end are confidence limits
Condience limits samel value as data m,eaurement - easier to interpret
Standrard error of for non parametic `?
No - data skwered - standard deviation doesnt accurately refeclt viration data around mean - impssible calculate SEM
Non parametric - quote range contains 50% results - median 50%above& below
25th centile 25% below 75% above
range betgween two is called interqaurtile range
P value
Probability event occuring
p =1 always occurs
p =0 never occurs
Compare difference between sample pop & true pop
Genereal - sample size signif smaller pop size
determ any difference occurd purely by chance
Acceptaed only probabilty of 1 in 20 p = 0.05 diffrence occured
Small enough to be disregarded - difference between group stat significant
If p>0.05 - not signifcant - occured by chance
Null hypothesis
Tests performed - assumption no signifcant difference between means samples / originate same parent population
If result produce p<0.05 - probability two samples oringation same population <1 in 20
Null hypotehsis reject - considered stat signif diffrence between samples
P >0.05 - higher probability diffrence occur by chance
Null hypotehsis no sdidference between samples
Type 1 error
Alpha error of false pos
Null hyptoehsis wronly reject - difference found when is none
Lower P value & larger size - smaller chance type 1 error
Accept p 0.05 - accept risk making type 1 1in20
Type 2 error
False Negative
Null hypoth accepted - no difference
3 factors
small size
large vary in pop
situation small diff clin imporat
20% chance type 2 erorr - study power
Power of study
Meausre Likelihood detecting deifference between groups if difference does exist
Power 1-B - b error or type 2 error
Effective probabilty avoiding type 2 weeoe
No difference between groups - concluded no clin improt difference in samples = provind adeqautge power
If type 2 error - study power insuff - conclude sample size too small
No diffce - sample end - meanfuul conculion
power porposed study calulcated prior start
Number patient - ensure suffienty power equations or normograms
How do you chose which tests to analyse data
Consider choosing appro stat test
Nature date
Qual or quant
Quant - type distrub
Parametric non para
two groups or more than two
Data pair unpair
Qualitative data
ASA grade, pain score
Using chi square
O number observed occurance - E number expect occur
Coprares freq observes results v frequency expcted if no difference
Ease - 2x2 contingency table
Two diff sample group & 2 outcome
Drug a and drug b
patient vomit & didnt vomit
Bext caluate number expected comot or not vomit if no differnece drugs
expected = colum total x row total / overall total
Number patients expect vom drug a no diff
repeat calculation in contingency table
Next for box cotnigency apply formula - results four caulation added give chi aquare results
P value depends on chi squares & degree variations
Unable use chi square
If expected occurance <5 chi square not usd
fisher exact test
Fisher exact test
Difference pair & unpair data
Unpair - two different group patient study
Datas pair - two vary test same patient =- anti htn two diff drugs study on same group patient
pARAMETIRC WHAT TEST -
kNOW PARATRIC - DETMRINE HOW MANY GROUPS
TWO GROUPS
pair student t test or unpair student T - depend if pair or nt
More than two groups = ANOVA
Student t test
Analyse normally distrub data - knowl differnece between means of 2 samples & SEM
T - Diffce betweens / est SEM
P value read tables t value - samples
ANOVA
Anal variance - compare parametric quant data - >2 groups matsanova complex - software ahdnle
Stat test - non parametic
Decide how many groups - two groups
wilcoxon signed rank - pair
mann whitney U if unpaired
> 2 groups - friedman pair
paired ksural wallis unpaire
Not normally distributed data
What is the more appropriate mean
Geometric or arithmetic
What is the SD
Positively skewed data where are the mode mean and median in relation to each other
what is the mode
where do mean and median lie when its normally distributed
The mode refers to the most frequently encountered value and in normally distributed data it coincides with the mean and median values.
In skewed data the geometric mean is the most appropriate measure (not the arithmetic mean).
Standard deviation (SD) is the square root of the variance and is a measure of distribution of the data.
In positively skewed data the mean usually lies to the right of the mode (not left).
In positively skewed data the mean usually lies to the right of the median (not left).
Double blind
how does this differ from crossover
In double blind placebo control clinical trials neither the patient nor the clinician knows which treatment option the patient has received. It would not be blind to the patient otherwise.
If everybody received both treatments then this would be a ‘double blind crossover study’.
The clinician remains blind to the treatments received by the patients until the study has finished.
Can we comment on a study design without knowing lots of info
Placebo effect is how much % different
What does p value mean
what p value is stat signif
It is not possible to say confidently that this drug trial was well designed without further information about the study and its conduct.
The placebo effect is often higher than 5%, with rates between 20 - 30% being common.
The result may indeed have occurred by chance alone in less than one in 20 occasions. This is the meaning of the ‘p value’, where a 0.05 is equal to 1/20.
Standard error is derived from the variance and ‘probable error’ is a fictitious term.
A p value of less than 0.05 is the conventional level of statistical significance, thus the results should be regarded as reaching conventional levels of statistical significance.
If the p-value is less than 0.05 indicates that there is strong evidence against the null hypothesis, as there is less than a 5% probability the null is correct (and the results are random).
What is the null hypothesis
the hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error.
N of 1 is useful when
Can the results be generalised
What t 1/2 is best
In an ‘n of 1’ trial the treatment and placebo are given at random treatment periods to the same patient.
The results are specific to one drug and the patient studied and cannot usually be generalised.
They are useful where the patient doubts the effectiveness of a treatment or where the practitioner has doubts. They are also useful for dosing or working out if a symptom is a side effect or not.
Drugs with short lived effects are best, as long wash-out periods need to be included for long acting drugs.