Maths and Stats Flashcards
log10(1) =
0
log10(10) =
1
log10(100) =
2
log10(1000) =
3
Differentiation equation and correspondence
dy/dx
Rate slope is changing
Ie steep is fast, lowest point on curve = rate 0
Integration equation and corresponds to
y = f(x)dx
Area under curve
Variance equation
npq
sum of (x-mean2)/n-1
SD equation
Square root of variance
Are the mean and variance dependant or independent parameters
Independent
Standard error of mean equation
SD of means of multiple samples
SD/ square root of n
What is the null hypothesis
That there is no difference
If confidence limit includes 0 then can’t reject null hypothesis
What is a type 1 (alpha) error
False positive (p value same as alpha)
What is a type 2 (beta) error
False negative
What is the p value
Probability of getting the observed value or more extreme when the null is true
ie p = 0.01 = 1/100 chance
Calculate power
1 - B error
How to increase power of study (3)
- Large sample size
- Low SD
- Parametric tests
Sensitivity
TP / TP + FN x 100
Specificity
TN / TN + FP x 100
PPV
TP / TP + FP x 100
Likelihood ratio equation
sensitivity / (1 - specificity)
y axis x axis
Range of correlation coefficient (r)
0 to (+/-)1 where 0 is no correlation and 1 is fully positive or negative correlation
NPV
TN / TN + FN x 100
What is r squared
Coefficient of determination
r=0.8, r squared=0.64 = 64% variability in y can be attributed to x
What is least squares regression
Finding mean of x and y and finding line of best fit from this
What compares two measuring devices
Bland Altman plot
Asolute risk =
event rate
ARR =
ARc - ARt
NNT =
1 / ARR
RR =
ARt / ARc
RRR =
1-RR
RR 1 =
RR >1 =
RR <1 =
no association
more risk
less risk
Relative risk can be used to assess which kind of study
Cohort study (prospective)
If confidence interval includes 1 is it statistically significant
No
Odds ratio can be used to assess which kind of study
Cohort (prospective) and case control (retrospective)
Odds =
No events/ No non events
Odds ratio =
Odds Tx / Odds Cx group
2 types of quantitative date
- Continuous (inc decimals)
- Discrete (whole numbers)
Pearson correlation coefficient used for
Parametric data
Paired or unpaired T test
2 groups of parametric data
ANOVA or multiple T tests
3 groups of parametric data
Statistical significance level in multiple T tests
0.05 / no. tests
Spearson rho correlation coefficient
Non parametric data
Mann Witney U test
2 groups of unpaired non parametric data
Wilcoxon
2 groups of paired non parametric data
Kruskal Wallis
3 groups of unpaired non parametric data
Friedman
3 groups of paired non parametric data
2 types of qualitative data
- Nominal (yes/no) (categories)
- Ordinal (GCS/ ASA etc) (Can use non parametric tests)
Fishers exact test
2x2 unpaired qualitative data
How to perform chi squared test
Calculate expected values if null hypothesis is true using totals from table.
Calculate chi squared number for each cell = sum of (O-E)2 / E
Calculate DoF = (rows-1) x (columns-1)
Cohort study
Prospective study
Two groups
Exposed to Tx
Monitor condition Ix
Case control study
Retrospective study
Two groups - 1 has known Dx, one does not
Work backwards to find exposure
Selection bias
Flaw in way population studied selection
Information bias
Systematic error in collection of data
Confounding factor
May be a factor which causes both outcomes
Phase 1 clinical trial
Small scale, healthy volunteers, asses safety
Phase 2 clinical trial
Test on patients with disease, drug dose range, small RCT
Phase 3 clinical trial
Large multi centre RCT
Phase 4 clinical trial
Post marketing surveillance
Does a per protocol analysis include patients who have dropped out
No
Does an intention to treat analysis include patients who have dropped out
Yes
