Equations And Stats etc Flashcards
How does standard deviation relate to variance
Sd is square root of variance
Mean mode median
Mean is sum of values / total points
Median is value in series and middle point
Mode is most frequent occurring
How are mean median mode effected in normal date, positive and negatively skewed data
Normal distribution mean = mode = median
Positive skewed mean > median > mode
Negative skewed mean < median
What is variance and how does it relate to standard deviation
Variance is the average of squared differences from the mean
Standard deviation is the square root of variance
Parametric tests
2 groups
Paired t
Unpaired t
More than 2
Anova one way
Anova two way
Correlation
Pearson’s
Non parametric tests
Don’t assume normal distribution
2 groups
Paired wilcoxin rank
Unpaired Mann Whitney
More than 2
Paire freidman
Unpaired Krushall Wallis
Correlation spearman’s rank
Qualitative data tests
Qualitative are all non parametric by default
Up to 2x2
Fishers exact
More than 2x2
Chi squared
Standard deviations include how much of the distribution
1 sad 68%
2 sd 96%
3 sd 99%
Qualitative data
Qualitative data is categorical data
Ie ordinal (order ie asa)
Nominal (no natural order ie gender)
Wha5 is statistical variability and what are measures of variability
Statistical variability is the spread of the data
Measure of variability usually accompanies measure of central tendency
Small variability = clustered around central tendency
Types
Range
IQ range (ie 25th to 75th centiles gets rid of outliers and is used with median)
Variance (average of the square difference from the mean- all data used)
Standard deviation is square root of variance (mean, v sensitive to outliers)
Type 1 error
If the null hypothesis is rejected when it is true (ie a false positive the tests shows a difference when there is non)
The risk of this happening is the a risk so sometimes used interchangeably
Type 2 error
Is the null hypothesis accepted when it is false (ie false negative the tests shows no difference when there is one)
The risk of this happening is the B risk
Way to reduce type 1 and 2 error
Increase sample size
Power analysis determines the smallest size required
Power = 1-b
Sensitivity
Sensitivity of a test is the proportion of true positives of everyone who has the disease
Ie true positives / everyone with disease
Ie true positives / true positives +false negatives
High sensitivity is ulseful for ruling OUT a disease
Specificity
Specificity is the number of true negatives of everyone who don’t have the disease
Ie true negatives / everyone without the disease
Ie true negatives / true negatives + false positives
Specificity useful for ruling IN a disease
Number needed to treat
Number needed to treat is a measure of the effectiveness of an intervention
Ie the average no of people treated to prevent or have one outcome
Number needed to treat is the inverse of absolute risk reduction (control group /event group)
Best NNT =1
If no difference between group nnt is inifinity
If nnt less than 0 implies harm
Odds ratio and relative risk
Odds ratio and relative risk are relative likelihood of an outcome occurring in 2 sample groups
Odds ratio is the ratio of outcome in intervention group compared to outcome in control group
Relative risk is occurrence of intervention group compare to control and requires to know total number of individuals therefore can only do in retrospective studies
Predictive values
An ideal test positive results is positive for disease and negative result is negative for disease
Test don’t exist like that
The probability that the test will give correct diagnosis is the predictive value of the test
PPV is the proportion of pets with a positive test that actually have disease
Ie true positives / true positives and false positives
NPV is the proportion of people with negative test that actually have the disease
Ie true negatives / true negatives and false negatives
Standard error of mean
Standard error measures accuracy with which a sample distribution represents a population by using standard deviation. In stats is sample mean deviates from actual mean of population this error is standard error of the mean
Risk scores vs risk prediction model
Risk scores assign weighting to factors pre identified as inpdenetent predictors out outcome
Get a no at end
Place patient on a scale of risk depending on no
Simple to use
Not that individualised
Risk prediction models put patient variable in and get a probability of risk from the model
More individualised
Examples of risk scores
ASA
Lees revised cardiac index
Ariscat (pulmonary complications)
Examples of risk prediction models
P possum
NELA
Sort (surgical outcome risk tool)
ACS NQUIP
Lees revised cardiac risk index
Risk score development. Africa complications
High risk surgery IHD CCF Cerebrovascular disease Insuliapn Creatinine over 176
Not generaliseable to low risk or emergency surgery
Ariscat
Risk score development pulmomary complications
Age Sats Recent chest infection Surgical incision Duration surgery Emergency
Negative is ppc are defined in various ways
P possum
Risk prediction model
Includes Age Bp Heart rate ECG GCS Na K WCc Urea
Op severity
Soiling
Malignancy
Blood loss
No morbidity
Over estimates mortality when over 15%
NELA j
Risk prediction model
Developed from p possum
Accurate and specific for emergency laparotomy
Sort
Surgical outcome risk tool
Prediction model
Variable ASA Surgical urgency Specialty Cancer Age Severity
ACS NSQUIP
Risk prediction model
21 variable input, 14 variable output ie VTE pneumonia
Very good
But based on private American population
