Statistics for AKT
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Transcript Statistics for AKT
Mean: true average
Median: middle number once ranked
Mode: most repetitive
Range : difference between largest and smallest.
Find out the Mean, Median, Mode and Range for following.
8, 9, 9, 10, 11, 11, 11, 11, 12, 13
The mean is the usual average:
(8 + 9 + 9 + 10 + 11 + 11 + 11 + 11 + 12 + 13) ÷ 10 = 105 ÷ 10 = 10.5
The median is the middle value. In a list of ten values, that will be the
(10 + 1) ÷ 2 = 5.5th value which will be 11.
The mode is the number repeated most often. 11
The largest value is 13 and the smallest is 8, so the range is
13 – 8 = 5.
Normal Distribution: Mean=Median=Mode
Positive Skewed: Mean>Median>Mode
Negative Skewed: Mean<Median<Mode
Test Result
Disease Present
Disease Absent
Positive
TP
FP
Negative
FN
TN
Sensitivity:
How good is the test at detecting those with the condition
TRUE POSITIVES
ACTUAL NUMBER OF CASES
Specificity:
How good is the test at excluding those without the
condition
TRUE NEGATIVES
ACTUAL NUMBER OF PEOPLE WITHOUT CONDITION
Positive Predictive Value:
How likely is a person who tests +ve to actually have the
condition
TRUE POSITIVES
NUMBER OF PEOPLE TESTING POSITIVE
Negative Predictive Value:
How likely is a person who tests –ve to not have the
condition
TRUE NEGATIVES
NUMBER OF PEOPLE TESTING NEGATIVE
Incorporates both sensitivity and specificity
Quantifies the increased odds of having the disease if you
get a positive test result, or not having the disease if you get
a negative test result.
Positive Likelihood ratio:
Sensitivity
(1 – Specificity)
Negative Likelihood ratio:
(1-Sensitivity)
Specificity
Odds are a ratio of the number of people who incur a
particular outcome to the number of people who do not
incur the outcome.
NUMBER OF EVENTS
NUMBER OF NON-EVENTS
Odds ratio:
The odds ratio may be defined as the ratio of the odds
of a particular outcome with experimental treatment and that
of control.
Odds ratios are the usual reported measure in case-control
studies.
It approximates to relative risk if the outcome of interest is
rare.
ODDS IN TREATMENT GROUP
ODDS IN CONTROL GROUP
For example, if we look at a trial comparing the use of
paracetamol for dysmenorrhoea compared to placebo
we may get the following results
Total no of
Patients
Pain relief
achieved
Paracetamol
60
40
Placebo
90
30
The odds of achieving significant pain relief with
paracetamol = 40 / 20 = 2
The odds of achieving significant pain relief with
placebo = 30 / 60 = 0.5
Therefore the odds ratio = 2 / 0.5 = 4
Prevalence: rate of a disorder in a specified population
Incidence: Number of new cases of a disorder
developing over a given time (normally 1 year)
Relative risk (RR) is the ratio of risk in the
experimental group (experimental event rate, EER) to
risk in the control group (control event rate, CER).
Relative risk is a measure of how much a particular risk
factor (say cigarette smoking) influences the risk of a
specified outcome such as lung cancer, relative to the
risk in the population as a whole.
Absolute risk: Risk of developing a condition
Relative risk: Risk of developing a condition as compared
to another group
EVENTS IN CONTROL GROUP – EVENTS IN TREATMENT
GROUP EVENTS IN CONTROL GROUP
X 100
- My lifetime risk of dying in a car accident is 5%
- If I always wear a seatbelt, my risk is 2.5%
- The absolute risk reduction is 2.5%
- The relative risk reduction is 50%
For example, if we look at a trial comparing the use of
paracetamol for dysmenorrhoea compared to placebo
we may get the following results
Total no of
Patients
Pain relief
achieved
Paracetamol
100
60
Placebo
80
20
Experimental event rate, EER = 60 / 100 = 0.6
Control event rate, CER = 20 / 80 = 0.25
Therefore the relative risk = EER / CER = 0.6 / 0.25 =
2.4
Relative risk reduction (RRR) or relative risk increase
(RRI) is calculated by dividing the absolute risk change
by the control event rate Using the above data,
RRI = (EER - CER) / CER
(0.6 - 0.25) / 0.25 = 1.4 = 140%
Numbers needed to treat (NNT) is a measure that
indicates how many patients would require an
intervention to reduce the expected number of
outcomes by one
It is calculated by 1/(Absolute risk reduction)
Absolute risk reduction = (Experimental event rate)
- (Control event rate)
A study looks at the benefits of adding a new anti platelet
drug to aspirin following a myocardial infarction. The
following results are obtained:
Percentage of patients having further MI within 3 months
Aspirin 4%
Aspirin + new drug 3%
What is the number needed to treat to prevent one patient
having a further myocardial infarction within 3 months?
NNT = 1 / (control event rate - experimental event rate)
1 / (0.04-0.03)
1 / (0.01) = 100
Remember that risk and odds are different.
If 20 patients die out of every 100 who have a
myocardial infarction then the risk of dying is 20 /
100 = 0.2 whereas the odds are 20 / 80 = 0.25.
The null hypothesis is that there are no differences
between two groups.
The alternative hypothesis is that there is a difference.
Type 1 error:
- Wrongly rejecting the null hypothesis
- False +ve
Type II error:
- Wrongly accepting the null hypothesis
- False -ve
Probability of establishing the expected difference
between the treatments as being statistically
significant
- Power = 1 – Type II error (rate of false –ve’s)
Adequate power usually set at 0.8 / 80%
Is increased with
- increased sample size
- increased difference between treatments
A result is called statistically significant if it is unlikely
to have occurred by chance
P values
- Usually taken as <0.05
- Study finding has a 95% chance of being true
- Probability of result happening by chance is 5%
1.
Parametric / Non-parametric
Parametric if: - Normal distribution
- Data can be measured
2.
Paired / Un-paired
Paired if data from a single subject group
(eg before and after intervention)
3.
Binomial – ie only 2 possible outcomes
Student’s T-test
- compares means
- paired / unpaired
Analysis of variance (ANOVA)
- use to compare more than 2 groups
Pearsons correlation coefficient
- Linear correlation between 2 variables
Mann Whitney
- unpaired data
Kruskal-Wallis analysis of ranks / Median test
Wilcoxon matched pairs
- paired data
Friedman's two-way analysis of variance / Cochran Q
Spearman or Kendall correlation
- linear correlation between 2 variables
Compares proportions
Chi squared ± Yates correlation (2x2)
Fisher’s exact test
- for larger samples
The standard deviation (SD) represents the average
difference each observation in a sample lies from the
sample mean
SD = square root (variance)
In statistics the 68-95-99.7 rule, or three-sigma rule, or
empirical rule, states that for a normal distribution
nearly all values lie within 3 standard deviations of the
mean
About 68.27% of the values lie within 1 standard
deviation of the mean.
Similarly, about 95.45% of the values lie within 2
standard deviations of the mean.
Nearly all (99.73%) of the values lie within 3 standard
deviations of the mean.
Thank you for all your patience!!!!