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Basic statistics 11/09/13. Topics to cover Averages: Mean, Median, Mode, Range, Confidence...
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Transcript of Basic statistics 11/09/13. Topics to cover Averages: Mean, Median, Mode, Range, Confidence...
Basic statistics
11/09/13
Topics to cover
Averages: Mean, Median, Mode, Range, Confidence intervals, Standard deviation
Incidence and prevalence Screening tests – positive and
negative predictive values, sensitivity and specificity
Basic statistics
Central Tendencies and Spread of Data
Measures of central tendency
15 patients with epilepsy were recruited into a trial. They were asked to record the number of seizures they had in a six month period. The results are presented below.
4 2 1 1 13 1 9 2 1 1 2 3 7 5 8
Measures of central tendency
Calculate the: Mean Median Mode Range
Measures of central tendency
Calculate the: Mean = 4 Median = 2 Mode = 1 Range = 12
Measures of central tendency Mean: sum of the observations divided by the
number of observations (1 + 1 + 1 + 1 + 1 + 2 + 2 + 2 + 3 + 4 + 5 + 7 + 8 + 9 + 13) /
15 = 4
Median: the middle value when the total observations are arranged in order of increasing value
1 1 1 1 1 2 2 2 3 4 5 7 8 9 13
Mode: the most commonly occurring value 1 1 1 1 1 2 2 2 3 4 5 7 8 9 13
Range: the difference between the highest and lowest values in a set of data
13 – 1 = 12
Standard deviation
A measure of the spread of the data
Can be used to calculate confidence intervals
Normal Distribution
Confidence intervals Used to assess statistical significance Provides a measure of the extent to
which a sample estimate is likely to differ from the true population value
Indicates with a standard level of certainty (usually 95%), the range of values within which the true population mean is likely to lie e.g. 25±5
Confidence intervals contd. For a given level of confidence:
a narrow interval indicates that the sample estimate has good (high) precision
a wide interval indicates that the sample estimate has poor (low) precision
Confidence intervals become narrower as: the sample size increases the variability of the data decreases the degree of confidence required for the
population mean decreases e.g. 90%, 95%, 99%
Basic statistics
Incidence and Prevalence
Incidence
In the last year there have been 24 new cases of colorectal carcinoma in your practice (list size 10276). What is the incidence of colorectal carcinoma?
Incidence = 24 / 10276 = 0.0023 Incidence per 1000 = 2.30 per 1000
Incidence
Number of new cases diagnosed in a population per unit of time
Incidence rate = (number of new cases diagnosed in a given period of time / population size) x 100, 000 (or 1000 etc.)
Prevalence 2593 of the 8725 patients
registered with your practice have a BMI of 30 or more. What is the prevalence of obesity?
Prevalence = (2593 / 8725) x 100 = 29.7%
Prevalence = (2593 / 8725) x 1000 = 297.2 per 1000
Prevalence
Total number of cases per population at a particular point in time (e.g. number per 100,000 population) Prevalence rate = (number of cases in
population / total size of population) x 100,000 (or 1000 etc.)
Prevalence = incidence x duration of condition
Relationship between incidence and prevalence
Basic statistics
Screening Test Statistics
Screening tests
A blood test to help diagnose cervical cancer has been developed. A study is done on 1000 patients comparing this test to the standard technique
Cervical cancer present
Cervical cancer absent
New test positive
100True positives (TP)
50False positives(FP)
New test negative
10False negatives(FN)
840True negatives(TN)
Positive and negative predictive values
Positive predictive value (PPV): proportion of people who test positive who actually have the disease PPV = TP / (TP + FP)
Negative predictive value (NPV): proportion of people told they don’t have the disease that really don’t have it NPV = TN / (TN + FN)
Give an indication of the reliability of a positive or negative test result
PPV and NPV
PPV = 100 / (100+50) = 0.67 = 67%
NPV = 840 / (840+10) = 0.99 = 99%
Cervical cancer present
Cervical cancer absent
New test positive
100 50New test negative
10 840
The higher the PPV, the more likely it is that a patient with a positive test result does have the disease
The higher the NPV, the more likely it is that someone who has tested negative really doesn’t have the disease
Sensitivity and specificity Sensitivity: the proportion of people with a
disease who are detected by the test (proportion of positives found) Sensitivity = TP / (TP + FN)
Specificity: the proportion of people who don’t have a disease who test negative (proportion of negatives found) Specificity = TN / (TN + FP)
Indicate the proportion of the population with/without the disease which will be detected by the test
Sensitivity and specificity
Sensitivity = 100 / (100+10) = 0.91 = 91%
Specificity = 840 / (840+50) = 0.94 = 94%
Cervical cancer present
Cervical cancer absent
New test positive
100 50New test negative
10 840
High sensitivity = few missed diagnoses High specificity = few false positives