 #  Mean: true average  Median: middle number once ranked  Mode: most repetitive  Range : difference between largest and smallest.

## Presentation on theme: " Mean: true average  Median: middle number once ranked  Mode: most repetitive  Range : difference between largest and smallest."— Presentation transcript:

 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 ResultDisease PresentDisease Absent PositiveTPFP NegativeFNTN

 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 Paracetamol6040 Placebo9030

 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 Paracetamol10060 Placebo8020

 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.

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