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[Covid-19: Thomas Bayes warns and we should listen. False negatives and the probability of encountering them.]

Martino Recchia1, Giulio Serra2

  • 1Medistat, Unità di Epidemiologia Clinica e Biostatistica, Milano; Mario Negri Institute Alumni Association (MNIAA), Milano.

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Sensitivity, Specificity, and Predicted Value01:13

Sensitivity, Specificity, and Predicted Value

In healthcare diagnostics, laboratory tests play a crucial role in identifying and diagnosing a wide range of medical conditions. However, interpreting test results is not always straightforward. An abnormal test result does not always confirm the presence of a disease, just as a normal result does not guarantee its absence. To assess the reliability of these diagnostic tools, healthcare practitioners rely on two key statistical indicators: sensitivity and specificity.
Sensitivity is the...
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Errors In Hypothesis Tests01:14

Errors In Hypothesis Tests

When performing a hypothesis test, there are four possible outcomes depending on the actual truth (or falseness) of the null hypothesis and the decision to reject or not.
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Accuracy and Errors in Hypothesis Testing01:13

Accuracy and Errors in Hypothesis Testing

Hypothesis testing is a fundamental statistical tool that begins with the assumption that the null hypothesis H0 is true. During this process, two types of errors can occur: Type I and Type II. A Type I error refers to the incorrect rejection of a true null hypothesis, while a Type II error involves the failure to reject a false null hypothesis.
In hypothesis testing, the probability of making a Type I error, denoted as α, is commonly set at 0.05. This significance level indicates a 5%...
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Testing a Claim about Population Proportion01:24

Testing a Claim about Population Proportion

A complete procedure for testing a claim about a population proportion is provided here.
There are two methods of testing a claim about a population proportion: (1) Using the sample proportion from the data where a binomial distribution is approximated to the normal distribution and (2) Using the binomial probabilities calculated from the data.
The first method uses normal distribution as an approximation to the binomial distribution. The requirements are as follows: sample size is large...
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Hypothesis: Accept or Fail to Reject?01:17

Hypothesis: Accept or Fail to Reject?

The outcome of any hypothesis testing leads to rejecting or not rejecting the null hypothesis. This decision is taken based on the analysis of the data, an appropriate test statistic, an appropriate confidence level, the critical values, and P-values. However, when the evidence suggests that the null hypothesis cannot be rejected, is it right to say, 'Accept' the null hypothesis?
There are two ways to indicate that the null hypothesis is not rejected. 'Accept' the null...
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Binomial Probability Distribution01:15

Binomial Probability Distribution

A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes.
The outcomes of a binomial experiment fit a binomial probability distribution. A statistical experiment can be classified as a binomial experiment if the following conditions are met:
There are a fixed number of trials. Think of trials as repetitions of an experiment. The letter n denotes the number of trials.
There are only two possible outcomes,...
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