Items tagged “statistics”

The sensitivity of a test/investigation is defined as the ability of the test to identify true positive cases of the disease under question. Sensitive tests are useful for ruling out disease.  Calculation Sensitivity = true positives detected by test / total cases of the disease where total ca...

Specificity of a test/investigation is the ability of a test to be correctly negative (true negative) in persons without the disease in question. Calculation Specificity = true negatives detected by test / total cases without the disease where, total cases without the disease = true negative ...

Positive predictive value of a test/investigation is defined as the proportion of patients with positive results being truly diseased. Calculation Positive predictive value = true positives (TP) detected / total positive results (total positive results = true positive (TP) + false positive (F...

Negative predictive value of a test/investigation is defined as the proportion of patients with negative results being truly disease free. Calculation Negative predictive value = true negatives detected / total negative results (where "total negative results" = true negative + false negative)...

The p-value is defined as the probability in observing a value or effect equivalent to a value or effect observed when the null hypothesis is true. In other words, the p-value is based on the assumption that the null hypothesis is true By convention, p-value ≤0.05 is considered statistically si...

The receiver operating characteristic (ROC) curve is a statistical relationship used frequently in radiology, particularly with regards to limits of detection and screening. The curves on the graph demonstrate the inherent trade-off between sensitivity and specificity: y-axis: sensitivity x-a...

Sensitivity and specificity are fundamental characteristics of diagnostic imaging tests. The two characteristics derive from a 2x2 box of basic, mutually exclusive outcomes from a diagnostic test: true positive (TP): an imaging test is positive and the patient has the disease/condition false ...

Sensitivity and specificity of multiple tests is a common statistical problem in radiology because frequently two tests (A and B) with different sensitivities and specificities are combined to diagnose a particular disease or condition. These two tests can be interpreted in an "and" or an "or" ...

Lead time bias is a bias that may be encountered in radiology literature on imaging detection of disease. Lead time is the time between detection of a disease with imaging and its usual clinical presentation. An imaging technique or modality may claim to lengthen survival time by earlier detect...

Length time bias can be encountered in the radiology literature, particular with regard to imaging screening. With length time bias, screening for a disease (D) appears more effective for a more indolent presentation of a disease (D1) than for quickly-symptomatic and quickly-fatal presentation ...

The normal distribution (or bell curve or Gaussian distribution) is a type of data spread that is encountered frequently in radiology and in other sciences. Data that are normally distributed can be evaluated using parametric statistics. When data are not normally distributed (e.g. skewed, or m...

Type I errors (alpha errors, α) occur when we accept that there is a difference between two experimental groups, when in fact, no difference exists. The threshold for accepting a type I error is the p-value. The traditionally accepted p-value of 0.05 indicates that the researchers are willing t...

Type II errors (beta errors, β) occur when we accept that there is no difference between two experimental groups, when in fact, there is a difference. The p-value does not give a direct indication of the likelihood of a type II error; if the p-value is >0.05, this does not necessarily mean that...

Bias refers to a methodological flaw in a research study which prevents generalization of a sample population out to the entire population. It is a systematic error. Errors in radiology research studies fall into one of two categories: random error systematic error/bias Random error cannot b...

Power is a critical concept when planning or evaluating a radiology study: power = (1 - β) Conventionally, power is set at 0.80-0.85. For radiologists, it may be useful to think of power as being similar to sensitivity: power is the ability of a study to detect a difference between two or more...

Z-scores are a way to translate individual data points into terms of a standard deviation.  Z = (X - Xbar) / σ X: individual data point Xbar: the arithmetic mean σ: the standard deviation The purpose of the Z-score is to allow comparison between values in different normal distributions. Two...

The standard error of the mean, SE(M) is a fundamental concept in hypothesis testing. When you pick a random sample out of a population (say a 100 data point sample out of a 10,000 data point population), what is the mean value of that sample? It's going to want to tend toward the population me...

Confidence intervals are often used in radiology literature to express the variability of an experimental result. They are usually reported as the upper and lower bound of variability (upper,lower) for your mean value, with x% certainty 1. If 95%, it means that if the study were redone many tim...