Statistics: detecting differences among groups

Once data is collected from both the experimental and the control groups, a statistical analysis is conducted to find out if there are meaningful differences between the two groups. A statistical analysis determines how likely any difference found is due to chance (and thus not meaningful). In psychology, group differences are considered meaningful, or significant, if the odds that these differences occurred by chance alone are 5 percent or less. Stated another way, if we repeated this...

The F-test is used to compare two sample variances to each other or compare the sample variance to the population variance. It is used to decide whether an indeterminate error can explain the difference in their values. The underlying assumptions that allow the use of the F-test include the data set or sets are normally distributed, and the data sets are independent of each other. The test statistic F is calculated by dividing one variance by another. In other words, the square of one standard...

Survival analysis is a cornerstone of medical research, used to evaluate the time until an event of interest occurs, such as death, disease recurrence, or recovery. Unlike standard statistical methods, survival analysis is particularly adept at handling censored data—instances where the event has not occurred for some participants by the end of the study or remains unobserved. To address these unique challenges, specialized techniques like the Kaplan-Meier estimator, log-rank test, and Cox...

In parametric statistics, two fundamental tests stand out for their utility and wide application: the Student's t-test and goodness-of-fit tests. These tests provide researchers with a robust method for drawing insights from data, testing hypotheses, and making informed decisions based on their findings.
The Student's t-test is a statistical test that examines if there is a statistically significant difference between the means of two groups. This test is instrumental when dealing with data...

The goodness–of–fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the test for homogeneity, can be used to conclude whether two populations have the same distribution. To calculate the test statistic for a test for homogeneity, follow the same procedure as with the test of independence. The hypotheses for the test for homogeneity can be stated as...

Statistical inference techniques, paramount in hypothesis testing, differentiate into two broad categories: parametric and nonparametric statistics.
Parametric statistics, as the name suggests, assumes that data follow a specific distribution, often a normal distribution. This assumption enables robust hypothesis testing and estimation. Parametric methods, like the Student's t-test or Goodness-of-fit test, are frequently employed in biostatistics due to their robustness. For instance, comparing...