Fisher's exact test is a statistical significance test widely used to analyze 2x2 contingency tables, particularly in situations where sample sizes are small. Unlike the chi-squared test, which approximates P-values and assumes minimum expected frequencies of at least five in each cell, Fisher's exact test calculates the exact probability (P-value) of observing the data or more extreme results under the null hypothesis. This feature makes it especially valuable when the assumptions of...

Learning to draw Fischer projections of molecules and understanding their relevance plays a crucial role in the visual depiction of organic molecules. A Fischer projection is a two-dimensional projection on a planar surface to simplify the three-dimensional wedge–dash representation of molecules. This is especially helpful in the case of molecules with multiple chiral centers that can be difficult to draw. Here, all the bonds of interest are represented as horizontal or vertical lines.

The F distribution was named after Sir Ronald Fisher, an English statistician. The F statistic is a ratio (a fraction) with two sets of degrees of freedom; one for the numerator and one for the denominator. The F distribution is derived from the Student's t distribution. The values of the F distribution are squares of the corresponding values of the t distribution. One-Way ANOVA expands the t test for comparing more than two groups. The scope of that derivation is beyond the level of this...

The Behrens-Fisher test is a statistical method designed to address the Behrens-Fisher problem, which arises when comparing the means of two normally distributed populations with unequal variances. Unlike the Student's t-test, which assumes equal variances, the Behrens-Fisher test allows for mean comparison without this restrictive assumption. This flexibility makes it particularly valuable in scenarios where two independent samples exhibit normality but lack variance homogeneity.
This test...

Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures...

The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...