Analysis of repeated measures data (one-, two-, and three-way) using a mixed effects model (similar to repeated measures ANOVA, but capable of handling missing data).Three-way ANOVA (limited to two levels in two of the factors, and any number of levels in the third).Tukey, Newman-Keuls, Dunnett, Bonferroni, Holm-Sidak, or Fisher’s LSD multiple comparisons testing main and simple effects. Two-way ANOVA, with repeated measures in one or both factors.Two-way ANOVA, even with missing values with some post tests.Calculate the relative risk and odds ratio with confidence intervals. Fisher's exact test or the chi-square test.Kruskal-Wallis or Friedman nonparametric one-way ANOVA with Dunn's post test.When this is chosen, multiple comparison tests also do not assume sphericity.

Greenhouse-Geisser correction so repeated measures one-, two-, and three-way ANOVA do not have to assume sphericity.

Many multiple comparisons test are accompanied by confidence intervals and multiplicity adjusted P values.

One-way ANOVA without assuming populations with equal standard deviations using Brown-Forsythe and Welch ANOVA, followed by appropriate comparisons tests (Games-Howell, Tamhane T2, Dunnett T3).

Ordinary or repeated measures ANOVA followed by the Tukey, Newman-Keuls, Dunnett, Bonferroni or Holm-Sidak multiple comparison tests, the post-test for trend, or Fisher’s Least Significant tests.

Perform many t tests at once, using False Discovery Rate (or Bonferroni multiple comparisons) to choose which comparisons are discoveries to study further.

Wilcoxon test with confidence interval of median.

Kolmogorov-Smirnov test to compare two groups.

Nonparametric Mann-Whitney test, including confidence interval of difference of medians.

Automatically generate volcano plot (difference vs.

Reports P values and confidence intervals. Using the same technique, we can get formulas for all remaining regressions. Using the formula for the derivative of a complex function we will get the following equations:Įxpanding the first formulas with partial derivatives we will get the following equations:Īfter removing the brackets we will get the following:įrom these equations we can get formulas for a and b, which will be the same as the formulas listed above. To find the minimum we will find extremum points, where partial derivatives are equal to zero. We need to find the best fit for a and b coefficients, thus S is a function of a and b. Let's describe the solution for this problem using linear regression F=ax+b as an example. Thus, when we need to find function F, such as the sum of squared residuals, S will be minimal

The best fit in the least-squares sense minimizes the sum of squared residuals, a residual being the difference between an observed value and the fitted value provided by a model.

We use the Least Squares Method to obtain parameters of F for the best fit. Thus, the empirical formula 'smoothes' y values. In practice, the type of function is determined by visually comparing the table points to graphs of known functions.Īs a result we should get a formula y=F(x), named the empirical formula (regression equation, function approximation), which allows us to calculate y for x's not present in the table. We need to find a function with a known type (linear, quadratic, etc.) y=F(x), those values should be as close as possible to the table values at the same points. We have an unknown function y=f(x), given in the form of table data (for example, such as those obtained from experiments). Exponential regressionĬorrelation coefficient, coefficient of determination, standard error of the regression – the same as above. Logarithmic regressionĬorrelation coefficient, coefficient of determination, standard error of the regression – the same as above. Hyperbolic regressionĬorrelation coefficient, coefficient of determination, standard error of the regression - the same as above. ab-Exponential regressionĬorrelation coefficient, coefficient of determination, standard error of the regression – the same. Power regressionĬorrelation coefficient, coefficient of determination, standard error of the regression – the same formulas as above. System of equations to find a, b, c and dĬorrelation coefficient, coefficient of determination, standard error of the regression – the same formulas as in the case of quadratic regression.

Exponential graph builder