Comparing means
Encyclopedia
The following tables provide guidance to the selection of the proper parametric
or non-parametric
statistical tests for a given data set.
Parametric statistics
Parametric statistics is a branch of statistics that assumes that the data has come from a type of probability distribution and makes inferences about the parameters of the distribution. Most well-known elementary statistical methods are parametric....
or non-parametric
Non-parametric statistics
In statistics, the term non-parametric statistics has at least two different meanings:The first meaning of non-parametric covers techniques that do not rely on data belonging to any particular distribution. These include, among others:...
statistical tests for a given data set.
Is there a difference ?
| 1 group | N ≥ 30 | One-sample t-test | ||
| N < 30 | Normally distributed | One-sample t-test | ||
| Not normal | Sign test Sign test In statistics, the sign test can be used to test the hypothesis that there is "no difference in medians" between the continuous distributions of two random variables X and Y, in the situation when we can draw paired samples from X and Y... |
|||
| 2 groups | Independent | N ≥ 30 | t-test | |
| N < 30 | Normally distributed | t-test | ||
| Not normal | Mann–Whitney U or Wilcoxon signed-rank test Wilcoxon signed-rank test The Wilcoxon signed-rank test is a non-parametric statistical hypothesis test used when comparing two related samples or repeated measurements on a single sample to assess whether their population mean ranks differ The Wilcoxon signed-rank test is a non-parametric statistical hypothesis test used... |
|||
| Paired | N ≥ 30 | paired t-test | ||
| N < 30 | Normally distributed | paired t-test | ||
| Not normal | Wilcoxon signed-rank test Wilcoxon signed-rank test The Wilcoxon signed-rank test is a non-parametric statistical hypothesis test used when comparing two related samples or repeated measurements on a single sample to assess whether their population mean ranks differ The Wilcoxon signed-rank test is a non-parametric statistical hypothesis test used... |
|||
| 3 or more groups | Independent | Normally distributed | 1 factor | One way anova Analysis of variance In statistics, analysis of variance is a collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation... |
| ≥ 2 factors | two or other anova Analysis of variance In statistics, analysis of variance is a collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation... |
|||
| Not normal | Kruskal–Wallis one-way analysis of variance by ranks | |||
| Dependent | Normally distributed | Repeated measures anova | ||
| Not normal | Friedman two-way analysis of variance Friedman test The Friedman test is a non-parametric statistical test developed by the U.S. economist Milton Friedman. Similar to the parametric repeated measures ANOVA, it is used to detect differences in treatments across multiple test attempts. The procedure involves ranking each row together, then... by ranks |
|||
| 1 group | np and n(1-p) ≥ 5 | z-approximation Z-transform In mathematics and signal processing, the Z-transform converts a discrete time-domain signal, which is a sequence of real or complex numbers, into a complex frequency-domain representation.... |
|
| np or n(1-p) < 5 | binomial Binomial test In statistics, the binomial test is an exact test of the statistical significance of deviations from a theoretically expected distribution of observations into two categories.-Common use:... |
||
| 2 groups | Independent | np < 5 | fisher exact test Fisher's exact test Fisher's exact test is a statistical significance test used in the analysis of contingency tables where sample sizes are small. It is named after its inventor, R. A... |
| np ≥ 5 | chi-squared test | ||
| Paired | McNemar McNemar's test In statistics, McNemar's test is a non-parametric method used on nominal data. It is applied to 2 × 2 contingency tables with a dichotomous trait, with matched pairs of subjects, to determine whether the row and column marginal frequencies are equal... or Kappa |
||
| 3 or more groups | Independent | np < 5 | collapse categories for chi-squared test |
| np ≥ 5 | chi-squared test | ||
| Dependent | Cochran´s Q Cochran's theorem In statistics, Cochran's theorem, devised by William G. Cochran, is a theorem used in to justify results relating to the probability distributions of statistics that are used in the analysis of variance.- Statement :... |
See also
- Statistical hypothesis testingStatistical hypothesis testingA statistical hypothesis test is a method of making decisions using data, whether from a controlled experiment or an observational study . In statistics, a result is called statistically significant if it is unlikely to have occurred by chance alone, according to a pre-determined threshold...
- Parametric statisticsParametric statisticsParametric statistics is a branch of statistics that assumes that the data has come from a type of probability distribution and makes inferences about the parameters of the distribution. Most well-known elementary statistical methods are parametric....
- Non-parametric statisticsNon-parametric statisticsIn statistics, the term non-parametric statistics has at least two different meanings:The first meaning of non-parametric covers techniques that do not rely on data belonging to any particular distribution. These include, among others:...