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The above study was not an example given in Chapter 18 of CiMC and was therefore discussed in detail, but bootstrap average regions are given and interpreted for three other data sets there, and we shall end just by showing a region plot from one of those, for...

A final example of bootstrap regions which do strongly overlap, and for which the hypothesis tests (such as ANOSIM) give no indication at all that the groups differ, is shown in Fig. 18.7 of CiMC. It can be reproduced here by opening the Fal macrofauna counts ...

PRIMER 8 with PERMANOVA+ is a substantial upgrade on its predecessor, offering a host of marvelous new tools and statistical methods. These range from simple utilities to make your life easier (such as a tool to easily rename the levels of a factor), through t...

Most of the methods in the list below are unique to PRIMER 8 and are not available in any other software package. Some of the methods are not new (such as the non-parametric univariate Mann-Whitney U test), but are implemented in a novel way in P8. Expanded ...

New default colour palette - The new colour palette for PRIMER graphics ensures distinctive colours by default that carefully accommodate several different forms of colour-blindness. New selection options - Select subsets of variables and/or samples by nam...

Adegoke (2019) Adegoke, N. (2019) Contributions to improve power, efficiency and scope of control-chart methods . PhD thesis, School of Natural and Computational Sciences (SNCS), Massey University, New Zealand, 284 pp. link to source A...

Summary statistics provide essential information to help you get to know your variables, their fundamental statistical properties and numerical characteristics. In P8, if you click on Tools > Summary Stats... you will see (Fig. 1.1) that we have greatly expand...

Given a set of values $\{ y_1, y_2, ..., y_n \}$ for any individual variable $Y$, the following summary statistics can be calculated by clicking on Tools > Summary Stats... in PRIMER 8: Average: $\hspace{1mm}$ $\bar{y} = \sum_{i=1}^n{y_i} / n $, the average ...

To show the utility of this tool, we will calculate some summary statistics from a study examining changes in macrofaunal communities inhabiting sediments near an oil platform (Ekofisk) in the North Sea, provided by . These data consist of counts of the abunda...

To run summary statistics on your variables separately for multiple groups of data, just choose a factor by which you would like to split the data in the dialog. For example, for the Ekofisk dataset, suppose we wished to obtain summary statistics (means and st...

For environmental data, we might choose to calculate different sorts of summary statistics than the kinds of things we would want to know about biotic data consisting of counts. For count data, quantities like the numbers of zeros, singletons, doubletons and f...

Overview The Wilcoxon signed-rank test was described by . It is designed for the situation where there are two groups of values, and any individual value in one group is paired with a specific value in the other group. For example, you might have a treatment a...

Overview The Mann-Whitney U test was described by and . Here, interest lies in comparing two groups of independent samples. This is a non-parametric analogue to a classical two-sample (unpaired) t-test. The null hypothesis Suppose we have independent response...

Overview The Kruskal-Wallis test was described by and . Its purpose is to compare two or more independent groups of samples and it is an extenstion of the Mann-Whitney U test. It operates on ranked values and will indeed yield an equivalent result to the Mann...

Overview The Kolmogorov-Smirnov test is a non-parametric test for comparing two distributions of a continuous variable. Rejection of the null hypothesis indicates that the two distributions differ from one another in some way (location, dispersion, skewness, e...

Overview PRIMER 8 offers several options to achieve a non-parametric bivariate test of association. Here, there are two variables sampled from the same set of sampling units and interest lies in examining the extent to which they co-vary. Do values of the two ...

An example of a paired design with two groups is provided by , who described a study by to investigate the total catch of five different groups of plankton (hence, five variables, named using Roman numerals I, II, III, IV and V) by 2 nets hauled horizontally ...

As an example of the Mann-Whitney U test, we will look at a dataset consisting of counts of the snapper (Chrysophrys auratus) sampled using baited remote underwater videos (BRUVs) from multiple areas inside vs outside several marine reserves along the north-ea...

We will use the Kruskal-Wallis test to compare counts of a bivalve species, Abra prismatica, occurring at sites classified into groups according to their proximity to the Ekofisk oilfield in the North Sea (). Macrofauna were sampled from each of 29 sites that ...

To demonstrate the Kolmogorov-Smirnov test in PRIMER, we shall return to the dataset consisting of length measurements (in mm) of the Sydney rock oyster (Saccostrea commercialis) settling on four different types of surfaces in intertidal estuarine environments...