Application of-different-statistical-tests-in-fisheries-science

Application of different statistical tests in
fisheries science
Statistical test:
A statistical test provides a mechanism for making
quantitative decisions about a process or processes. The
intent is to determine whether there is enough evidence
to "reject" a conjecture or hypothesis about the process.
Hypothesis testing:
A statistical hypothesis, sometimes called confirmatory
data analysis, is a hypothesis that is testable on the basis
of observing a process that is modeled via a set
of random variables.A statistical hypothesis test is a
method of statistical inference. Commonly, two statistical
data sets are compared, or a data set obtained by
sampling is compared against a synthetic data set from
an idealized model. A hypothesis is proposed for the
statistical relationship between the two data sets, and
this is compared as an alternative to an idealized null
hypothesis that proposes no relationship between two
data sets. The comparison is deemed statistically
significant if the relationship between the data sets would
be an unlikely realization of the null hypothesis according
to a threshold probability—the significance level.

Hypothesis tests are used in determining what outcomes
of a study would lead to a rejection of the null hypothesis
for a pre-specified level of significance
Types of statistical test in fisheries:
There is a wide range of statistical tests. The decision of
which statistical test to use depends on the research
design, the distribution of the data, and the type of
variable. In general, if the data is normally distributed,
you will choose from parametric tests. If the data is non-
normal, you will choose from the set of non-parametric
tests. Below is a table listing just a few common
statistical tests and their use
Type of Test Use
Correlational These tests look for an association between variables
Pearson
correlation
Tests for the strength of the association between two continuous
variables
Spearman
correlation
Tests for the strength of the association between two ordinal variables
(does not rely on the assumption of normally distributed data)
Chi-square
Tests for the strength of the association between two categorical
variables
Comparison of Means: look for the difference between the means of variables
Paired T-test Tests for the difference between two related variables
Independent T-
test
Tests for the difference between two independent variables
ANOVA
Tests the difference between group means after any other variance in
the outcome variable is accounted for
Regression: assess if change in one variable predicts change in another variable
Simple regression
Tests how change in the predictor variable predicts the level of change
in the outcome variable
Multiple
regression
Tests how change in the combination of two or more predictor
variables predict the level of change in the outcome variable
Non-parametric: used when the data does not meet assumptions required for parametric

tests
Wilcoxon rank-
sum test
Tests for the difference between two independent variables—takes into
account magnitude and direction of difference
Wilcoxon sign-
rank test
Tests for the difference between two related variables—takes into
account the magnitude and direction of difference
Sign test
Tests if two related variables are different—ignores the magnitude of
change, only takes into account direction
Types of statistical hypothesis test:
There are mainly two types of hypothesis.
1.Null Hypothesis
2.Alternative Hypothesis
Null Hypothesis:
In inferential statistics, the term "null hypothesis" is a
general statement or default position that there is no
relationship between two measured phenomena, or no
association among groups. Rejecting or disproving the
null hypothesis—and thus concluding that there are
grounds for believing that there is a relationship between
two phenomena (e.g. that a potential treatment has a
measurable effect)—is a central task in the modern
practice of science; the field of statistics gives precise
criteria for rejecting a null hypothesis.

Alternative Hypothesis:
The alternative hypothesis is the hypothesis used
in hypothesis testing that is contrary to the
null hypothesis. It is usually taken to be that the
observations are the result of a real effect (with some
amount of chance variation superposed).
Independent t-test
Dependent variable: Continuous Independent variable:
Binary (Group) Use: A t-test is used to compare the
means of two independent groups. Independent groups
means that different people are in each group. Plot: Box-
plots (exploratory)or Confidence Interval plots with
results

Paired t-test Dependent variable: Continuous (at least
interval) Independent variable: Time point 1 or 2/
condition Use: A paired samples t-test can only be used
when the data is paired or matched. Either there are
before/after measurements of the same variable or the t-
test can be used to compare how a group of subjects
perform under two different test conditions. The test
assesses whether the mean of the paired differences is
zero. Plot: Histogram of differences
P-test
The p-test statistic typically follows a standard normal
distribution when large sample sizes are used, and
researchers use Z-tests to determine whether a
hypothesis passes based on a specific significance level
will be rejected. The larger the p-value in the p-test, the
more likely the hypothesis is true. The p-value is used in
the context of null hypothesis testing in order to quantify
the idea of statistical significance of evidence. Null
hypothesis testing is a reductio ad absurdum argument
adapted to statistics. In essence, a claim is shown to be
valid by demonstrating the improbability of the
consequence that results from assuming the counter-
claim to be true.
As such, the only hypothesis that needs to be specified in
this test and which embodies the counter-claim is
referred to as the null hypothesis (that is, the hypothesis
to be nullified). A result is said to be statistically
significant if it allows us to reject the null hypothesis.

That is, as per the reductio ad absurdum reasoning, the
statistically significant result should be highly improbable
if the null hypothesis is assumed to be true. The rejection
of the null hypothesis implies that the correct hypothesis
lies in the logical complement of the null hypothesis.
However, unless there is a single alternative to the null
hypothesis, the rejection of null hypothesis does not tell
us which of the alternatives might be the correct one.
F test:
An F-test is any statistical test in which the test
statistic has an F-distribution under the null hypothesis.
It is most often used when comparing statistical
models that have been fitted to a data set, in order to
identify the model that best fits the population from
which the data were sampled.
Analysis of variance(ANOVA)
Biologist and statistician Ronald Fisher developed the
ANOVA models
Analysis of variance (ANOVA) is a collection of statistical
models used to analyze the differences among group
means and their associated procedures (such as
"variation" among and between groups), developed by
statistician and evolutionary biologist Ronald Fisher. In

the ANOVA setting, the observed variance in a particular
variable is partitioned into components attributable to
different sources of variation. In its simplest form,
ANOVA provides a statistical test of whether or not the
means of several groups are equal, and therefore
generalizes the t-test to more than two groups. ANOVAs
are useful for comparing (testing) three or more means
(groups or variables) for statistical significance. It is
conceptually similar to multiple two-sample t-tests, but is
more conservative (results in less type I error) and is
therefore suited to a wide range of practical problems.
One-way ANOVA
What is this test for:
The one-way analysis of variance (ANOVA) is used to
determine whether there are any statistically significant
differences between the means of three or more
independent (unrelated) groups. This guide will provide a
brief introduction to the one-way ANOVA, including the
assumptions of the test and when you should use this
test.
What does this test do:
The one-way ANOVA compares the means between the
groups you are interested in and determines whether any
of those means are statistically significantly different
from each other. Specifically, it tests the null hypothesis:

where µ = group mean and k = number of groups. If,
however, the one-way ANOVA returns a statistically
significant result, we accept the alternative hypothesis
(HA), which is that there are at least two group means
that are statistically significantly different from each
other.At this point, it is important to realize that the one-
way ANOVA is an omnibus test statistic and cannot tell
you which specific groups were statistically significantly
different from each other, only that at least two groups
were. To determine which specific groups differed from
each other, you need to use a post hoc test. Post hoc
tests are described later in this guide.
Two-way ANOVA:
The two-way ANOVA compares the mean differences
between groups that have been split on two independent
variables (called factors). The primary purpose of a two-
way ANOVA is to understand if there is an interaction
between the two independent variables on the dependent
variable.
Three-way ANOVA
The three-way ANOVA is used to determine if there is an
interaction effect between three independent variables on
a continuous dependent variable (i.e., if a three-way
interaction exists). As such, it extends the two-way
ANOVA, which is used to determine if such an interaction
exists between just two independent variables (i.e.,
rather than three independent variables).

Regression testing :
Regression testing is a type of software testing which
verifies that software which was previously developed
and tested still performs the same way after it was
changed or interfaced with other software. Changes may
include software enhancements, patches,
configuration changes, etc. During regression testing,
new software bugs or regressions may be uncovered.
Sometimes a software change impact analysis is
performed to determine what areas could be affected by
the proposed changes. These areas may
include functional and non-functional areas of the
system.The purpose of regression testing is to ensure
that changes such as those mentioned above have not
introduced new faults. One of the main reasons for
regression testing is to determine whether a change in
one part of the software affects other parts of the
software. Common methods of regression testing include
re-running previously completed tests and checking
whether program behavior has changed and whether
previously fixed faults have re-emerged. Regression
testing can be performed to test a system efficiently by
systematically selecting the appropriate minimum set of
tests needed to adequately cover a particular change.In
contrast, non-regression testing aims to verify whether,
after introducing or updating a given software
application, the change has had the intended effect.
Correlation test:
The correlation is one of the most common and most
useful statistics. A correlation is a single number that
describes the degree of relationship between two

variables. In statistics, dependence or association is any
statistical relationship, whether causal or not, between
two random variables or bivariate data. Correlation is any
of a broad class of statistical relationships involving
dependence, though in common usage it most often
refers to the extent to which two variables have a linear
relationship with each other. Familiar examples of
dependent phenomena include the correlation between
the physical statures of parents and their offspring, and
the correlation between the demand for a product and its
price.Correlations are useful because they can indicate a
predictive relationship that can be exploited in practice.
Correlation Coefficient formula:

Importance of statistical test and data in
fisheries:
Greater Use of Fishery-Dependent Data:
NMFS and the councils should invest in finding ways to
improve data from commercial and recreational fisheries
to make these data more useful in stock assessments,
rather than establishing new fishery-independent
surveys. Existing surveys should be made more cost-
effective by incorporating new technologies and
management methods.
Accuracy of test to Survey Data:
Frequency and Spatial Extend of Surveys.An examination
of the costs and benefits of data collection should include
the frequency and timing of surveys in each region, with
consideration of factors such as the biology of the
managed species, state of the stocks, the current and
potential economic value of the species, and the
availability of other accurate indices of trend.The range of
a stock can be monitored through spatial distribution of
abundance indices in the surveys and the locations of

commercial or recreational catches. Using fishery activity
to detect changes in a species range may not be effective
however, if management is changed in such a way that
fishing time or place are restricted (e.g., trip limits for
summer flounder reduce fishing activities far from
port).Different statistical test is needed to run a survey.
Statistical test to predict something :
Production of fish can be predicted by statistical test.By
which we can get clear concept about production.
Data from Commercial Fisheries:
If confounding influences can be accounted for, fishery
dependent data can provide an important source of
information regarding trends in fish populations and,
more generally, trends in the fishery. Many different
motivations influence the time, place, and gear employed
by fishermen. These motivations may be unrelated to the
condition of the fish stock, but nonetheless will affect the
use of fishing effort and catch for stock assessment.
Consequently, research is needed to understand the
motivations of harvesters to enable accurate
interpretation of the fishery-dependent data, including
the determinants of catch in commercial, recreational,
and subsistence fisheries.

Conclusion:
Statistics is the science of collecting, analyzing and
making inference from data. Statistical methods and
analyses are often used to run fisheries research findings
and to support hypotheses and give credibility
to research methodology and conclusions. Biostatistics is
the application of statistics to a wide range of topics
in fisheries biology. The science of biostatistics
encompasses the design of biological experiments of
fishery; the collection, summarization, and analysis of
data from those experiments; and the interpretation of,
and inference from, the results.so statistical application
and test are inextricably involved in fisheries science.
Reference:
http://sfrc.ufl.edu/syllabi/FAS5335c-FAS4932.pdf
http://www.mn.uio.no/cees/english/research/news/events/isec20
12/programme/fisheries/fisheries.html
https://en.wikipedia.org/wiki/Statistical_hypothesis_testing
http://support.minitab.com/en-us/minitab/17/topic-library/basic-
statistics-and-graphs/hypothesis-tests/basics/what-is-a-
hypothesis-test/
https://en.wikipedia.org/wiki/Null_hypothesis
http://www.investopedia.com/terms/p/p-test.asp
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