Multinomial test

Nonparametric statistics | Statistical tests | Categorical variable interactions

In statistics, the multinomial test is the test of the null hypothesis that the parameters of a multinomial distribution equal specified values; it is used for categorical data. Beginning with a sample of items each of which has been observed to fall into one of categories. It is possible to define as the observed numbers of items in each cell. Hence Next, defining a vector of parameters where:These are the parameter values under the null hypothesis. The exact probability of the observed configuration under the null hypothesis is given by The significance probability for the test is the probability of occurrence of the data set observed, or of a data set less likely than that observed, if the null hypothesis is true. Using an exact test, this is calculated as where the sum ranges over all outcomes as likely as, or less likely than, that observed. In practice this becomes computationally onerous as and increase so it is probably only worth using exact tests for small samples. For larger samples, asymptotic approximations are accurate enough and easier to calculate. One of these approximations is the likelihood ratio. An alternative hypothesis can be defined under which each value is replaced by its maximum likelihood estimate The exact probability of the observed configuration under the alternative hypothesis is given by The natural logarithm of the likelihood ratio, between these two probabilities, multiplied by is then the statistic for the likelihood ratio test (The factor is chosen to make the statistic asymptotically chi-squared distributed, for convenient comparison to a familiar statistic commonly used for the same application.) If the null hypothesis is true, then as increases, the distribution of converges to that of chi-squared with degrees of freedom. However it has long been known (e.g. Lawley) that for finite sample sizes, the moments of are greater than those of chi-squared, thus inflating the probability of type I errors (false positives). The difference between the moments of chi-squared and those of the test statistic are a function of Williams showed that the first moment can be matched as far as if the test statistic is divided by a factor given by In the special case where the null hypothesis is that all the values are equal to (i.e. it stipulates a uniform distribution), this simplifies to Subsequently, Smith et al. derived a dividing factor which matches the first moment as far as For the case of equal values of this factor is The null hypothesis can also be tested by using Pearson's chi-squared test where is the expected number of cases in category under the null hypothesis. This statistic also converges to a chi-squared distribution with degrees of freedom when the null hypothesis is true but does so from below, as it were, rather than from above as does, so may be preferable to the uncorrected version of for small samples. (Wikipedia).

What is Multivariate Testing? | Data Science in Minutes

In this tutorial, we will explain: how a multivariate test differs from an A/B Test, how to create and conduct a multivariate test, and what questions you should be asking of your test. Multivariate testing is a technique for testing a hypothesis in which multiple variables are modified.

From playlist Data Science in Minutes

Parametric and nonparametric tests

Parametric tests are most commonly used in healthcare research. They include tests such as Student's t-test and ANOVA. There is, however a rich set of non-parametric tests that are much more appropriate to use in certain circumstances.

From playlist Learning medical statistics with python and Jupyter notebooks

Multimeter Review / DMM Review / buyers guide / tutorial

A list of my multimeters can be purchased here: http://astore.amazon.com/m0711-20?_encoding=UTF8&node=5 In this video I do a review of several digital multimeters. I compare features and functionality. I explain safety features, number of digits, display count, accuracy and resolution. Th

From playlist Multimeter reviews, buyers guide and comparisons.

Solving a multi-step equation by multiplying by the denominator

👉 Learn how to solve multi-step equations with variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-s

From playlist How to Solve Multi Step Equations with Variables on Both Sides

Solve an equation for x by clearing fractions with multiple steps

From playlist How to Solve Multi Step Equations with Variables on Both Sides

Solving a multi-step equation with fractions and variable on both sides

From playlist How to Solve Multi Step Equations with Variables on Both Sides

How to do a One-Way Chi-Square Using a Multinomial Test in JASP (15-9)

We learn how to calculate a One-Way Chi-Square in JASP using the setting for Multinomial Test. For the null hypothesis, we assume that the observed values do not differ from randomness or that there is no preference among the three types of materials: Straw, Sticks, or Brick and mortar. We

From playlist Discovering Statistics with JASP

3_5_1 The Integral Test and Comparison Tests

The integral test for convergence of a series.

From playlist Advanced Calculus / Multivariable Calculus

The Multinomial Distribution : Data Science Basics

How the Bernoulli and Binomial distributions are part of something bigger. My Patreon : https://www.patreon.com/user?u=49277905 Icon Resources : Fish icons created by Freepik - Flaticon https://www.flaticon.com/free-icons/fish Sea life icons created by smalllikeart - Flaticon https://w

From playlist Probability Distributions

How to solve a multi step equation with fractions

From playlist How to Solve Multi Step Equations with Variables on Both Sides

Introduction to Probability and Statistics 131B. Lecture 14.

UCI Math 131B: Introduction to Probability and Statistics (Summer 2013) Lec 14. Introduction to Probability and Statistics View the complete course: http://ocw.uci.edu/courses/math_131b_introduction_to_probability_and_statistics.html Instructor: Michael C. Cranston, Ph.D. License: Creativ

From playlist Introduction to Probability and Statistics 131B

How to do a One-Way Goodness of Fit Chi-Square in JASP (15-10)

We learn how to calculate a One-Way Chi-Square goodness of fit test in JASP using the setting for Multinomial Test. For the null hypothesis, we assume that the observed values in one group (the Pigs) do not differ from the values in a comparison population (the Bears) or that there is no d

From playlist Discovering Statistics with JASP

David Knowles: "Probabilistic programming for genomics"

Computational Genomics Winter Institute 2018 "Probabilistic programming for genomics" David Knowles, Stanford University Institute for Pure and Applied Mathematics, UCLA February 27, 2018 For more information: http://computationalgenomics.bioinformatics.ucla.edu/programs/2018-cgwi/

From playlist Computational Genomics Winter Institute 2018

Scikit-Learn incorporation - Natural Language Processing With Python and NLTK p.15

Despite coming packed with some classifiers, NLTK is mainly a toolkit focused on natural language processing, and not machine learning specifically. A module that is focused on machine learning is scikit-learn, which is packed with a large array of machine learning algorithms which are o

From playlist NLTK with Python 3 for Natural Language Processing

Comparison Test (silent)

A silent video testing series for convergence or divergence using the comparison test

From playlist 242 spring 2012 exam 3

R - Multinomial Log Regression Example

Lecturer: Dr. Erin M. Buchanan Missouri State University Spring 2016 This video covers how to run and interpret a multinomial logistic regression using mlogit - from assessing ratio of cases, additivity, to understanding the reshaping of data and interpreting the output. Note: This vid

From playlist Learn and Use G*Power

Stanford Webinar - How to Analyze Research Data: Kristin Sainani

In this webinar, Associate Professor Kristin Sainani walks you through the steps of a complete data analysis, using real data on mental health in athletes. She provides practical, hands-on tips for how to approach each step of the analysis and how to improve rigor and reproducibility of yo

From playlist Statistics and Data Science

Text Classification Using Naive Bayes | Naive Bayes Algorithm In Machine Learning | Simplilearn

This video on "Text Classification Using Naive Bayes" is a brilliant introductory walk through to the Classification of Text using Naive Bayes Algorithm. 🔥Free Machine Learning Course: https://www.simplilearn.com/learn-machine-learning-basics-skillup?utm_campaign=TextClassificationNaiveBay

From playlist 🔥Machine Learning | Machine Learning Tutorial For Beginners | Machine Learning Projects | Simplilearn | Updated Machine Learning Playlist 2023

R - Multinomial Logisitic Regression Example

Lecturer: Dr. Erin M. Buchanan Missouri State University Spring 2018 This video replaces a previous live in-class video. You will learn about how to analyze a multinomial logistic regression. We start by exploring power using G*Power, then the simple data screening required for log regre

From playlist Learn and Use G*Power

Multimeter Calibration - Some future testing..

A list of my multimeters can be purchased here: http://astore.amazon.com/m0711-20?_encoding=UTF8&node=5 The calibration of my Major Tech MT22 raised some interesting responses so we'll take this topic a little further. I have ordered a DMMCheck and PentaRef from Voltagestandard.com.

From playlist Multimeter reviews, buyers guide and comparisons.

Multinomial test

Related pages