The chi-square test is used to determine if an observed distribution of data differs from the theoretical distribution. It compares observed frequencies to expected frequencies based on a hypothesis. The chi-square value is calculated by summing the squared differences between observed and expected frequencies divided by the expected frequency. The chi-square value is then compared to a critical value from the chi-square distribution table based on the degrees of freedom. If the chi-square value is greater than the critical value, the null hypothesis that the distributions are the same can be rejected.
The document discusses goodness-of-fit tests for categorical data. It introduces notation for categorical variables with multiple categories and hypotheses for goodness-of-fit tests. Expected counts are calculated based on hypothesized proportions. The chi-square statistic is used to calculate test statistics and P-values are found using the chi-square distribution. Examples demonstrate applying goodness-of-fit tests to determine if variable categories occur with equal frequency.
The document discusses the chi-square test, which offers an alternative method for testing the significance of differences between two proportions. It was developed by Karl Pearson and follows a specific chi-square distribution. To calculate chi-square, contingency tables are made noting observed and expected frequencies, and the chi-square value is calculated using the formula. Degrees of freedom are also calculated. Chi-square test is commonly used to test proportions, associations between events, and goodness of fit to a theory. However, it has limitations when expected values are less than 5 and does not measure strength of association or indicate causation.
- A sample is a small group selected from a population to represent that population. Sampling provides benefits like being less time-consuming, less expensive, and allowing results to be repeated.
- There are two main types of samples: probability and non-probability. Probability samples include simple random, systematic, stratified, and cluster samples. Sample size is determined based on factors like the type of study, expected results, costs, and available resources.
- Inferential statistics allow generalization from a sample to a population through hypothesis testing and significance tests. Tests include t-tests, F-tests, chi-squared tests, and correlation/regression to analyze relationships between variables. Significant results suggest differences are likely not due to chance
1) The chi-square test is a statistical test commonly used to compare observed data with data we would expect to obtain according to a specific hypothesis.
2) It allows evaluation of whether an observed distribution of data differs from an expected theoretical distribution in a statistically significant way.
3) The chi-square test calculates a chi-square statistic and assesses its significance using the chi-square distribution, with degrees of freedom equal to the number of independent variables - 1.
This document explains how to conduct a chi-square test for independence to determine if there is a significant association between two categorical variables. The test involves stating the null and alternative hypotheses, formulating an analysis plan specifying the significance level and test method, analyzing sample data to calculate degrees of freedom, expected frequencies, the test statistic, and p-value, then interpreting the results by comparing the p-value to the significance level. An example considers using this test to see if gender is related to voting preference in an election survey.
The chi-square test is used to compare observed data with expected data. It was developed by Karl Pearson in 1900. The chi-square test calculates the sum of the squares of the differences between the observed and expected frequencies divided by the expected frequency. The chi-square value is then compared to a critical value to determine if there is a significant difference between the observed and expected results. The degrees of freedom, which determine the critical value, are calculated based on the number of rows and columns in a contingency table. The chi-square test can be used to test goodness of fit, independence of attributes, and other hypotheses.
Chi square test social research refer.pptSnehamurali18
This document discusses various statistical tests, including parametric tests that require normally distributed data like t-tests and ANOVA, non-parametric tests that don't require normality like the Mann-Whitney U test, and the chi-square test. It explains that chi-square is used to determine if there is a relationship between two categorical variables by comparing observed and expected frequencies in a contingency table. It provides steps for conducting a chi-square test including stating hypotheses, calculating expected values, determining degrees of freedom, finding the test statistic, and interpreting results. Two examples of applying chi-square to test associations between disease prevalence and other factors are also presented.
The chi-square test is used to determine if an observed distribution of data differs from the theoretical distribution. It compares observed frequencies to expected frequencies based on a hypothesis. The chi-square value is calculated by summing the squared differences between observed and expected frequencies divided by the expected frequency. The chi-square value is then compared to a critical value from the chi-square distribution table based on the degrees of freedom. If the chi-square value is greater than the critical value, the null hypothesis that the distributions are the same can be rejected.
The document discusses goodness-of-fit tests for categorical data. It introduces notation for categorical variables with multiple categories and hypotheses for goodness-of-fit tests. Expected counts are calculated based on hypothesized proportions. The chi-square statistic is used to calculate test statistics and P-values are found using the chi-square distribution. Examples demonstrate applying goodness-of-fit tests to determine if variable categories occur with equal frequency.
The document discusses the chi-square test, which offers an alternative method for testing the significance of differences between two proportions. It was developed by Karl Pearson and follows a specific chi-square distribution. To calculate chi-square, contingency tables are made noting observed and expected frequencies, and the chi-square value is calculated using the formula. Degrees of freedom are also calculated. Chi-square test is commonly used to test proportions, associations between events, and goodness of fit to a theory. However, it has limitations when expected values are less than 5 and does not measure strength of association or indicate causation.
- A sample is a small group selected from a population to represent that population. Sampling provides benefits like being less time-consuming, less expensive, and allowing results to be repeated.
- There are two main types of samples: probability and non-probability. Probability samples include simple random, systematic, stratified, and cluster samples. Sample size is determined based on factors like the type of study, expected results, costs, and available resources.
- Inferential statistics allow generalization from a sample to a population through hypothesis testing and significance tests. Tests include t-tests, F-tests, chi-squared tests, and correlation/regression to analyze relationships between variables. Significant results suggest differences are likely not due to chance
1) The chi-square test is a statistical test commonly used to compare observed data with data we would expect to obtain according to a specific hypothesis.
2) It allows evaluation of whether an observed distribution of data differs from an expected theoretical distribution in a statistically significant way.
3) The chi-square test calculates a chi-square statistic and assesses its significance using the chi-square distribution, with degrees of freedom equal to the number of independent variables - 1.
This document explains how to conduct a chi-square test for independence to determine if there is a significant association between two categorical variables. The test involves stating the null and alternative hypotheses, formulating an analysis plan specifying the significance level and test method, analyzing sample data to calculate degrees of freedom, expected frequencies, the test statistic, and p-value, then interpreting the results by comparing the p-value to the significance level. An example considers using this test to see if gender is related to voting preference in an election survey.
The chi-square test is used to compare observed data with expected data. It was developed by Karl Pearson in 1900. The chi-square test calculates the sum of the squares of the differences between the observed and expected frequencies divided by the expected frequency. The chi-square value is then compared to a critical value to determine if there is a significant difference between the observed and expected results. The degrees of freedom, which determine the critical value, are calculated based on the number of rows and columns in a contingency table. The chi-square test can be used to test goodness of fit, independence of attributes, and other hypotheses.
Chi square test social research refer.pptSnehamurali18
This document discusses various statistical tests, including parametric tests that require normally distributed data like t-tests and ANOVA, non-parametric tests that don't require normality like the Mann-Whitney U test, and the chi-square test. It explains that chi-square is used to determine if there is a relationship between two categorical variables by comparing observed and expected frequencies in a contingency table. It provides steps for conducting a chi-square test including stating hypotheses, calculating expected values, determining degrees of freedom, finding the test statistic, and interpreting results. Two examples of applying chi-square to test associations between disease prevalence and other factors are also presented.
Marketing Research Hypothesis Testing.pptxxababid981
This document provides an overview of parametric and non-parametric hypothesis tests. It defines parametric tests as those that assume an underlying normal distribution, and lists common parametric tests like the z-test, t-test, F-test, and ANOVA. Non-parametric tests make no distributional assumptions and common examples discussed include the Mann-Whitney U test, chi-square test, and Kruskal-Wallis test. The document provides details on assumptions and procedures for conducting each of these important statistical hypothesis tests.
The chi-square test is used to determine if an observed distribution of data differs from the distribution expected if the null hypothesis is true. It compares observed frequencies to expected frequencies based on a theoretical distribution. The chi-square value is calculated by summing the squared differences between observed and expected frequencies divided by the expected frequencies. The calculated value is then compared to critical values from a chi-square distribution table to determine if the null hypothesis can be rejected.
This document provides information on chi-square tests and other statistical tests for qualitative data analysis. It discusses the chi-square test for goodness of fit and independence. It also covers Fisher's exact test and McNemar's test. Examples are provided to illustrate chi-square calculations and how to determine statistical significance based on degrees of freedom and critical values. Assumptions and criteria for applying different tests are outlined.
This document provides an overview of parametric and non-parametric statistical tests. Parametric tests assume the data follows a known distribution (e.g. normal) while non-parametric tests make no assumptions. Common non-parametric tests covered include chi-square, sign, Mann-Whitney U, and Spearman's rank correlation. The chi-square test is described in more detail, including how to calculate chi-square values, degrees of freedom, and testing for independence and goodness of fit.
Application of Statistical and mathematical equations in Chemistry Part 2Awad Albalwi
Application of Statistical and mathematical equations in Chemistry
Part 2
Accuracy
Precision
Propagation of Error
Confidence Limits
F-Test Values
Student’s t-test
Paired Sample t-test
Q test
Least Squares Method
correlation coefficient
The Chi-Square test of independence is used to determine if two categorical variables are independent or dependent. It examines if understanding one variable depends on the other. The test calculates an observed versus expected frequency for each cell. If the Chi-Square value exceeds the critical value, the null hypothesis of independence is rejected, indicating a dependent relationship. The document provides an example comparing education level and news source, finding the variables are dependent based on a significant Chi-Square value.
The document discusses the Chi-square (χ2) test, which is a non-parametric test used to test hypotheses about distributions of frequencies across categories of data. It can be used to test for comparing variance and to test for independence between two variables. The summary provides steps for applying the Chi-square test, including calculating expected frequencies, observed vs expected values, the Chi-square statistic, and comparing it to critical values. An example application to test the effectiveness of vaccination in preventing smallpox is shown.
The document discusses various statistical tests for analyzing relationships between variables, including tests for statistical independence, chi-square tests, and analysis of variance (ANOVA). It explains that statistical independence is when the probability of two variables occurring together equals the product of their individual probabilities. Chi-square tests compare observed and expected frequencies to test if variables are independent. ANOVA decomposes variance and can test if population means are equal. It distinguishes explained from unexplained variance.
Data categories are groupings of data with common characteristics or features. They are useful for managing the data because certain data may be treated differently based on their classification. Understanding the relationship and dependency between the different categories can help direct data quality effort
Week 5 Lecture 14 The Chi Square TestQuite often, patterns of .docxcockekeshia
Week 5 Lecture 14
The Chi Square Test
Quite often, patterns of responses or measures give us a lot of information. Patterns are generally the result of counting how many things fit into a particular category. Whenever we make a histogram, bar, or pie chart we are looking at the pattern of the data. Frequently, changes in these visual patterns will be our first clues that things have changed, and the first clue that we need to initiate a research study (Lind, Marchel, & Wathen, 2008).
One of the most useful test in examining patterns and relationships in data involving counts (how many fit into this category, how many into that, etc.) is the chi-square. It is extremely easy to calculate and has many more uses than we will cover. Examining patterns involves two uses of the Chi-square - the goodness of fit and the contingency table. Both of these uses have a common trait: they involve counts per group. In fact, the chi-square is the only statistic we will look at that we use when we have counts per multiple groups (Tanner & Youssef-Morgan, 2013). Chi Square Goodness of Fit Test
The goodness of fit test checks to see if the data distribution (counts per group) matches some pattern we are interested in. Example: Are the employees in our example company distributed equal across the grades? Or, a more reasonable expectation for a company might be are the employees distributed in a pyramid fashion – most on the bottom and few at the top?
The Chi Square test compares the actual versus a proposed distribution of counts by generating a measure for each cell or count: (actual – expected)2/actual. Summing these for all of the cells or groups provides us with the Chi Square Statistic. As with our other tests, we determine the p-value of getting a result as large or larger to determine if we reject or not reject our null hypothesis. An example will show the approach using Excel.
Regardless of the Chi Square test, the chi square related functions are found in the fx Statistics window rather than the Data Analysis where we found the t and ANOVA test functions. The most important for us are:
· CHISQ.TEST (actual range, expected range) – returns the p-value for the test
· CHISQ.INV.RT(p-value, df) – returns the actual Chi Square value for the p-value or probability value used.
· CHISQ.DIST.RT(X, df) – returns the p-value for a given value.
When we have a table of actual and expected results, using the =CHISQ.TEST(actual range, expected range) will provide us with the p-value of the calculated chi square value (but does not give us the actual calculated chi square value for the test). We can compare this value against our alpha criteria (generally 0.05) to make our decision about rejecting or not rejecting the null hypothesis.
If, after finding the p-value for our chi square test, we want to determine the calculated value of the chi square statistic, we can use the =CHISQ.INV.RT(probability, df) function, the value for probability is .
This document describes how to conduct a chi-square goodness of fit test. The test involves:
1) Stating the null and alternative hypotheses. The null hypothesis specifies the expected probabilities, while the alternative is that at least one expected probability is incorrect.
2) Developing an analysis plan specifying the significance level and test to be used.
3) Analyzing sample data to calculate degrees of freedom, expected frequencies, the test statistic, and p-value.
4) Interpreting the results by comparing the p-value to the significance level and rejecting or failing to reject the null hypothesis. An example problem demonstrates applying the test to determine if observed outcomes match a casino's claimed probabilities.
For more classes visit
www.snaptutorial.com
1
To make tests of hypotheses about more than two population means, we use the:
t distribution
normal distribution
chi-square distribution
analysis of variance distribution
This document provides information about goodness-of-fit tests and chi-square tests of independence. It discusses how goodness-of-fit tests can determine if a sample frequency distribution fits a predicted population distribution. It also explains how chi-square tests of independence analyze contingency tables to see if two categorical variables are associated or independent. The document outlines how to calculate expected frequencies, test statistics, degrees of freedom, and p-values for these tests. It provides an example of analyzing a 2x2 contingency table to test the independence of personality type and recreational activity preference.
Chi square test- a test of association, Pearson's chi square test of independence, Goodness of fit test, chi square test of homogeneity, advantages and disadvantages of chi square test.
The document discusses hypothesis testing and statistical analysis techniques. It covers univariate, bivariate, and multivariate statistical analysis, which involve one, two, or three or more variables, respectively. The key steps of hypothesis testing are outlined, including deriving a null hypothesis from the research objectives, obtaining and measuring a sample, comparing the sample value to the hypothesis, and determining whether to support or not support the hypothesis based on consistency. Type I and Type II errors in hypothesis testing are defined. Common statistical tests like chi-square, t-tests, ANOVA, and correlation are introduced along with concepts like significance levels, p-values, and degrees of freedom.
A chi-squared test (χ2) is basically a data analysis on the basis of observations of a random set of variables. Usually, it is a comparison of two statistical data sets. This test was introduced by Karl Pearson in 1900 for categorical data analysis and distribution. So, it was mentioned as Pearson’s chi-squared test.
Describing and Interpreting an Immersive Learning Case with the Immersion Cub...Leonel Morgado
Current descriptions of immersive learning cases are often difficult or impossible to compare. This is due to a myriad of different options on what details to include, which aspects are relevant, and on the descriptive approaches employed. Also, these aspects often combine very specific details with more general guidelines or indicate intents and rationales without clarifying their implementation. In this paper we provide a method to describe immersive learning cases that is structured to enable comparisons, yet flexible enough to allow researchers and practitioners to decide which aspects to include. This method leverages a taxonomy that classifies educational aspects at three levels (uses, practices, and strategies) and then utilizes two frameworks, the Immersive Learning Brain and the Immersion Cube, to enable a structured description and interpretation of immersive learning cases. The method is then demonstrated on a published immersive learning case on training for wind turbine maintenance using virtual reality. Applying the method results in a structured artifact, the Immersive Learning Case Sheet, that tags the case with its proximal uses, practices, and strategies, and refines the free text case description to ensure that matching details are included. This contribution is thus a case description method in support of future comparative research of immersive learning cases. We then discuss how the resulting description and interpretation can be leveraged to change immersion learning cases, by enriching them (considering low-effort changes or additions) or innovating (exploring more challenging avenues of transformation). The method holds significant promise to support better-grounded research in immersive learning.
Marketing Research Hypothesis Testing.pptxxababid981
This document provides an overview of parametric and non-parametric hypothesis tests. It defines parametric tests as those that assume an underlying normal distribution, and lists common parametric tests like the z-test, t-test, F-test, and ANOVA. Non-parametric tests make no distributional assumptions and common examples discussed include the Mann-Whitney U test, chi-square test, and Kruskal-Wallis test. The document provides details on assumptions and procedures for conducting each of these important statistical hypothesis tests.
The chi-square test is used to determine if an observed distribution of data differs from the distribution expected if the null hypothesis is true. It compares observed frequencies to expected frequencies based on a theoretical distribution. The chi-square value is calculated by summing the squared differences between observed and expected frequencies divided by the expected frequencies. The calculated value is then compared to critical values from a chi-square distribution table to determine if the null hypothesis can be rejected.
This document provides information on chi-square tests and other statistical tests for qualitative data analysis. It discusses the chi-square test for goodness of fit and independence. It also covers Fisher's exact test and McNemar's test. Examples are provided to illustrate chi-square calculations and how to determine statistical significance based on degrees of freedom and critical values. Assumptions and criteria for applying different tests are outlined.
This document provides an overview of parametric and non-parametric statistical tests. Parametric tests assume the data follows a known distribution (e.g. normal) while non-parametric tests make no assumptions. Common non-parametric tests covered include chi-square, sign, Mann-Whitney U, and Spearman's rank correlation. The chi-square test is described in more detail, including how to calculate chi-square values, degrees of freedom, and testing for independence and goodness of fit.
Application of Statistical and mathematical equations in Chemistry Part 2Awad Albalwi
Application of Statistical and mathematical equations in Chemistry
Part 2
Accuracy
Precision
Propagation of Error
Confidence Limits
F-Test Values
Student’s t-test
Paired Sample t-test
Q test
Least Squares Method
correlation coefficient
The Chi-Square test of independence is used to determine if two categorical variables are independent or dependent. It examines if understanding one variable depends on the other. The test calculates an observed versus expected frequency for each cell. If the Chi-Square value exceeds the critical value, the null hypothesis of independence is rejected, indicating a dependent relationship. The document provides an example comparing education level and news source, finding the variables are dependent based on a significant Chi-Square value.
The document discusses the Chi-square (χ2) test, which is a non-parametric test used to test hypotheses about distributions of frequencies across categories of data. It can be used to test for comparing variance and to test for independence between two variables. The summary provides steps for applying the Chi-square test, including calculating expected frequencies, observed vs expected values, the Chi-square statistic, and comparing it to critical values. An example application to test the effectiveness of vaccination in preventing smallpox is shown.
The document discusses various statistical tests for analyzing relationships between variables, including tests for statistical independence, chi-square tests, and analysis of variance (ANOVA). It explains that statistical independence is when the probability of two variables occurring together equals the product of their individual probabilities. Chi-square tests compare observed and expected frequencies to test if variables are independent. ANOVA decomposes variance and can test if population means are equal. It distinguishes explained from unexplained variance.
Data categories are groupings of data with common characteristics or features. They are useful for managing the data because certain data may be treated differently based on their classification. Understanding the relationship and dependency between the different categories can help direct data quality effort
Week 5 Lecture 14 The Chi Square TestQuite often, patterns of .docxcockekeshia
Week 5 Lecture 14
The Chi Square Test
Quite often, patterns of responses or measures give us a lot of information. Patterns are generally the result of counting how many things fit into a particular category. Whenever we make a histogram, bar, or pie chart we are looking at the pattern of the data. Frequently, changes in these visual patterns will be our first clues that things have changed, and the first clue that we need to initiate a research study (Lind, Marchel, & Wathen, 2008).
One of the most useful test in examining patterns and relationships in data involving counts (how many fit into this category, how many into that, etc.) is the chi-square. It is extremely easy to calculate and has many more uses than we will cover. Examining patterns involves two uses of the Chi-square - the goodness of fit and the contingency table. Both of these uses have a common trait: they involve counts per group. In fact, the chi-square is the only statistic we will look at that we use when we have counts per multiple groups (Tanner & Youssef-Morgan, 2013). Chi Square Goodness of Fit Test
The goodness of fit test checks to see if the data distribution (counts per group) matches some pattern we are interested in. Example: Are the employees in our example company distributed equal across the grades? Or, a more reasonable expectation for a company might be are the employees distributed in a pyramid fashion – most on the bottom and few at the top?
The Chi Square test compares the actual versus a proposed distribution of counts by generating a measure for each cell or count: (actual – expected)2/actual. Summing these for all of the cells or groups provides us with the Chi Square Statistic. As with our other tests, we determine the p-value of getting a result as large or larger to determine if we reject or not reject our null hypothesis. An example will show the approach using Excel.
Regardless of the Chi Square test, the chi square related functions are found in the fx Statistics window rather than the Data Analysis where we found the t and ANOVA test functions. The most important for us are:
· CHISQ.TEST (actual range, expected range) – returns the p-value for the test
· CHISQ.INV.RT(p-value, df) – returns the actual Chi Square value for the p-value or probability value used.
· CHISQ.DIST.RT(X, df) – returns the p-value for a given value.
When we have a table of actual and expected results, using the =CHISQ.TEST(actual range, expected range) will provide us with the p-value of the calculated chi square value (but does not give us the actual calculated chi square value for the test). We can compare this value against our alpha criteria (generally 0.05) to make our decision about rejecting or not rejecting the null hypothesis.
If, after finding the p-value for our chi square test, we want to determine the calculated value of the chi square statistic, we can use the =CHISQ.INV.RT(probability, df) function, the value for probability is .
This document describes how to conduct a chi-square goodness of fit test. The test involves:
1) Stating the null and alternative hypotheses. The null hypothesis specifies the expected probabilities, while the alternative is that at least one expected probability is incorrect.
2) Developing an analysis plan specifying the significance level and test to be used.
3) Analyzing sample data to calculate degrees of freedom, expected frequencies, the test statistic, and p-value.
4) Interpreting the results by comparing the p-value to the significance level and rejecting or failing to reject the null hypothesis. An example problem demonstrates applying the test to determine if observed outcomes match a casino's claimed probabilities.
For more classes visit
www.snaptutorial.com
1
To make tests of hypotheses about more than two population means, we use the:
t distribution
normal distribution
chi-square distribution
analysis of variance distribution
This document provides information about goodness-of-fit tests and chi-square tests of independence. It discusses how goodness-of-fit tests can determine if a sample frequency distribution fits a predicted population distribution. It also explains how chi-square tests of independence analyze contingency tables to see if two categorical variables are associated or independent. The document outlines how to calculate expected frequencies, test statistics, degrees of freedom, and p-values for these tests. It provides an example of analyzing a 2x2 contingency table to test the independence of personality type and recreational activity preference.
Chi square test- a test of association, Pearson's chi square test of independence, Goodness of fit test, chi square test of homogeneity, advantages and disadvantages of chi square test.
The document discusses hypothesis testing and statistical analysis techniques. It covers univariate, bivariate, and multivariate statistical analysis, which involve one, two, or three or more variables, respectively. The key steps of hypothesis testing are outlined, including deriving a null hypothesis from the research objectives, obtaining and measuring a sample, comparing the sample value to the hypothesis, and determining whether to support or not support the hypothesis based on consistency. Type I and Type II errors in hypothesis testing are defined. Common statistical tests like chi-square, t-tests, ANOVA, and correlation are introduced along with concepts like significance levels, p-values, and degrees of freedom.
A chi-squared test (χ2) is basically a data analysis on the basis of observations of a random set of variables. Usually, it is a comparison of two statistical data sets. This test was introduced by Karl Pearson in 1900 for categorical data analysis and distribution. So, it was mentioned as Pearson’s chi-squared test.
Describing and Interpreting an Immersive Learning Case with the Immersion Cub...Leonel Morgado
Current descriptions of immersive learning cases are often difficult or impossible to compare. This is due to a myriad of different options on what details to include, which aspects are relevant, and on the descriptive approaches employed. Also, these aspects often combine very specific details with more general guidelines or indicate intents and rationales without clarifying their implementation. In this paper we provide a method to describe immersive learning cases that is structured to enable comparisons, yet flexible enough to allow researchers and practitioners to decide which aspects to include. This method leverages a taxonomy that classifies educational aspects at three levels (uses, practices, and strategies) and then utilizes two frameworks, the Immersive Learning Brain and the Immersion Cube, to enable a structured description and interpretation of immersive learning cases. The method is then demonstrated on a published immersive learning case on training for wind turbine maintenance using virtual reality. Applying the method results in a structured artifact, the Immersive Learning Case Sheet, that tags the case with its proximal uses, practices, and strategies, and refines the free text case description to ensure that matching details are included. This contribution is thus a case description method in support of future comparative research of immersive learning cases. We then discuss how the resulting description and interpretation can be leveraged to change immersion learning cases, by enriching them (considering low-effort changes or additions) or innovating (exploring more challenging avenues of transformation). The method holds significant promise to support better-grounded research in immersive learning.
The binding of cosmological structures by massless topological defectsSérgio Sacani
Assuming spherical symmetry and weak field, it is shown that if one solves the Poisson equation or the Einstein field
equations sourced by a topological defect, i.e. a singularity of a very specific form, the result is a localized gravitational
field capable of driving flat rotation (i.e. Keplerian circular orbits at a constant speed for all radii) of test masses on a thin
spherical shell without any underlying mass. Moreover, a large-scale structure which exploits this solution by assembling
concentrically a number of such topological defects can establish a flat stellar or galactic rotation curve, and can also deflect
light in the same manner as an equipotential (isothermal) sphere. Thus, the need for dark matter or modified gravity theory is
mitigated, at least in part.
ESR spectroscopy in liquid food and beverages.pptxPRIYANKA PATEL
With increasing population, people need to rely on packaged food stuffs. Packaging of food materials requires the preservation of food. There are various methods for the treatment of food to preserve them and irradiation treatment of food is one of them. It is the most common and the most harmless method for the food preservation as it does not alter the necessary micronutrients of food materials. Although irradiated food doesn’t cause any harm to the human health but still the quality assessment of food is required to provide consumers with necessary information about the food. ESR spectroscopy is the most sophisticated way to investigate the quality of the food and the free radicals induced during the processing of the food. ESR spin trapping technique is useful for the detection of highly unstable radicals in the food. The antioxidant capability of liquid food and beverages in mainly performed by spin trapping technique.
Or: Beyond linear.
Abstract: Equivariant neural networks are neural networks that incorporate symmetries. The nonlinear activation functions in these networks result in interesting nonlinear equivariant maps between simple representations, and motivate the key player of this talk: piecewise linear representation theory.
Disclaimer: No one is perfect, so please mind that there might be mistakes and typos.
dtubbenhauer@gmail.com
Corrected slides: dtubbenhauer.com/talks.html
Current Ms word generated power point presentation covers major details about the micronuclei test. It's significance and assays to conduct it. It is used to detect the micronuclei formation inside the cells of nearly every multicellular organism. It's formation takes place during chromosomal sepration at metaphase.
The cost of acquiring information by natural selectionCarl Bergstrom
This is a short talk that I gave at the Banff International Research Station workshop on Modeling and Theory in Population Biology. The idea is to try to understand how the burden of natural selection relates to the amount of information that selection puts into the genome.
It's based on the first part of this research paper:
The cost of information acquisition by natural selection
Ryan Seamus McGee, Olivia Kosterlitz, Artem Kaznatcheev, Benjamin Kerr, Carl T. Bergstrom
bioRxiv 2022.07.02.498577; doi: https://doi.org/10.1101/2022.07.02.498577
2. Introduction
Definition
Degree of Freedom
The contingency table
Types of test
Goodness of fit test
Null and alternate hypothesis
Characteristics of chi-square test
Application of chi-square test
Determination of chi-square test with example
Conclusion
Reference
3. The Chi-square test is one of the most commonly used non-
parametric test, in which the sampling distribution of the test
statistic is a Chi-square distribution, when the null hypothesis is
true.
Chi-square test is a useful measure of comparing
experimentally obtained result with those expected theoretically
and based on the hypothesis.
It can be applied when there are few or no assumption about
the population parameter.
It can be applied on categorical data or qualitative data using a
contingency table.
4. A Chi-square statistic is a test that measures how
expectations compare to actual observed to actual
observed data.
Null Hypothesis -Observed=Expected
Alternate Hypothesis- Observed is not equal to Expected
It was first of all used by Karl Pearson in the year 1900.
It is denoted by the Greek sign χ2.
5. Following is the formula-
It is a mathematical expression, representing the ration between
experimentally obtained result(O) & the theoretically expected
result(E) based on certain hypothesis. It uses data in the form of
frequencies (i.e., the number of occurrence of an event).
Chi-square is calculated by dividing the square of the overall deviation
in the observed and expected frequencies by the expected frequency.
6. In test, while the comparing the calculated value of with the table
value, we have to calculated the degree of freedom. The degree of
freedom is calculated from the number of classes.
Therefore, the number of degrees of freedom in a test is equal to the
number of classes/categories minus one.
If there are two classes , three classes, & for classes, the degree of
freedom would be 2-1, 3-1, & 4-1, respectively. In a contingency table,
the degree of freedom is calculated in a different manner:
where r = number of row in table,
c = number of column in a table.
d.f. = (r-1)(c-1)
7. The term CONTINGENCYTABLE was first used by Karl Pearson.
A contingency table is a type in a matrix format that displays the
frequency distribution of the variables.
They are heavily used in survey research, business intelligence,
engineering & scientific research. They provide a basic picture of the
interrelation between two variables and can help find interactions
between them.
The value depends on the number of classes or in on the number of
degrees of freedom & the critical level of probability.
2-2 table when there are only two sample, each divided into classes &
a 2-2 contingency table is prepared. It is also known as Four fold or Four
cell table.
Column 1 Column 2 Row total
Row 1 + + RT 1
Row 2 + + RT2
Column total CT 1 CT 2
Degree of freedom=
(r-1)(c-1)
=(2-1)(2-1)
=1.1
=1
8. Chi-square performs two types of test-
1) Goodness of FitTest (single C variables)
2) The test of independence (between multiple C
variables)
9. The goodness of fit test is a statistical hypothesis test to see how well
sample data fit a distribution from a population with a normal distribution.
EXAMPLE-
We sample and collected data and its comes out below ratio:
Observed Expected (Observed-
Expected)
(Observed-
Expected)2
(Observed-
Expected)2
/E
MALE 13 10 3 9 0.9
FEMALE 7 10 -3 9 0.9
10. Null Hypothesis: ratio of 50-50 exists in office
Alternate Hypothesis in office: ratio of 50:50 is not there.
Males employees<Females employees
Probability of 50:50
Males employees>Female employees
11. oDegree of freedom in our example => Number of classes/categories – 1
=> 2 – 1 =1
oCalculatedChi-square value = 1.8
oCritical value from the chart = 3.8
oIf calculated Chi-square value </= the value of chart . We can not reject
the null hypothesis.
oNull hypothesis – Observed = Expected
oAlternate hypothesis – Observed is not equal to Expected
12. The Chi- square distribution has some important characteristics-
i. This test is based on frequencies, whereas, theoretical distribution the
test is based on mean and standard deviation.
ii. The other distribution can be used for testing the significance of the
difference between a single expected value and observed proportion.
However this test can be used for testing difference between the
entire set of the Expected and the Observed frequencies
iii. A new chi- square distribution is formed for every increase in is the
number of Degree of Freedom.
iv. This rest is applied for testing the hypothesis but is not useful for
estimation.
13. The Chi-square test is applicable for varied problems in agriculture,
biology and medical science-
A. To test the goodness of fit.
B. To test the independence of attributes.
C. To test the homogeneity of independent estimates of the
population variance.
D. To test the detection of linkage.
14. Example-Two varieties of snapdragon, one with red flower and other with white
flower crossed.The result obtained in F2 generation are: 22 red, 52 pink, and 23
white flower plants. Now it is desired to ascertain these figures shows that
segregation occurs in the simple Mendelian ratio of 1:2:1.
Solution-
Null hypothesis-H0: The genes carrying red colour and white colour
characters are segregating in simple Mendelian ratio of 1:2:1.
Expected frequencies-
Red = ¼ . 97=24.25
Pink = 2/4 . 97=48.50
White = ¼ . 97= 24.25
= 5.06/24.25 + 12.25/48.50
+ 1.56/24.25
= 0.21+0.25+0.06
= 0.53 Ans.
Red Pink White Total
Observed
frequency(O)
22 52 23 97
Expected
frequency(E)
24.25 48.50 24.25 97
Deviation(O-E) -2.25 3.50 -1.25
15. The calculated Chi square value( 0.53) is less than the tabulated chi-
square value ( 5.99 ) at 5% level of probability for 2 d.f. . The hypothesis
is, in agreement with the recorded facts.
16. I. Notes provided by subject teacher Mrs. Maya Shedpure.
II. Khan and Khanum, Fundamentals of Biostatistics.
III. Search engine( Google,YouTube, websites )