ANOVA (analysis of variance) is a statistical technique used to determine if multiple samples come from populations with equal means. It compares two estimates of variance: between-column variance, which is the variance among sample means; and within-column variance, which is the variance within each sample. The F-test for ANOVA calculates the F-statistic as the ratio of between-column variance to within-column variance. This value is then compared to a critical value from the F-distribution table to determine whether to reject or fail to reject the null hypothesis that the population means are equal.
a full lecture presentation on ANOVA .
areas covered include;
a. definition and purpose of anova
b. one-way anova
c. factorial anova
d. mutiple anova
e MANOVA
f. POST-HOC TESTS - types
f. easy step by step process of calculating post hoc test.
a full lecture presentation on ANOVA .
areas covered include;
a. definition and purpose of anova
b. one-way anova
c. factorial anova
d. mutiple anova
e MANOVA
f. POST-HOC TESTS - types
f. easy step by step process of calculating post hoc test.
Analysis of data is a process of inspecting, cleaning, transforming, and modeling data with the goal of discovering useful information, suggesting conclusions, and supporting decision-making.
Analysis of variance (ANOVA) is an analysis tool used in statistics that splits an observed aggregate variability found inside a data set into two parts: systematic factors and random factors. The systematic factors have a statistical influence on the given data set, while the random factors do not.
Analysts use the ANOVA test to determine the influence that independent variables have on the dependent variable in a regression study.
The t- and z-test methods developed in the 20th century were used for statistical analysis until 1918, when Ronald Fisher created the analysis of variance method.
ANOVA is also called the Fisher analysis of variance, and it is the extension of the t- and z-tests. The term became well-known in 1925, after appearing in Fisher's book, "Statistical Methods for Research Workers."
It was employed in experimental psychology and later expanded to subjects that were more complex.ANOVA (Analysis Of Variance) is a collection of statistical models used to assess the differences between the means of two independent groups by separating the variability into systematic and random factors. It helps to determine the effect of the independent variable on the dependent variable. Here are the three important ANOVA assumptions:
1. Normally distributed population derives different group samples.
2. The sample or distribution has a homogenous variance
3. Analysts draw all the data in a sample independently.
ANOVA test has other secondary assumptions as well, they are:
1. The observations must be independent of each other and randomly sampled.
2. There are additive effects for the factors.
3. The sample size must always be greater than 10.
4. The sample population must be uni-modal as well as symmetrical.
TYPES OF ANOVA
1. One way ANOVA analysis of variance is commonly called a one-factor test in relation to the dependent subject and independent variable. Statisticians utilize it while comparing the means of groups independent of each other using the Analysis of Variance coefficient formula. A single independent variable with at least two levels. The one way Analysis of Variance is quite similar to the t-test.
2 TWO WAY ANOVA
The pre-requisite for conducting a two-way anova test is the presence of two independent variables; one can perform it in two ways –
Two way ANOVA with replication or repeated measures analysis of variance – is done when the two independent groups with dependent variables do different tasks.
Two way ANOVA sans replication – is done when one has a single group that they have to double test like one tests a player before and after a football game
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Analysis of data is a process of inspecting, cleaning, transforming, and modeling data with the goal of discovering useful information, suggesting conclusions, and supporting decision-making.
Analysis of variance (ANOVA) is an analysis tool used in statistics that splits an observed aggregate variability found inside a data set into two parts: systematic factors and random factors. The systematic factors have a statistical influence on the given data set, while the random factors do not.
Analysts use the ANOVA test to determine the influence that independent variables have on the dependent variable in a regression study.
The t- and z-test methods developed in the 20th century were used for statistical analysis until 1918, when Ronald Fisher created the analysis of variance method.
ANOVA is also called the Fisher analysis of variance, and it is the extension of the t- and z-tests. The term became well-known in 1925, after appearing in Fisher's book, "Statistical Methods for Research Workers."
It was employed in experimental psychology and later expanded to subjects that were more complex.ANOVA (Analysis Of Variance) is a collection of statistical models used to assess the differences between the means of two independent groups by separating the variability into systematic and random factors. It helps to determine the effect of the independent variable on the dependent variable. Here are the three important ANOVA assumptions:
1. Normally distributed population derives different group samples.
2. The sample or distribution has a homogenous variance
3. Analysts draw all the data in a sample independently.
ANOVA test has other secondary assumptions as well, they are:
1. The observations must be independent of each other and randomly sampled.
2. There are additive effects for the factors.
3. The sample size must always be greater than 10.
4. The sample population must be uni-modal as well as symmetrical.
TYPES OF ANOVA
1. One way ANOVA analysis of variance is commonly called a one-factor test in relation to the dependent subject and independent variable. Statisticians utilize it while comparing the means of groups independent of each other using the Analysis of Variance coefficient formula. A single independent variable with at least two levels. The one way Analysis of Variance is quite similar to the t-test.
2 TWO WAY ANOVA
The pre-requisite for conducting a two-way anova test is the presence of two independent variables; one can perform it in two ways –
Two way ANOVA with replication or repeated measures analysis of variance – is done when the two independent groups with dependent variables do different tasks.
Two way ANOVA sans replication – is done when one has a single group that they have to double test like one tests a player before and after a football game
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
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Analysis of variance
1. ANALYSIS OF VARIANCE: ANOVA
• ANOVA: It is a statistical technique that
is used to determine whether several
samples come from populations with
equal means.
• Statements of hypotheses:
H0: µ1 = µ2 = µ3
H1: µ1 ≠ µ2 ≠ µ3
2. ANOVA: BASIC CONCEPTS
• ANOVA is based on a comparison of two
different estimates of the variance: among the
samples and within the samples
• Between-Column Variance: An estimate of the
population variance derived from the variance
among the sample means.
• Within-Column Variance: An estimate of the
population variance based on the variances
within the k samples, using a weighted average
of the k sample variances.
3. ANOVA
• Variance among the Sample Means:
S2x = Σ(x - x)2
k-1
• Estimate of Between-Column Variance:
σ2b = Σnj (xj - x)2
k-1
Where σ2b = estimate of the population variance based on the
variance among the sample means (the between-column variance),
nj = size of the jth sample, xj = sample mean of the jth sample, x =
grand mean and k = number of samples
4. ANOVA
• Calculating the Variance within the Samples:
σ2w = Σ[(nj – 1)/(nT – k)]sj2
Where, σ2w = our second estimate of the population
variance based on the variances within the samples (the
within-column variance), nj = size of the jth sample, sj2 =
sample variance of the jth sample, k = number of
samples, and nT = Σnj = total sample size
5. The F Hypothesis Test
• Step I: State null and alternate hypotheses
• Step II: Calculate F statistic, as follows
F = between-column variance = σ2b / σ2w
within-column variance
• Step III: F test has two degrees of
freedom, Numerator degrees of freedom =
(number of samples – 1) and Denominator
degrees of freedom = Σ(nj – 1) = (nT – k)
6. The F Hypothesis Test
• Step IV: From F table in which columns
represent the number of degrees of freedom for
the numerator and the rows represent the
degrees of freedom for the denominator, find out
critical value of F statistic for a certain level of
significance.
• Step V: In case calculated value of F statistic
exceeds the critical (Table) value, null
hypothesis is rejected. If not, we would accept it.
