Mean comparison ii variance analysis
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Analysis of variance (ANOVA) is a statistical test used to identify differences between sample means. It partitions variability, attributing portions to the effect of an independent variable on a dependent measure. The ANOVA yields an F ratio statistic determined by dividing between-groups variance by within-groups variance. This ratio indicates whether differences among two or more means are statistically significant or likely due to random error.
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ANOVA
ANOVA
โข Analysis of Variance
โข Statistical method to analyzes variances to determine if the means from more than
two populations are the same
โข compare the between-sample-variation to the within-sample-variation
โข If the between-sample-variation is sufficiently large compared to the within-sample-
variation it is likely that the population means are statistically different
โข Compares means (group differences) among levels of factors. No
assumptions are made regarding how the factors are related
โข Residual related assumptions are the same as with simple regression
โข Explanatory variables can be qualitative or quantitative but are categorized
for group investigations. These variables are often referred to as factors
with levels (category levels)
ANOVA Assumptions
โข Assume populations , from which the response values for the groups
are drawn, are normally distributed
โข Assumes populations have equal variances
โข Can compare the ratio of smallest and largest sample standard deviations.
Between .05 and 2 are typically not considered evidence of a violation
assumption
โข Assumes the response data are independent
โข For large sample sizes, or for factor level sample sizes that are equal,
the ANOVA test is robust to assumption violations of normality and
unequal variances
ANOVA and Variance
Fixed or Random Factors
โข A factor is fixed if its levels are chosen before the ANOVA investigation
begins
โข Difference in groups are only investigated for the specific pre-selected factors
and levels
โข A factor is random if its levels are choosen randomly from the
population before the ANOVA investigation begins
Randomization
โข Assigning subjects to treatment groups or treatments to subjects
randomly reduces the chance of bias selecting results
ANOVA hypotheses statements
One-way ANOVA
One-Way ANOVA
Hypotheses statements
Test statistic
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Under the null hypothesis both the between and within group variances estimate the
variance of the random error so the ratio is assumed to be close to 1.
Null Hypothesis
Alternate Hypothesis
One-Way ANOVA
One-Way ANOVA
One-Way ANOVA Excel Output
Treatme
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4. Post must be at least 150 words and cite all of your references even it its the book.
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ANOVA
ANOVA
โข Analysis of Variance
โข Statistical method to analyzes variances to determine if the means from more than
two populations are the same
โข compare the between-sample-variation to the within-sample-variation
โข If the between-sample-variation is sufficiently large compared to the within-sample-
variation it is likely that the population means are statistically different
โข Compares means (group differences) among levels of factors. No
assumptions are made regarding how the factors are related
โข Residual related assumptions are the same as with simple regression
โข Explanatory variables can be qualitative or quantitative but are categorized
for group investigations. These variables are often referred to as factors
with levels (category levels)
ANOVA Assumptions
โข Assume populations , from which the response values for the groups
are drawn, are normally distributed
โข Assumes populations have equal variances
โข Can compare the ratio of smallest and largest sample standard deviations.
Between .05 and 2 are typically not considered evidence of a violation
assumption
โข Assumes the response data are independent
โข For large sample sizes, or for factor level sample sizes that are equal,
the ANOVA test is robust to assumption violations of normality and
unequal variances
ANOVA and Variance
Fixed or Random Factors
โข A factor is fixed if its levels are chosen before the ANOVA investigation
begins
โข Difference in groups are only investigated for the specific pre-selected factors
and levels
โข A factor is random if its levels are choosen randomly from the
population before the ANOVA investigation begins
Randomization
โข Assigning subjects to treatment groups or treatments to subjects
randomly reduces the chance of bias selecting results
ANOVA hypotheses statements
One-way ANOVA
One-Way ANOVA
Hypotheses statements
Test statistic
=
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๐๐๐กโ๐๐ ๐บ๐๐๐ข๐ ๐๐๐๐๐๐๐๐
Under the null hypothesis both the between and within group variances estimate the
variance of the random error so the ratio is assumed to be close to 1.
Null Hypothesis
Alternate Hypothesis
One-Way ANOVA
One-Way ANOVA
One-Way ANOVA Excel Output
Treatme
ANOVA Test
This document provides information about a group presentation on analyzing variance (ANOVA) tests. It includes the course name and number, group members, instructor name, and grade. The presentation outline defines ANOVA tests, describes types like one-way and two-way, and discusses applications in healthcare like comparing drug efficacy. It also explains concepts like within-group and between-group variation, the F-test significance, and the ANOVA table. References are provided at the end.
F unit 5.pptx
This document discusses different types of statistical analysis techniques. It begins by defining descriptive analysis as studying distributions of one variable and bivariate/multivariate analysis as studying relationships between two or more variables. It then discusses various types of statistical analyses including correlation analysis, causal analysis, multiple regression analysis, multiple discriminant analysis, multivariate ANOVA, and canonical analysis. It also covers inferential analysis, characteristics and importance of statistical methods, assumptions of parametric tests, examples of parametric and non-parametric tests, and provides details on the chi-square test.
Analysis of variance
This document provides an overview of analysis of variance (ANOVA) techniques. It discusses one-way and two-way ANOVA, including their assumptions, calculations, and applications. For example, it explains how to set up a two-way ANOVA table and calculate values like sums of squares, degrees of freedom, mean squares, and F values. It also gives an example of using one-way ANOVA to analyze differences in crop yields between four plots of land.
STATISTICAL TOOLS IN RESEARCH
The document discusses various statistical tools used in research including measures of central tendency (mean, median, mode), measures of dispersion (standard deviation, interquartile range, coefficient of variation), t-tests, ANOVA, regression, correlation and more. It provides examples of when each tool would be used, such as using regression to model relationships between variables or ANOVA to test for differences between group means. The document aims to increase awareness of these common statistical tools for analyzing data in research studies across various fields.
One way repeated measure anova
Repeated measures ANOVA is used to compare mean scores on the same individuals across multiple time points or conditions. It extends the dependent t-test to allow for more than two time points or conditions. Key assumptions include having a continuous dependent variable, at least two related groups or conditions, no outliers, normally distributed differences between groups, and sphericity. Repeated measures ANOVA separates variance into between-subjects, between-measures, and error components to test if there are differences in mean scores between related groups while accounting for correlations between measures on the same individuals.
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Desmond Ayim-Aboagye is a Ghanaian psychologist of religion, educationist, and philosopher known for his research in psychology of religion, transcultural psychiatry, behavioral economics, social psychiatry, and pain psychology. He has developed numerous scientific theories and discovered several psychiatric disorders related to war. He received his B.A. and M.A. from Andrews University and PhD from the University of Uppsala. Currently he is a professor and dean at Regent University College of Science and Technology in Ghana.
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Biography of desmond ayim aboagye
Desmond Ayim-Aboagye is a Ghanaian psychologist of religion, educator, and philosopher. He received his PhD from the University of Uppsala in Sweden and currently works as a professor and dean at Regent University College of Science and Technology in Ghana. His research focuses on psychology of religion, transcultural psychiatry, behavioral economics, social psychiatry, and pain psychology. Through his research, he has developed theories on disorders related to war such as Hannibal Odyssey Complex and theories on the role of traditional healers in treating mental illness in West Africa. He has published extensively on indigenous psychiatry, psychology of religion, and pain psychology.
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Mean comparison ii variance analysis
- 1. MEAN COMPARISON II Desmond Ayim-Aboagye, Ph.D ONE-VARIABLE ANALYSIS OF VARIANCE
- 2. Analysis of Variance (ANOVA) โข It is the most familiar procedure for behavioural scientists. โข It was originated by Statistician known as Fisher. โข F distribution used to test hypothesis regarding significant differences among two or more means.
- 3. ANOVA โข The ANOVA and its F test can search for reliable differences among the magnitudes of two, three, four, or even more means simultaneously. โข The ANOVA enables investigators to analyze data addressing complex questions (i.e., beyond those posed by standard two-group experiments).
- 4. OVERVIEW OF ANOVA โข The analysis of variance (ANOVA) is a statistical test used to identify differences between or among distinct sample means. As a statistical technique, the ANOVA partitions or divides variability, attributing portions of it to the effect of an independent variable on a dependent measure.
- 5. TOTAL VARIANCE โข Variance of all participantsโ scores from the three samples combined would be labeled the total variance. (each sample is exposed to oneโ and only oneโ level of independent variable.) โข Total variance entails the combined variance of all the scores or observations within an experiment.
- 6. F Ratio โข The ANOVA yields an F Ratio, a t test statistic that is determined by dividing between- groups variance (largely based on an independent variable) by within-groups variance (random error).
- 7. ANOVA โข The ANOVA provides a statistic, the F ratio, comprised of two elements: โข 1. The numerator of the F ratio indicates the variability between or among means of two or more samples (i.e., between-group variance) โข The denominator of the F ratio identifies the variability among the observations within each sample (i.e., within-group variance)
- 8. F Ratio โข F = between-group variance โข within-group variance