ONE-WAY-ANALYSIS-OF-VARIANCE.pptx

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ONE-WAY ANALYSIS OF VARIANCE
• ANOVA or one-way ANOVA, is an abbreviation of
analysis of variance. It is a method used to summarize
the differences between several means and
simultaneously comparing these means in one step.

MEAN OF COMBINED SAMPLE
• Data from the ith sample can be summarized into
sample size ni, sample mean xi, and sample
variance s2
i . If we pool data together, the (grand)
mean of this combined sample can be calculated
from

• BETWEEN SUM OF SQUARES
represents the
variation or
differences between
the sample means

ANOVA PROCESS
1. WITHIN MEAN SQUARE 2. BETWEEN MEAN SQUARE
serves as an estimate of the
common variance σ2 as stipulated
by the one-way ANOVA model.
represents the average
variation between the k sample
means.

TEST STATISTIC F
• t is the test statistic for comparing the two
population means.
• when k = 2, the F test is equivalent to the two-
sided two-sample t test.

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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

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