# Analysis-of-Variance

Analysis-of-Variance

Statistical variances

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Analysis of Variance (ANOVA) is a collection of statistical method used to analyse and test the differences between group means and their connected procedures. In the ANOVA scenery the practical variance in a certain variable is subdivided into components attributable to diverse foundations of variation. The ANOVAS are vital for comparing three or more means. They provide statistical test of several groups and simplifies the t-test to more than two groups (Kanji, 2006).

When one needs to know if one measurement variable is connected with another one, then linear regression and correlation is essential. R It measures the strength of the association and makes an equation that is necessary to describe the relationship and predict indefinite values. linear regression and correlation are used when one has measuring variables. Correlation refers to the extent at which two variables are having a linear relationship with each other. It associates the relative position of cases along two variables. A relationship is said to be positive When there is an increase in the level of one variable and associated with the increase another. While a negative relationship occurs when there is an increase in one level and is associated with a decrease in the other. Correlation is used to represent association between two quantitative variables. the association is considered linear when one variable increases or decreases a stable amount for a module with an increase or decrease in the other. While regression involves approximating the best straight line to summarise the association (Bobko, 2001).

In this journal humprey claims that the method adopted shows neural nets are mathematical techniques rather than models of cognitive processing. applied mathematics is more than simply applying results from pure mathematics. models of meural nets are at times intimately associated with a learning algorithm (Humphreys, 2004).

The cross classified type of data examination is shared in research and evaluation, karl pearson’s chi square tests family represents the most utilized statistical analysis that answers questions about association among category variables. However, the results are commonly misinterpreted leading to statements that have limited statistical support from the analysis performed. This study focuses mainly on the chi-square tests of independence and homogeneity of variance. The reason for misinterpretation of tests in the Karl Pearson family of chi-square tests (independence, homogeneity, and goodness-of-fit) basically using the same formula. These three tests are different with particular hypotheses, sampling methodologies, interpretations, and options following refusal of the null hypothesis (Franke & et.al, 2011).

The Chi-square statistic is a distribution free test/ non-parametric tool that is designed to analyse group variances when the dependent variable is measured at a nominal level. It is used for testing hypothesis and when all variables measurement level is nominal or ordinary: the sample sizes of learning groups are unequal: The original is measured at an interval ratio but it violates the assumptions of homoscedasticity or equal variance. It allows evaluation of both multiple group studies and dichotomous independent variables, the calculations required for computing Chi-square provides considerable information of how each of the groups performed in the study. The advantages of the Chi-square are its robustness with respect to distribution of the data; its simplicity in computing; its use where parametric assumptions are not achieved and its elasticity in managing data from both two group and multiple group studies. The Limitations are; its sample size requirements (Mchugh, 2013).

Z-test is a statistical test with normal distribution that is applied and used for dealing with problems relating to large samples using population samples the study further explains classifications of z tests. Such as:

z test for single proportion tests a hypothesis on a particular value of the population proportion.

z test for difference of proportions tests the hypothesis that two populations have the same proportion.

z -test for single mean tests a hypothesis on a specific value of the population mean.

z test for single variance is used to test a hypothesis on a specific value of the population variance.

Z-test tests equality of variance as well as tests the hypothesis of equality of two population variances when the sample size of each sample is 30 or larger (Shasha, 2011).

REFERENCES

Bobko, P. (2001) Correlation and Regression: Application for industrial organizational

psychology and management. Thousand Oaks: Sage Publications

Franke, T.M, Ho, T., & Christie, C.A(2011). The Chi-square Test: Often Used and More

Often Misinterpreted. American Journal of Evaluation, 33(3). 448-458.

Doi:10.1177/1098214011426584

Humphreys P. (2004) Extending ourselves: Computational science, empiricism, and

scientific method. Oxford University Press, New York

Kanji, G.K. (2006). 100statistical tests. London: Sage Publications

Mchugh, M.L. (2013). The Chi-square test of independence. Biochemia Medica Biochem

Med, 143-149.doi 10.11613/bm.2013.018

Shasha, D.E., & Wilson, M. (2011). Statistics is easy! San Rafael, CA: Morgan & Claypool