Statistical Tests - Assignment

Added on - 31 May 2021

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1Statistical TestsStudent Name:Student ID:Unit Name:Unit ID:Date Due:Professor Name:
2Analysis of Variance testAssumptions of ANOVA F –test are as followsI.Samples are selected in a random manner from treatment populations.II.All the treatment populations follow Gaussian (Normal) distribution.III.All the treatment populations have same variances and are homogeneous innature.IV.There is no correlation between the mean and variances of the samples.V.The primary effects are additive in nature, that is block and treatment effects areadditive.VI.The residuals follow Gaussian distribution and are independent in nature.Null and Alternate Hypotheses for ANOVA are as followsExample: The effect of soya protein level of three separate foods is being found.Data for the test: Quantity of soya protein levels for 1122 samples. The response factor isSoya Protein Level (%), where the factor is FOOD type and measurement levels are 3(vitamin A, B, and D).Null hypothesis: H0: There is no significant effect of soya protein level due to differentfood products (μ1=μ2=μ3).Alternate hypothesis: HA: There is a significant effect of soya protein level due to differentfood products.The Fisher-F value is found as described in the following table (Meyers, Gamst &Guarino,2016).
3Figure1: ANOVA TableIf the F value falls in the critical region corresponding to p-value as less than 0.05, then thenull hypothesis gets rejected. Otherwise, null hypothesis fails to get rejected.The validity of the assumptions is then cross-checked.I.Independence of the sample gets checked from the measures of ANOVA. If repeatedmeasures are present then samples are not potentially independent.II.For checking normality of the sample data, Shapiro-Wilk test is performed alongwith Box-plot construction.III.Variances of the samples are cross-checked for equality and assumption of variancehomogeneity is established.
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