ANOVA 1 Basics Steps for calculation One Way Classification

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Hypothesis Testing • ANOVA - Analysis of Variance • To test the equality of two population means we have z-test (large sample) and t-test (small sample). But, to test the equality of three or more population means we can't use Z-test -r t-test. • We can use ANOVA to test the equality of 'k' (= 3 or more) population means, for a completely randomized experimental design and also using data obtained from an observational study. • *We will never know the values of all the population means but we need to test the following hypotheses: • Ho: All the (3 or more) population means are equal • OR • Ho: There is no significant difference between the (3 or more) population means • Ha: Not all the population means are equal • OR • Ha: At least two population means have different valuess • It is very important to note that if any two or more population means are different, we accept that one is greater than the other mean(s) and, hence, ANOVA is always considered as the 'Upper Tail' (i.e. One Tailed) Test'. • *ANOVA is a statistical procedure used to determine the observed differences in the 'k' sample means are large enough to reject the (above) Ho. • *Assumptions of ANOVA: • 1) For each population, the response variable is normally distributed. • 2)The variance of the response variable (σ^2) is same for all populations. • 3)The observations are independent. • *One Way Classification • When there is only one independent variable (i.e. treatment, characteristic, factor) the effect of which is to be studied on the dependent variable (i.e. production, performance etc), then it is called 'One Way Classification'. The independent variable will have two or more levels, i.e. machines, methods, fertilizers etc... • Steps for Computation • 1. Find the sum of values of all the items of all the samples • T = ∑x1 + ∑x2 + ∑x3 • 2. Calculation of correction factor • T^2 / N (Where N is the total number of items in all the samples) • 3. Find the square of all the items of all the samples and add then together. ∑x1^2 + ∑x2^2 + ∑x3^2 • 4. Find out the total sum of squares (SST) by subtracting the correction factor from the sum of squares of all the items of the samples. SST = ∑x1^2 + ∑x2^2 + ∑x3^2 – Correction Factor • 5. Find out the sum of squares between the samples (SSC). • SSC = (∑x1)^2/N1 + (∑x2)^2/N2 + (∑x3)^2/N3 - T^2/N • 6. Find the sum of squares within samples (SSE) by subtracting the sum of squares between samples from the total sum of squares. SSE = SST – SSC • 7. ANOVA Table: • Sum of squares Degrees of freedom Mean sum of squares F • – ratio • SSC V1 = (k - 1) MSC = SSC/k – 1 • F=MSC/MSE • SSE V2 = (N – k) MSE = SSE/N – c • • SST N – 1 • #Statistics #HypothesisTesting #ANOVA #anova #Ftest #OneTailedTest #OneWayClassification #Variance #Exam #Problem #Solution • Statistics, Hypothesis, Hypothesis Testing, F-test, One Tailed Test, ANOVA, anova, One Way Classification, Imp Problems, Exam Problems, p-Value, MBA, MCA, CA, CFA, CPA, CMA, CS, MCom, BBA, BCom, BA, MA, PhD, MPhil, Research, Analysis, Quantitative Techniques, CAIIB, UPSC, Solution, Exam Problem, • www.prashantpuaar.com

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