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The Quantitative Methods

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Added on  2020-03-16

The Quantitative Methods

   Added on 2020-03-16

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Quantitative MethodsStudent name:UniversityLecturer name:13th October 2017
The Quantitative Methods_1
Question 1:a)Column scatterplotb)Assumptions to be madei)Checking equality of variancesSolutionTest of Homogeneity of VariancesRecall_scores Levene Statisticdf1df2Sig..100233.905As can be seen, p > 0.05, equal variances can be assumed.ii)Check normality of residualsSolutionTests of NormalityAdvertisementKolmogorov-SmirnovaShapiro-WilkStatisticdfSig.StatisticdfSig.Recall_scoresSpokesperson.21012.152.92412.319
The Quantitative Methods_2
Demonstration.22512.094.86612.059Testimonial.14312.200*.92912.372*. This is a lower bound of the true significance.a. Lilliefors Significance CorrectionAs can be seen, p > 0.05 in all the three factors. We can therefore conclude that the assumption on normality is achievediii)Independent factorsThe factors are independent of each other hence the assumption on independence is met.We now sought to test the following hypothesis;H0:μ1=μ2=μ3HA:AtleastoneofthemeansisdifferentTested at α = 0.05Computation of ANOVASTEP 1 Compute CM, the correction for the mean.CM=(∑∑xij)2N=2089236=436392136=121220STEP 2 Compute the total SS. The total SS = SS(Total) = sum of squares of all observations −CM.SS(Total)=452+...+722−121220SS(Total)=126073−121220=4853STEP 3 Compute SST, the treatment sum of squares. First we compute the total (sum) for each treatment.T1 = 45+ 68+...+66+64 = 598T2 = 70+ 58+...+74+68 = 773T3 = 62+ 73+...+48+72 = 718Then,SST=∑Ti2ni−CM=598212+773212+718212−121220=1334.722STEP 4 Compute SSE, the error sum of squares.
The Quantitative Methods_3

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