Write Down the Appropriate Statistical Model Covered - ANOVA - Statistics Assignment Help

Assignment Task

Questions -

A new online newspaper offers advertising space on its website. The newspaper wants to quantify if the reader response to advertisements in the newspaper is affected by which sections of the newspaper the advert is placed. Every time an advert on the website is clicked, the reader is taken to the advertiser’s promotional website and the click visit counted on the newspaper database. The data was recorded and analysed in R below.

Clicks A count of how many readers clicked a specific advert. Section The section the advert was placed Business: The business section News: The general news section Sports: The sports section

# Section n mean sd # 1 Business 20 9.1 1.744163 # 2 News 20 8.9 3.059068 # 3 Sports 20 7.0 2.575185

Clicks.aov = aov(Clicks ~ Section, data = online_news) summary(Clicks.aov)

# Df Sum Sq Mean Sq F value Pr(>F)

# Section 2 53.7 26.867 4.235 0.0193 *

# Residuals 57 361.6 6.344 # ---

# Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

a) Write down the appropriate statistical model covered in the unit to compare the number of clicks over the three newspaper sections. In your answer, carefully define all parameters.

b) A colleague mentions that the data could be analysed by conducting pairwise multiple comparisons of the means with two sample t-tests. Explain the advantages and disadvantages of this approach compared to doing an F-test (ANOVA).

c) State three main assumptions required to conduct a One Way Analysis of Variance (ANOVA). If possible, validate the assumptions for the ANOVA on the previous page. If not possible, state what further output is required and how it validates the assumption.

d) Assuming the requirements for an ANOVA have been fully validated, use the previous output to perform an ANOVA test to compare the three means.

i) State the appropriate hypotheses using the parameters defined in a).

ii) State the test statistic and its value. iii) State the null distribution of the test statistic iv) Give the statistical and contextual conclusion with justification. 3

e) A follow up problem is to determine whether there is any difference in the mean number of advert clicks for the business and news sections as a whole against the mean number of advert clicks in the sports section. That is, conduct a significance test on the contrast C = µBusiness+µNews 2 − µSports. In your answer:

i) State the appropriate hypotheses.

ii) Calculate the observed value of the (raw) contrast.

iii) Calculate the standard error of the contrast.

iv) State the null distribution of the test statistic.

v) Compute an approximate rejection region for c at level α = 0.01.

vi) Draw your statistical conclusion.

vii) Draw your contextual conclusions

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