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11. One-Way Analysis of Variance.md

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Quizz

1.An online retailer strongly suspects that customers purchase more in the following month if they are shown a company ad more often. To confirm that hunch they randomly select 50 customers who are then sent one ad, 45 customers who are sent two ads, and 52 customers who are sent three ads. Which is the null hypothesis?

  • the spending means for the three groups are the same.

  • the spending means increase with the number of ads

This is the "nothing extraordinary going on" hypothesis.


  1. Based on the description of the experiment in the previous question and the boxplots below, do you think that the assumptions of ANOVA are met?

image

yes, The observations are independent by design and the variances seem to be equal by looking at the boxplots.


  1. Based on the ANOVA table below and the boxplots, what is the conclusion of the analysis?

image

  • There is no statistically significant effect.

  • There is sufficient evidence to conclude that the spending means increase with the number of ads.

  • There is sufficient evidence to conclude that the spending means are not equal, but based on this analysis alone we cannot conclude that the spending means increase with the number of ads.


4.Does eye color effect the type of vision correction that patients choose? From a large dataset of patients having vision correction, 70 patients were chosen randomly from those having brown eyes, 70 from those having green eyes, and 70 from those having blue eyes. For each patient, the type of vision correction was coded as follows: glasses=1, contact lenses=2, corrective surgery=3. Those numbers were used for an ANOVA, which resulted in a p-value of 0.5%. Does the p-value of 0.5% mean that there is strong evidence that that eye color has an effect on the type of vision correction that patients choose?

no, These are categorical (not quantitative) data, and so are not normal. Thus ANOVA is not applicable and the pp-value is not meaningful.


  1. A clinical trial aims to discern whether twelve interventions against high blood pressure have different effects. The study randomizes 10,000 subjects into twelve groups. Each group is administered one of the twelve interventions. After a month the change in blood pressure is measured for each subject. The ANOVA table gives a p-value of 17%. The investigators also perform pairwise two-sample t-tests for all pairs of treatments and find that two pairs show a statistically significant difference. Which of the following options describes a valid conclusion?

  • There is not enough evidence to conclude that the twelve treatment means are different.

  • We can conclude that there are differences between the two pairs of treatments that were found to be significant by the two-sample t-tests.

ANOVA is not significant.