Boxplots and Quantitative/Categorical Relationships Section 2.4 Boxplots and Quantitative/Categorical Relationships

Review A naturalist counts the number of baby birds, or clutch size, in 130 different nests. The standard deviation of clutch sizes is closest to… 95% of the data falls between about 3 and 11. The mean is about 7. Thus by the 95% rule, the sd is about (7-3)/2 = 2 or about (11-7)/2 = 2. 1 2 3 4

Boxplot Which boxplot goes with the histogram of waiting times for the bus? (a) (b) (c) The data do not show any low outliers.

Tea and the Immune System Participants were randomized to drink five or six cups of either tea or coffee every day for two weeks (both drinks have caffeine but only tea has L-theanine) After two weeks, blood samples were exposed to an antigen, and production of interferon gamma (immune system response) was measured Explanatory variable: tea or coffee Response variable: measure of interferon gamma Mednick, Cai, Kanady, and Drummond (2008). “Comparing the benefits of caffeine, naps and placebo on verbal, motor and perceptual memory,” Behavioral Brain Research, 193, 79-86.

Tea and the Immune System If the tea drinkers have significantly higher levels of interferon gamma, can we conclude that drinking tea rather than coffee caused an increase in this aspect of the immune response? Yes No Randomized experiment – possible to make conclusions about causality

Side-by-Side Boxplots

The variables are year (categorical) and number of times a week the student goes off-campus. We see that There is no association between the variables There is an association and seniors are more likely to go off-campus There is an association and seniors are less likely to go off campus

The variables are year (categorical) and number of times a week the student goes off-campus. We see that Every group has outliers. Only sophomores have outliers Only seniors have outliers Seniors and Juniors have outliers

The group with the largest standard deviation is: First Years Sophomores Juniors Seniors