What test can be performed to compare the mean adult height between the first (Q1) and the

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What test can be performed to compare the mean adult height between the first (Q1) and the fourth (Q4) quartiles? (Assume that the underlying variances of adult height in Q1 and Q4 are the same.)


Pediatrics

A study was conducted to assess the association between climate conditions in infancy and adult blood pressure and anthropometric measures (e.g., height, weight) [19]. There were 3964 British women born between 1919 and 1940 who were divided into quartiles (n = 991 per quartile) according to mean summer temperature (°C) in the first year of life. The data in Table 8.34 were presented.

Table 8.34: Mean adult height by mean summer temperature in the first year of life

 Range of temperature (°C) Mean adult height (cm) Group Quartile 95% CI Q1 159.1 (158.8, 159.4) 991 159.0 (158.7, 159.3)


We will assume that the distribution of adult height within a quartile is normally distributed and that the sample sizes are large enough that the t distribution can be approximated by a normal distribution. 

Distribution
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