mixtools (version 1.0.4)

Waterdata: Water-Level Task Data Set

Description

This data set arises from the water-level task proposed by the Swiss psychologist Jean Piaget to assess children's understanding of the physical world. This involves presenting a child with a rectangular vessel with a cap, affixed to a wall, that can be tilted (like the minute hand of a clock) to point in any direction. A separate disk with a water line indicated on it, which can similarly be spun so that the water line may assume any desired angle with the horizontal, is positioned so that by spinning this disk, the child subject may make the hypothetical surface of water inside the vessel assume any desired orientation. For each of eight different orientations of the vessel, corresponding to the clock angles at 1:00, 2:00, 4:00, 5:00, 7:00, 8:00, 10:00, and 11:00, the child subject is asked to position the water level as it would appear in reality if water were in the vessel. The measurement is the acute angle with the horizontal, in degrees, assumed by the water line after it is positioned by the child. A sign is attached to the measurement to indicate whether the line slopes up (positive) or down (negative) from left to right. Thus, each child has 8 repeated measurements, one for each vessel angle, and the range of possible values are from -90 to 90. The setup of the experiment, along with a photograph of the testing apparatus, is given by Thomas and Jamison (1975). A more detailed analysis using a subset of 405 of the original 579 subjects is given by Thomas and Lohaus (1993); further analyses using the functions in mixtools are given by Benaglia et al (2008) and Levine et al (2011), among others. There are two versions of the dataset included in mixtools. The full dataset, called WaterdataFull, has 579 individuals. The dataset called Waterdata is a subset of 405 individuals, comprising all children aged 11 years or more and omitting any individuals with any observations equal to 100, which in this context indicates a missing value (since all of the degree measurements should be in the range from -90 to +90, 100 is not a possible value).

Usage

Waterdata

Format

These data frames consist of 405 or 579 rows, one row for each child. There are ten columns: The age (in years) and sex (where 1=male and 0=female) are given for each individual along with the degree of deviation from the horizontal for 8 specified clock-hour orientations (11, 4, 2, 7, 10, 5, 1, and 8 o'clock, in order).

Source

Benaglia, T., Chauveau, D., and Hunter, D.R. (2009), An EM-Like Algorithm for Semi- and Non-Parametric Estimation in Multivariate Mixtures, Journal of Computational and Graphical Statistics, 18: 505-526. Levine, M., Hunter, D.R., and Chauveau, D. (2011), Maximum Smoothed Likelihood for Multivariate Mixtures, Biometrika, 98(2): 403-416. Thomas, H. and Jamison, W. (1975), On the Acquisition of Understanding that Still Water is Horizontal, Merrill-Palmer Quarterly of Behavior and Development, 21(1): 31-44. Thomas, H. and Lohaus, A. (1993), Modeling Growth and Individual Differences in Spatial Tasks, University of Chicago Press, Chicago, available on JSTOR.