Kramer & Gottman (1992) studied to what extent the quality of social interaction with peers influences the attitude of children toward their newly born siblings. To this end, they collected data on the quality of play of children with their best friends. In our analyses we collapsed over the response variable ``attitude toward sibling'' in order to concentrate on finding patterns in quality of play between children as a function of sex, age, and time of measurement. The reference point for the measurements was taken as the moment of the sibling's birth, and the major question was whether the quality of play of the elder child was different before and after the sibling's birth. The full background to the study can be found Kramer & Gottman (1992)
The data are a condensation of those contained in Anderson (1996, Table 3). The original seven types of three-year-old to five-year-old first-born children were reduced to four types of children, because the original groups contained very few children. The groups now form a fully crossed design of girls versus boys, and younger versus older children. These two variables were interactively coded, as they both were design variables and we wanted to reduce the four-way table to a three-way one. Moreover, this removed the design interaction from the data The cells of the resulting three-way table contained the information on how often each of eleven play qualities occurred during play sessions of a child with his or her best friend. The children were observed at five occasions (3 and 1 months before a sibling was born to their families and 1, 3, and 5 months after its birth; in the sequel these time points will be indicated by -3, -1, +1, +3, +5, respectively). The eleven play qualities were: sustained communication, coordinated or successful gossip, coordinated or positive play, excitement, amity, shared or successful fantasy, unsustained communication, uncoordinated or poor play, negative emotion, conflict, and prohibitions. Thus, the data make up a 4 (Groups) by 11 (Play qualities) by 5 (Time points) contingency table.
|2.||Gossip||Coordinated or succeful gossip|
|6.||Fantas||Shared or succesfull fantasy|
|8.||Poor||Uncoordinate or poor play|
|1.||-3||Three months before sibling was born|
|2.||-1||One months before sibling was born|
|3.||+1||One months after sibling was born|
|4.||+3||Three months after sibling was born|
|5.||+5||Five months after sibling was born|
A three-way data array X = (x(i,j,k)) has the following form
|-----|i=1 |-----| |i=2 |-----| | |.. | | | |.. | | |____|i=I=4 k=K=5 | |____| k=2 |_____| k=1 j=1,.,J=11
The actual data file has the following form:
j=1,.,J=11 |-----|i=1 | |i=2 | |.. k= 1 | |.. |_____|i=I=4 |-----|i=1 | |i=2 | |.. k= 2 | |.. |_____|i=I=4 |-----|i=1 | |i=2 | |.. k=5 | |.. |_____|i=I=4
Thus the first mode (i) is nested in the third mode (k) and there are 4 (Groups) times 5 (Time points) rows and 11 (Play quality) columns.
Categorical data in contingency tables are usually divested of the influence of the marginal proportions which represent the model of independence. Thus the original frequencies are transformed in chi-term ( = observed - expected)/sqrt(expected). These chi-terms are the basis for the correspondence analysis. For details see Kroonenberg (2008). Applied multiway data analysis. Hoboken NJ: Wiley (Chapter 17).
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