Background to the Peer Play Data

Data analysed in: Kroonenberg, P. M. (2008). Applied multiway data analysis. Hoboken NJ: Wiley.

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)

References

• Kramer, L. & Gottman, J. M. (1992). Becoming a sibling: "With a little help from my friends". Developental Psychology, 28, 685-699.
• Anderson, C. J. (1996). The analysis of three-way contingency tables by three-mode association models. Psychometrika, 61, 465-483.

Data description

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.

Rows (1st mode): Groups

Columns (2nd mode): Play quality

Slices (3rd mode): Time points

Data arrangement

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.

Data handling

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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