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Wave
Hearing the term wave might bring images of water moving toward shore. Waves in statistical analysis are similar to those of the ocean. Just like crests (highs) and troughs (lows) in examining patterns of moving water, waves are cycles of data analysis that extend in time for individuals (students) or groups of individuals (families or schools). A crest would represent when researchers are gathering data. A trough would represent a break in data collection. As such, waves are repeated measures of data collection. Statisticians collect data over multiple repeated measures in time because they are often interested in addressing research questions about human development or historical change. Sections that follow include examples of research studies where waves are used, important statistical considerations in the analysis of wave data, and historical trends in types of statistical techniques used to study wave data.
Two Examples of Wave Analysis
Wave analyses help researchers understand change and growth given a variety of variables of interest in the social sciences. Consider the investigator who would like to study whether motivation about learning remains stable, decreases, or increases in time as students move through the grade levels. Each grade level would represent a wave. The investigator might administer a motivation survey to students during every spring of each academic year starting with grade 3 and moving through high school. The goal would be to determine whether the average motivation scores stay the same or whether they change for the same group of students.
As another example, a researcher might want to study the recreational spending habits of families throughout the course of the year. Records of expenditure might be collected once every three months. The investigator might study how these expenses are correlated with those for essential needs (e.g., health or food). This example also involves waves of data collection like the motivation example. However, it is different in some ways. First, the units of analysis are not the same. Here, the investigator studied families, whereas in the motivation example, the study focused on students. Second, the frequency and duration of each wave are different. The motivation researcher studied change across years. By comparison, the family studies researcher was interested in fewer waves (four per year) and a shorter duration of time (every three months). Finally, there are more variables to analyze in the family spending study. Not only are there measures of time, but also the researcher examined two types of spending: essential needs and recreation. Differences in units of analysis, frequency and duration of time, and amount and type of variables studied lead to different statistical method considerations in the analysis of wave data.
Statistical Method Considerations
Statisticians have to think carefully about several data analysis considerations when conducting investigations that require waves: (1) the interval of the wave, (2) the frequency of waves, and (3) the amount and type of variables studied. Reviews of literature help investigators make decisions about all of these design elements. The interval of the wave is the length of each time period. In studies about learning, for example, report-card marking periods, semesters, or years make sense as these are typical intervals of time that define the academic calendar.
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- Descriptive Statistics
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