Chapter Summary
This chapter outlines methods for ordering condensed data according to time, processes, and cases. The ordering provides foundations for determining sequences and hierarchies for further analytic work.
Contents
Introduction Ordering by Time
Event-Listing Matrix Growth Gradient Time-Ordered Matrix Ordering Processes
Decision Modeling Event–State Network
Composite Sequence Analysis Ordering by Cases
Case-Ordered Descriptive Meta-Matrix Closure and Transition
Introduction
A third major family of displays orders data by time, processes, and cases, preserving the chronological flow and permitting a good look at what led to what, and when. Once past initial description, some form of ordering is typically very helpful. Ordering matrices by time enables the analysis of phases, stages, cycles, and possibly influences and affects (the preferred terms over the outmoded “cause and effect”), suggesting causation.
Life is chronology; we live in a flow of events. But although we can think of ourselves as being in the midst of a river of events, that metaphor breaks down because the river’s flow is not one- dimensional. Some events occur in one domain of life, others elsewhere. Some events are close to us, some distant. Some events are related coherently to other events, and others are adventitious. And though it may be stating the obvious, events long ago in time have consequences for the present.
Distant events can have consequences for close events.
As for cases, looking across them deepens our understanding and can increase generalizability.
But cross-case analysis is tricky. Simply summarizing superficially across some themes or main variables by itself tells us little. We have to look carefully at the complex configuration of processes within each case and understand the local dynamics before we can begin to see a patterning of variables that transcends particular cases. Thus, combining “process” and “variable” approaches is needed for methods of ordering.
Ordering by Time uses chronology as an organizing framework for examining data as they change across time. Ordering Processes examines how “big picture” composite journeys can be diagrammed. Ordering by Cases hierarchically arranges individuals, groups, and sites according to designated variables of interest.
Ordering by Time
An event-listing matrix documents selected actions during selected periods of time. A growth gradient illustrates the development of a variable throughout a range of time. And a time-ordered matrix shows the concurrent pathways of multiple variables and researcher evaluation notes during selected periods of time.
Event-Listing Matrix Description
An event listing is a matrix that arranges a series of concrete events by chronological time periods, sorting them into several categories (see Display 8.1).
Applications
Qualitative researchers are always interested in events—what they are, when they happened, and what their connections to other events are (or were)—to preserve chronology and illuminate the processes occurring. A process, after all, is essentially a string of coherently related events.
Typically, these interests lead to the production of an extended narrative arranged in a proper time sequence (usually without flashbacks or flash forwards).
Narratives are indispensable if we are to understand a complex chronology in its full richness.
The problem is that going straight to an extended narrative from written-up field notes runs an acute risk: You can tell a story that is partial, biased, or dead wrong—even though it may look vivid, coherent, and plausible to a reader. The event listing is a good way of guarding against false chronologies. It creates a matrix-based outline for your narrative.
Example
In the school improvement study, we (Miles and Huberman) wanted to display events during the adoption and implementation of an innovation at the school level, showing them by different phases or time periods of the process.
Keeping the classic left-to-right convention for the passage of time, we might make columns of the matrix list successive time periods. These could be defined arbitrarily (e.g., Year 1, Year 2), or more organically by empirically derived phases or stages of the adoption-implementation process.
Perhaps some events are more critical than others, serving to cause new events or to move the
process forward into a new phase. Rows of the matrix, in this case, deal with the locale of events:
state, district, and local levels.
Display 8.1 shows how this technique worked out for a 1970s innovation called SCORE-ON, a laboratory for teaching remedial math and reading skills to children “pulled out” of their regular classes. The time periods (Contextual Press 1976–1978, Emergence of the Problem Oct. 1978, etc.) were initially defined conceptually from a general adoption-implementation model, but labels for each period came from the actual core activities during that period. A new time period was defined when a significant shift in activities occurred. The analyst marked “barometric events” (those that moved the process on into the next time period or phase) with an asterisk.
The analyst focused mainly on Smithson School (bottom row) and wanted to have that as the most local of the locales. However, the innovation was also implemented in other schools (next row up).
And events could be sorted into district and state/macro levels, which, in turn, influenced the lower levels.
An exploratory interview question asked people to describe the history of the innovation (“Can you tell me how SCORE-ON got started in this school?”). Follow-up probes fleshed out the sequence from innovation awareness to adoption, how and by whom key decisions were made and the reasons involved. Other questions dealt with outside agencies and events and “anything else going on at the time that was important.” Similar questions were asked about events during the implementation process.
The analyst looked at coded field notes (here, the codes are any that include the subcode CHRONOLOGY) and extracted accounts of specific events, such as “4th grade teachers report 40 pupils 1-3 grade levels behind” or “officials see SCORE-ON at ‘awareness fair’.” The analyst defined an event as a specific action or occurrence mentioned by any respondent and not denied by anyone else. If at least two people said the event was important, crucial, or “made a big difference”
to what happened subsequently, an asterisk was assigned to designate it as a “barometric event.”
Analysis
A quick scan across the display shows us that the process of change is strikingly rapid. A problem seen in one elementary school in the fall of 1978 by the fourth-grade teachers apparently leads to the discovery and introduction of an innovation (SCORE-ON) that was in place in five district schools by the fall of 1979.
A look at the asterisks helps explain some of the speed: the active involvement of central office officials after they saw the innovation at an awareness fair, leading to justificatory events such as the pupil folder screening and to specific school-level planning and the appointment of specific teachers to manage the remedial laboratory. State-level competency requirements were the backdrop, and the teachers’ report of problems was probably an alarm or trigger that set off actions already fueled by concern at the district level about meeting state requirements.
When we note the repercussions of an externally driven budget crisis during the latter school year (September 1979–May 1980), we can infer that the original availability of Title I funds might have played a strong part in the original changes.
These are plausible hunches about the meaning of the data in Display 8.1. To check them out, the analyst can piece together a focused narrative that ties together the different streams into a meaningful account, a narrative that could only with difficulty have been assembled—or understood—from the diverse accounts spread through the field notes. Here are some excerpts from the focused narrative the analyst produced. They should be read in conjunction with Display 8.1:
A special impetus was given in the fall of 1978, when the six fourth-grade teachers at Smithson noticed that they had an unusually large cohort (40) of incoming pupils who were one or more grade levels behind in reading achievement. . . . Thirty- eight of these forty had come out of the [existing] FACILE program in the first to third grades. It is not clear how so many of these pupils got to the fourth grade, but no one was surprised. . . .
The teachers were worried that either promoting or retaining so many pupils would cause problems; they were leaning
toward retention, but feared a massive protest by parents. Essentially, they were covering themselves by announcing early in the year that they had inherited, not created, the problem. . . .
During this phase, a circular announcing Federal funding . . . came to the central office from the State superintendent. An awareness conference, presenting a series of projects, many of them keyed to remedial skill development, was to take place nearby. At Mrs. Bauers’ initiative—and with an eye to a solution for the problem at Smithson School—a contingent from the central office (Mrs. Bauers, Mrs. Robeson, Mr. Rivers) attended the presentations and was attracted to SCORE-ON. It seemed a relatively flexible program, easy to integrate into the school in pull-out form. It was directed specifically to the bottom quartile in reading and math.
Note several things here: (a) the narrative, which is both straightforwardly descriptive and analytic, helps knit together and flesh out events at different levels of the chart, (b) the analyst can add explanatory conditions or states that show how one event led to another, (c) the return to the field notes often turns up other critical events or supporting information not originally in the display, and (d) the narrative is more understandable when read in conjunction with the display, and vice versa.
When the first version of the display is filled in, start a draft of a focused narrative. That step will require you to return to the field notes as you go. Stay open to the idea of adding new events to the listing or subtracting events that seem trivial or irrelevant.
For a careful reconstruction, the events in a listing can be dated within cells. Time periods can be specified much more narrowly or cover a very brief time span (e.g., 1 hour in a classroom). Events from a listing also can be shown as a network-like flow that includes more general states or conditions, such as “lack of enthusiasm” (see “Event–State Network” later in this chapter).
Barometric or significant events in cells can be color coded in red to highlight their importance during the at-a-glance review.
The problems we face in understanding event flows are those of sorting out the different domains of events, preserving the sequence, showing the salience or significance of preceding events for following events—and doing all of this in an easily visible display that lets us construct a valid chronology. The event listing helps ground the analyst’s understanding of a complex flow of events, especially for longitudinal qualitative studies, and increases confidence in the associated chronological account. It also lays the basis for the beginnings of a causal analysis: what events led to what further events and what mechanisms underlay those associations (see Chapter 9).
Notes
Event listings can be limited much more sharply to “critical incidents,” defined as important or crucial, and/or limited to an immediate setting or compressed time frame. These matrices can be done at many different levels of detail, but keep the rows to a maximum of four or five levels, and be sure they represent a meaningfully differentiated set of categories. Do not go finer than the study questions dictate.
Even more selectively, events can be shown as a flow limited to an individual’s major events, each demarcated and connected with the causal pushes that may have moved the process from one event to another. Display 8.2 shows a diagram adapted from display work models by Pillet (personal communication, 1983).
The case here is one of Saldaña’s (1998, 2003, 2008a) longitudinal qualitative studies of a young man from kindergarten through his late 20s. The successive Educational and Occupational experiences are indicated in the left column; at the right, we see the researcher’s summary of the Personal major crises and forces moving concurrently throughout the education and work history of the case studied. The researcher uses this not just as an event-listing chronology but as a visual chronicle of significant periods and epiphanies from a young life.
Growth Gradient Description
A growth gradient is a graphic display that illustrates the amounts, levels, or qualities of changes across time through the use of points and links accompanied with text (see Display 8.3).
Applications
Display 8.2
Event History of a Case Study
Events can sometimes be conceptualized as associated with some underlying variable that changes through time. That variable can serve as the purpose for or central theme of a growth gradient. The illustration provides a long-term picture of a process or a cumulative, “connect the dots” map of related events.
A growth gradient tells the story of a variable’s journey across time. So it is particularly appropriate for qualitative longitudinal or evaluation studies, for ethnographies, and especially for those research projects with a mixed-methods component.
Example
I n Display 8.3, we see a simple network display designed to show the growth gradient of an innovation’s use in one case for our (Miles and Huberman) school improvement study. The network is ordered chronologically, with five distinct and separated periods. The vertical dimension shows the numbers of users, and the horizontal dimension represents time. The points or nodes are noteworthy events, and the lines or links have the implicit meaning “is followed by.” Each point is labeled with a more specific month and sometimes a date to mark an event that seemed to the analyst significant to the innovation’s implementation and history.
Analysis
Here the analyst is interested in the main variable, internal diffusion (spread) of an innovation, defined as growth in the number of teachers using it. That variable is represented in network form as a single line between points. But the analyst has attached various critical events to the line—
appointments of key personnel, training, and the like—that help expand our understanding of the movements of the main variable. You can get a clear idea of the tempo of expansion and can see which events were especially critical (e.g., the August 1 workshops in 1977). More generally, you can see that workshops appear to be the main mechanism for expanding use of the innovation.
The growth gradient also reveals that it took between 4 and 5 years in the 1970s to achieve
The growth gradient also reveals that it took between 4 and 5 years in the 1970s to achieve
“extensive” use of the innovation across various school sites. Some administrators may perceive this as a typical time frame for substantive change to occur and declare the innovation project a success.
Other administrators, especially in the fast-paced 21st century, may interpret this as a too slow- moving process that, next time, might be integrated more rapidly into the curriculum through earlier workshop presentations, strategically scheduled right before the school year begins.
Growth gradients can map out not just increases but also decreases, stability, surges, turning points, the erratic, and the idiosyncratic through time (Saldaña, 2003). These patterns are particularly revealing when they seem to emerge gradually or accumulate considerably. You can also map out two or three variables at the same time on a growth gradient, which may reveal some interesting interrelationships and possibly causation factors at work (see Chapter 9).
At least one axis of a growth gradient is time, and the other axis is a range, continuum, or dynamic of some type, be it numbers (1, 2, 3), general amounts (few, some, many), evaluative measures (poor, satisfactory, excellent), frequency (rarely, sometimes, often), direction (negative, neutral, positive), intensity (weak, moderate, strong), position (conservative, moderate, liberal), quality (fractured, ambivalent, unified), and so on. The items you place on nodes in a growth gradient should be related in some way to the primary variable you’re examining. The brief event phrases you place on the nodes should be “just enough” to help you properly interpret changes and turning points in the historic timeline.
Notes
Don’t be reluctant to use what may seem like a quantitative method with qualitative data. The growth gradient is an effective application for simultaneously assessing long-term quantitative and qualitative change. See Belli, Stafford, and Alwin (2009) for calendar and time diary methods for long-term data collection, management, and analysis of qualitative data.
Time-Ordered Matrix Description
A time-ordered matrix has its columns arranged chronologically by time period to determine when particular phenomena occurred. Row contents depend on what else you’re studying. This matrix is somewhat comparable with the event-listing matrix profiled above, but the time-ordered matrix emphasizes sequence, timing, and stability of processes and experiences (see Display 8.4).
Display 8.4
Time-Ordered Matrix: Changes in the CARED Innovation (a Work Experience Program)
Source: Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.). Thousand Oaks, CA: Sage Publications.
Applications
With qualitative data, you can track sequences, processes, and flows, and are not restricted to
“snapshots.” The time-ordered matrix displays time-linked data referring to phenomena that are bigger than specific “events,” so as to understand (and perhaps later explain) what was happening.
Use a descriptive time-ordered matrix like this when your data are fairly complete, to begin developing possible explanations that can be tested by moving back to the coded field notes.
Example
In our (Miles and Huberman) school improvement study, we were concerned with how an innovation changed and transformed across time during several years of implementation. We predicted that most innovations would show such changes as they were adapted to the needs of users and the pressures of the local situation.
We broke down the innovation into specific Developer Components or Other Aspects, using these as rows of the matrix. The columns of the matrix are time periods from early through later use. If a change in a component occurred during the time period, we could enter a short description of the change. A blank cell would mean no change—a nice feature that permits seeing stability, as well as change.
Display 8.4 shows how this matrix looked. The innovation, CARED, is a work experience program for high school students. The official components were those specified by the original program developer. These Developer Components do not necessarily exhaust important aspects of
the innovation, so there are rows for Other Aspects, such as time and credits or student selection.
Such aspects usually appear after initial fieldwork and direct experience with the use and meaning of the innovation.
The columns are time periods, starting with the initial planning period (because we expected changes while this relatively demanding and complex innovation was readied for use). The three succeeding school years follow.
In this case, the analyst was looking for changes in the innovation, component by component.
Those changes could be found in the coded field notes, where innovation users were asked whether they had made any changes in the innovation’s standard format. Follow-up probes asked for parts that had been added, dropped, revised, combined, or selected out for use. We used the decision rule that if a reported change was confirmed by at least one other staff member and not disconfirmed by anyone else, it should be entered in the matrix.
Analysis
Only a few analytic observations culled from the matrix are described below.
Looking across the rows of Display 8.4, you can begin to see drifts or gradual shifts expressing an accumulated tendency underlying specific changes. For example, the row “Program requirements/curriculum” shows an increasing tendency to make stiffer achievement demands on students (the tactic here is noting patterns, themes—see Chapter 11). The component “Student responsibility and time use” suggests that a process of exerting more and more control over student behavior is occurring (e.g., the accountability scheme, the system of passes, etc.).
At this point, the analyst can deepen understanding by referring back to other aspects of the field notes, notably what else people said about the changes or the reasons for them. In this example, a staff member said, “Your neck is on the block . . . the success and failures of the students rebound directly on you.” So the increased emphasis on control might come from the staff’s feelings of vulnerability and mistrust of students (tactic: noting relations between variables).
What else is happening? We can note an important structural shift in the second year: moving away from random student selection to self-selection. The field notes showed that this decision was precipitated by principals and counselors who opposed entry by college-bound students and wanted the program to be a sort of safety valve for poorly performing, alienated students. Thus, the program became a sort of “dumping ground” or “oasis” (tactic: making metaphors) for such students. But look at the “Program size” row. Though the program doubles in the second year, it cuts back substantially in the third year. In this case, severe funding problems were beginning to develop (tactic: finding intervening variables).
The report could either contain the analytic text, pulling together the strands we just wove, or present the table along with it. But Display 8.4 may be too busy and unfocused for the reader—it is more an interim analysis exhibit than a report of the findings. One way of resolving these problems is to boil down the matrix to (a) verify the tendencies observed in the initial analysis and (b) summarize the core information for the researcher and the reader.
Display 8.4 could be condensed in myriad ways. One approach is to standardize the several drifts by naming them—that is, finding a gerund such as controlling or tightening up that indicated what was going on when a change was made in the innovation (tactic: clustering) and then tying that drift to its local context, inferring what the changes mean for the case. The result appears in Display 8.5 as a summary table.
Reading the Tendency column and using the tactic of counting the number of mentions for each theme confirms the accuracy of the initial analysis. The core themes are, indeed, stiffer achievement demands (“Going academic”), more control, increased routinization (“Simplifying”), and reduced individualization (“Standardizing”). You might even try for an overarching label to typify the set—
something like “Self-protective erosion,” thus subsuming particulars into the general—and this