When we conduct a study using cross-sectional design, we take a group of samples from a set, or continuum, to see if there are any differences in the section of the continuum. For example, say we wanted to conduct a study examining the differences in behavior between children of different age groups. We would define children as the continuum and the different age groups as the different sections within the continuum, and these sections, we can call cohorts. We could even more specifically conduct the study to see if children of different age groups have different social strategies. So, in order to conduct such a cross-sectional design study, we would choose children from different age groups, such as ages 5, 10, and 15 to examine how children's behavior changes over time. We would also have to make the assumption that the children in the younger age groups will behave in the exact same ways as the children in the older age groups (Devin Kowalczyk, "Cross-Sectional Designs: Definition & Examples"). In other words, 5 year olds will soon do what 10 year olds do, and 10 year olds will soon do what 15 year olds do. A cross-sectional design is considered a quasi-experiment as opposed to a true experiment. In order for an experiment to be considered true, the experiment must use "randomly assigned groups so that everyone has an equal chance of being in the experiment or control group" (Chapter One: "Issues in the Use of Longitudinal and Cross-Sectional Designs"). In contrast, quasi-experiments make use of "naturally formed groups" as opposed to random groups (Kowalczyk). To conduct a study examining the different social strategies of children using cross-sectional design, we select a large group of children of specific age groups and then run a series of tests on social strategies. It's important that the group be large enough in order to eliminate developmental and cultural differences becoming part of the variables. If the group is large enough, we gain a better perspective of what the average outcomes are, which helps us better establish the control groups within each age group. Once we have our results, we then cross-compare the different age groups to observe the differences in behavior. Using a cross-sectional design has one advantage in that a study can be conducted in a shorter amount of time as opposed to waiting for a group of 5 year olds to reach the age of 15 and observe the changes in social behavior over the course of 10 years (Kowalczyk). However a cross-sectional design also has quite a few shortfalls in that some assumptions must be made, and a longitudinal design can overcome that.
A longitudinal design is a research method in which one group of people is studied over a long length of time in order to observe the changes. One example is that we might want to study how television viewing affects human development over time. To conduct such a study, we would choose one large group of people, such as 3 year olds, conduct a series of tests and asks a series of questions to see how television viewing is currently effecting the 3 year olds, collect their contact information, and then invite the participants to return for another study after a certain length of time, such as a year or two. When the participants return, more tests are conducted and more questions are asked with the purpose of determining if any changes in the participants can be seen as a result of television viewing. More specifically, say we are examining if a television program increases or decreases violent behavior over time. We would run a series of tests to determine how violent the subjects are currently. The subjects would log how much time they spend watching the program, and then every month for a year, or for as long as the program runs, the subjects would be tested again to see if there are any changes in violence (Kowalczyk, "Longitudinal Designs: Definition & Examples"). Conducting longitudinal studies makes it much easier to attribute causes to observed phenomena because no assumptions need to be made about causes, such as the assumption that age contributes to behavior and that a 10 year old will soon be acting like a 15 year old. However, longitudinal designs can also be considered quasi-experiments and validity can often be questioned in terms of "selection, attrition, instrumentation, and regression to the mean" ("Issues"). One way to avoid the problems caused by both cross-sectional designs and longitudinal designs are to combine the two.
The sequential design is actually a combination of both a cross-sectional design and a longitudinal design. Using a sequential design, we study several cohorts, or age groups, over a long period of time. Sequential design is a combination of both cross-sectional design and longitudinal design in the following ways: (1) Using cross-sectional design, we study a bunch of different groups immediately; (2) using longitudinal design, we study one group over a long period of time; but (3) using a sequential design, we study a bunch of different groups over a long period of time. In particular, using a sequential design, we study a bunch of different groups over a long period of time in order to observe the changes between groups over a long period of time (Kowalczyk, "Cross-sectional, Longitudinal & Sequential Designs: Advantages and Disadvantages").