Inferential statistics: concepts and applications

¶ … inferential statistics? What are the differences? When should descriptive and inferential statistics be used?

Descriptive and inferential statistics: Summary explains the similarities and differences between descriptive and inferential stations and when each method should be used. Descriptive statistics comprises the kind of analyses to describe a study population that is small enough to include every case. Descriptive statistics can also describe the actual sample under study, but allow a researcher to extend conclusions to a broader population.

With descriptive statistics, a researcher can describe how issues affect study groups and how variables are related in to other study groups. However, the research cannot describe how those issues affect the members of the study groups and how these variables are related in those groups. Furthermore, the researcher would not be able to conclude how the results could be generalized to all groups and would not know where the groups in the study were representative of all groups.

These shortcomings of descriptive statistics are where inferential statistics come into play.

Inferential statistics extends conclusions to a broader population by making sure the study if representative of the group the researcher wishes to generalize to. This is accomplished by choosing a sample that is representative of the group to which the researcher plans to generalize. Tests of significance confirm generalization. A Chi-Sqaure or a T-Test tells the researcher the probability that the results found in the study group are representative of the population that group was chosen to represent. Chi-Sqaure or a t-test gives informs the researcher of the probability that the results found could have occurred by chance when there is really no relationship at all between the variables you studied in the population.

What are the similarities between single-case and small-N research designs? What are the differences? When should single-case and small-N research designs be used?

Cooper, Heron, and Heward (2007) explain single-case and small-n research designs. These are most often used in applied fields of psychology, education, and human behavior in which the subject serves as his/her own control, rather than utilizing another individual/group. Researchers utilize single-case and small-n designs because they are sensitive to individual organism differences vs. group designs which are sensitive to averages of groups. Small-n research includes more than one subject in a research study, but the subject still serves as his/her own control just like in the single-case design.

Single-case and small-n research have three major requirements (Kazdin):

Continuous Assessment: The research repeatedly observes the behavior of the individual over the course of the intervention. Thus, any treatment effects are observed long enough to convince the researcher that the treatment produces a lasting effect.

Baseline Assessment: Before the treatment is implemented, a researcher looks for behavioral trends. If a treatment reverses a baseline trend (e.g., things were getting worse as time went on in baseline, but the treatment reversed this trend) this is considered powerful evidence suggesting (though not proving) a treatment effect.

Variability in Data: Because behavior is assessed repeatedly, the single-subject/small-n design allows the researcher to see how consistently the treatment changes behavior from day-to-day. Large-group statistical designs do not typically provide this information because repeated assessments are not usually taken and the behavior of individuals in the groups is not scrutinized; instead, the research reports group means.

Single-subject research is the extreme case of small-n research in that a single-subject design uses only one case or one group to investigate a specific phenomenon while small-N research. Small-N designs my actually produce worse results than single-case designs (Comparative qualitative research methods). Attempts to boost N. may lead to poor estimation of causal effects because additional cases may not be comparable. A larger N. imposes a heavy burden for data collection, especially if a question is new or understudied because it is not know if collaborative research can add up to a whole.

What are true experiments? How are threats to internal validity controlled by true experiments? How are they different from experimental designs?

In true experimental research, the researcher not only manipulates the independent variable, but also randomly assigns individuals to the various treatment categories (i.e., control and treatment) (Research methods).True experimental design employs both a control group and a means to measure the change that occurs in both groups. In this way, true experimental research attempts to control for all confounding variables, or at least consider their impact, while attempting to determine if the treatment is what truly caused the change. Note that individual background variables such as sex and ethnicity do not satisfy the requirements of true experimental design since they cannot be purposively manipulated in this way (Practical assessment research and evaluation).

True experiments are different from experimental design in that they are the only experiments that allow researchers to make causal conclusions based on study results and, therefore, provide greater internal validity (True experiments). It is only through random assignment that researchers can be assured that groups are truly comparable and that observed differences in outcomes are not the result of extraneous factors or pre-existing differences (Practical assessment research and evaluation). This means that the researcher needs so have control of the situation to have a reasonable chance of saying factors X and Y really affect outcome Z (True experiments). Internal validity is controlled in true experiments by assigning subjects to conditions randomly (i.e., only by chance can other variables be confounded with the independent variable) as well as controlling what, when, where, and how by controlling the way the experiment is conducted (True experiments - single-factor designs) through the use of control groups, random assignments to control and experimental groups and random assignments of groups to control and experimental conditions (True-experimental designs).

What are quasi-experimental designs? Why are they important? How are they different from experimental designs?

Practical assessment research and evaluation explains the quasi-experimental design. It consists of administering an outcome measure to two groups or to a program/treatment group and a comparison. For example, one group of students might receive reading instruction using one type of program while the other receives a different type of program. After twelve weeks, a reading comprehension test can determine which program was more effective.