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Definition of Statistics

Statistics can be defined in a layman’s language as the science that deals with the collection and analysis of information that is in numbers. This paper endeavors to answer some statistics-related questions, including similarities and differences between descriptive and inferential statistics, case study method, and single subject experimental designs, small-N and quasi-experimental designs.


Descriptive and Inferential Statistics

Pagano (2008) defines descriptive statistics as the analysis that is used when a research is conducted with an intention to describe a certain population. In such a case, the population is normally kept small enough to enable the consideration of a number of parameters. On the other hand, Pagano (2008) defines inferential statistics as the analysis that are done when the researcher wants to infer or generalize the data. In inferential statistics, the researcher makes generalization from the study of a sample population.

Similarities and Differences between Inferential and Descriptive Statistics

Pagano (2008) identified a number of similarities between inferential and descriptive statistics. He noted that in each case there is a collection of data, evaluation, and deduction of basic information like mean, variance, and standard deviation of the populations the researcher is studying. Pagano (2008) also noted that the two use a similar combination of methods to represent the study findings. Such representation methods include; tables, graphs and statistical discussions.

However, the two statistics have a number of differences. Pagano (2008) noted that descriptive statistics describes a population whereas inferential statistics gives a generalization of a much bigger population from the findings of a sample population. In addition, unlike is the case with inferential statistics, the population for descriptive statistics must be small enough so that all the parameters can be included in the analysis. Finally, whereas descriptive statistics is a description of, let’s say, people, inferential statistics is a deduction of what these people might be thinking (Pagano, 2008).

Davis (2003) added that descriptive statistics are used in describing the main features of the data being studied while inferential statistics are used for the generalizations that are more than the sample data. He further noted that inferential statistics is also used in trying to infer what the population might be thinking from a sample data. It is, therefore, useful in judging the probability that a difference observed between groups is dependable or it occurred by chance.

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Case Study Method, Single-Subject Experimental Designs, and Small-N Research Designs

According to Davis (2003), case study research method is an investigative research that seeks to make inquiries into contemporary issues in a given context. It is mostly used in cases where there are no evident boundaries between the context and the issues. Ground breaking research must have a variety of sources and as such, this kind of research should be extensive. This method creates an understanding of complex issues and, also, strengthens the existing knowledge of topics that had been researched on previously. On the other hand, Davis (2003) explains that the single-subject experimental design or the single–case experimental research design is a kind of study in which the subject or organism under the study serves as its own control. The single subject experimental design is normally used to improve on the case study research design. It is mostly applied in the scientific field, psychology, human behavior, and education.

Similarities and Differences between Case Study Research Design and Single-Case Experimental Design

Kabe & Gupta (2007) noted that both two methods are involving and extensive. Like case study, single-case experimental research design has previously found applications in various fields but they are popularly used in the scientific and psychology disciplines. Their major difference is that case study can be used for studying more than one subject whereas single-subject experimental research requires only a single subject, which also serves as the control experiment.

The Use of Case Study and Small–N Research Designs

Kabe and Gupta (2007) explain that the case study has found application in many fields, especially where an understanding into a complex phenomenon of life or where further knowledge is required. They point out that small-N research design is used when minute details of behavioral change and performance of an individual are the central point of interest of the researcher. It is also used in a case where the researcher is interested in a specific subject or in cases where the experimentation is difficult and there is a limited number of subjects to be researched on.

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True Experiments and Its Internal Validity Control

According to Surhone, Trimpledon, and Marseken (2010), true experiments are the research methods that involve both the dependent and independent variables. They noted that true experiments are mostly applicable in social sciences. It involves the manipulation of the independent variable while measuring the dependent variable. They further explained that the subjects in true experiments are randomly allocated in a bid to reduce the chances of experimenter bias.

According to Surhone, Trimpledon, and Marseken (2010), these experiments have very many limitations compared to their advantages. Some of their limitations include experimenter biasness during sampling and difficulty in controlling all the variables. Additionally, in the cases where the purpose of the experiment is to assess the impact of a program, the experimental frameworks will be constrained by the feasibility and logistical issues. Besides that, in natural settings, such experiments are liable to obstacles, such as the difficulty in obtaining permission to conduct the experiments. For example, people may object an approach in which only those who are randomly chosen are treated.

The major advantage of true experiments is that they control threats to internal validity of the experiments. Such threats to internal validity are confounds that can be used as possible alternatives for research findings. They include: instrumentation, history, subject attrition, testing, regression, selection, additive effects with selection and maturation. All these threats can be controlled using true experiments by having researchers ignore them when making causal inferences. However, certain threats like Hawthorne effects can not be controlled by true experiments. Their effects arise when people’s behavior change due to a feeling that the researchers are interested in them. Such a condition may also arise in a situation where the participant groups share experiment information, especially on their expectations. (Surhone, Trampled & Marseken, 2010).

Quasi-Experimental Designs

According to Hansen and Klopfer (2006), quasi-experimental design is a kind of experiment in which the experimenter does not have any or have little control over the allocation of treatments to the subjects under study. This implies that there is no random assignment of treatment to participants. Quasi-experimental designs are meant to serve as an alternative in situations where true experiments are impossible. Even though it does not use random sampling, quasi-experiments are more efficient in lowering threats to internal validity than true experiments. According to Hansen and Klopfer (2006), the major threats to quasi-experimental design are the confounding variables. However, the two noted that the experiment can be designed in a way that enables them to reduce the effects of these threats.

Researchers have successfully come up with four quasi-experimental design approaches, which are presently in use. These include: mixed designs, matching, single subject designs, and developmental designs (Pagano, 2008). There are also five quasi-experimental designs that have found different applications in statistics.

Importance of Quasi-Experimental Designs

Quasi-experimental designs have been found to be advantageous because they do not pose much difficulty in their set up like in the case of true experiments. They also minimize threats to external validity. In addition, their findings can also be applied to other studies of similar requirements because they are carried out in natural settings. Quasi-experiments can, therefore, be used where true experiments are not applicable. These include such situations in which the participants’ assignment is uncontrollable by researchers or those in which the independent variable cannot be subjected to manipulation (Davis, 2003).

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Differences between Experimental Designs and Quasi-Experimental Designs

Pagano (2008) points out that there are minimal differences between experimental designs and quasi-experimental designs. He noted that the two are supportive of each other such that when one is not applicable in a given situation, the other serves as an alternative. For instance, quasi-experimental design serves as an alternative where true experiments can not be applicable. However, the major difference between the two is that there is no random assignment of participants in quasi-experimental designs.


In conclusion, it is clear that statistics presents an array of methods for the researchers to choose from in accordance with the kind of study they are undertaking. Otherwise, statistics in itself is so wide that it can be very confusing to those who are not well-conversant with these scientific methods.

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