Cecil Thompson

SR 958-52

Omega Graduate School

Prof. Sean Taladay, Ed.D

May 2, 2024

Assignment #1 – Core Essential Elements

Assumptions Testing and Data Distributions: When conducting assumptions tests on a dataset, what are the key assumptions researchers need to evaluate for parametric statistical tests? How can data distributions, as depicted in histograms and box - whisker plots, help researchers identify potential violations of these assumptions and make appropriate decisions for data analysis?

Parametric vs. Nonparametric Procedures : Explore scenarios where researchers might choose parametric procedures (e.g., t - tests and Pearson's r) or nonparametric equivalents for hypothesis testi ng. What factors influence this decision - making process, and how do these statistical procedures differ in robustness to violations of assumptions and data characteristics?

Purpose and Structure of Literature Review : Investigate the significance of the literature review in a research study. How does it contribute to developing research questions, identifying gaps in existing knowledge, and establishing the study's theoretical framework? Discuss how a well - structured literature review strengthens the overall foundation of a research project.

1.There are certain common assumptions that researchers tend to make when conducting

parametric statistical tests. The main assumptions they make, and seek to validate through these tests, are those that have to do with the “shape” of the distribution (e.g., normal or skewed distribution) of their selected population and the manner in which the data are “dispersed” (e.g., standard deviation, etc.). If the researcher were to make an assumption that the dataset is normally distributed, the sample mean and the median should, predictively, be very nearly equal. The question is, how can the researcher determine in advance, whether the assumptions about the shape and spread of the data are correct?

There are two ways in which one could visually determine whether the researcher’s assumptions about the shape and the spread of the data are valid. If the dataset is represented graphically, in the form of a histogram or a boxplot, the researcher would be able to verify the truth of his assumptions by the general shape of the histogram or the boxplot, and hence, by the closeness between the value of the mean (s) and the median(s), in either one, or both of these graphs.

2. I believe that in order to explore scenarios that exemplify when it is applicable to use

either parametric or nonparametric procedures, one should first attempt to define the two forms of statistical procedures in respect to their similarities or differences. In Tanya Hoskin ‘s (n.d.) effort to define the two statistical procedures apart, she cites the Handbook of Nonparametric Statistics I (THNS 1) as saying that “A precise and universally acceptable definition of the term ‘nonparametric’ is not presently available’ (THNS 1, 1962, p.2).”

After more than four decades as an educator, I have grown fairly comfortable with the conviction that the best way to define a thing, especially an abstraction, is to do so in terms of how its behavior render it both analogous and antithetical to some other thing. Hoskin claims that in order to acquire a practical intellectual grasp of the nature of “parametric” and “nonparametric” procedures, one must first obtain a complete working knowledge of the essential statistical substrates that underlie the two statistical procedures in question. Such statistical substrates would naturally include, random variables, probability distribution, parameters, population sample, sampling distributions, and the Central Limit Theory. She further argues that, since it is not possible to explain these topics in under three chapters in a statistics textbook, it is necessary to explain them by showing how they are connected to one another (Hoskin).

However, Hoskin (n.d.) goes on to say that nonparametric procedures belong to a category of statistical procedures that does not depend on assumptions “. . . about the shape or form of the probability from which the data were drawn” (Hoskin). Thus, it seems that this statement of Hoskin’s is as good a definition of the parametric procedure as any. For, by inference, unlike the nonparametric procedure, the parametric statistical procedure is one that relies upon assumptions about what the shape and spread of the data drawn from a particular population might look like.

Since researchers are not able to extract information from every member of a particular population, in their effort to try to find the answer to a specific question about it, they are forced to draw the closest possible representative sample from the population they are studying. In so doing, statisticians make assumptions about the shape and the spread of the sample data. This is done in an effort to narrow down the information gathered to fit the population in a general way. But because there is no certainty that the assumptions made will pan out, the statistician must rely on the conventionally accepted statistical gages that confines the findings from the data to the most “centralized tendencies” that reflect the character of the population, as a whole. In that way, the statistician has to rely heavily on the usual statistical measures such as the mean, median, standard deviation, proportion, etc. These measures serve as the “parameters” by which the assumptions will have to be validated (Hoskin). So, by using these “parameters” in the attempt to determine the accuracy of the assumptions, the statistician is, in effect, applying a “parametric” procedure.

In one example, a researcher has chosen to conduct an experimental study with the intent of establishing that a particular trait or behavior is native to a select population placed under a certain specific condition. A sample of 100 individuals is picked at random. And from it, two theoretically representative groups are also selected at random. Without their knowing what is being administered to the members of each group, one group is given a “treatment” and the other group is given a “placebo”.

The statistician “assumes” that, in the case of the experimental (treatment) group, the spread of the sample data will cause the amplitude to be roughly in the center of the frequency distribution, and the mean will be in the center, at zero. The statistician’s overall assumption for this group, then, would be that the distribution of its sample data is normal, and the median would spread out equally from the mean, to the left and to the right (-34% and 34%) of the center.

In relation to the “placebo” group, the statistician would have made the assumption that the distribution would be skewed. And, as such, the amplitude of the frequency would be either left or right of center, and the mean and median would not be “coincidental”. The parametric test to be applied, in this case, where there are two distinct groups, would be subjected to the “Two-sample t-test”. In the meantime, if this were tested as a nonparametric procedure, the test applied would be the “Wilcoxon rank-sum test”.

In this other example, a research situation is set up in which the level of association between two quantitative variables in a single group is being studied. If this is a “function” type association, the concern would be about the strength of the “relationship” that exists between independent and dependent variables within that single group. An exemplary research study for this situation could be one in which the researcher is seeking to determine the extent to which the “aspiration-gap” for K-12 Black students, who are taught mostly by White teachers, widens with the increase of White teachers and the decrease of Black teachers. If the statistician assumes a normal distribution, here, the value of the parameters (mean and median) should be close.

Here, the strength of the relationship between the independent and dependent variables would be indicated by the value of the correlation coefficient. The test used to find the correlation coefficient under the parametric procedure is the Pearson r. Beyond that, the statistician chooses to add on “effect size” testing —Eta2. However, when done from the point of view of the nonparametric procedure, the applicable test would be Spearman’s Rank Correlation.

3. Galvin (2014) explains that the three most probable reasons for writing a "Literature

Review", when looking at them as a collective whole, are the ways in which they are cemented together into a single base upon which the larger work (the dissertation) is built. He writes that the literature review, first and foremost, is a direct extension of the proposal in its labor to set up a link between prior research in subject and the dissertation in question. Secondly, it is the means by which to bring clarity and relevance to the research questions. And finally, the literature review provides an overview of the topic. In these three ways, it demonstrates how thorough a command the researcher must possesses about the work in his field of study (Galvin, 2014, pp. 11-13).

Galvin (2014) tells us that Chapter 2 of the thesis or dissertation is completely devoted to the Literature Review. Amid the several other functions, beyond the three above, the Literature Review serves the overarching function of justifying the dissertation’s raison d’etre (the purpose for the research). At this higher level, the Literature Review, as with the rest of the thesis or dissertation, must be edited to the point of near perfection. For that reason, Galvin says, there has to be a "self-editing checklist” that the researcher and his committee follow (Galvin, pp. 13-15). So, moving forward, the question is, “Where should I begin?”

He says that the person doing a Literature Review should consider writing a description of the topic and a "working draft of the reading list." The researcher who is setting up the machinery for writing a Literature Review most already have established a broad all-encompassing topic to be later narrowed down so that it can be used as a tool to help select the pieces that are going to be the basis of the review (Galvin, p. 17).

As soon as the researcher has decided on this general topic, he may want to proceed in the order laid out through the fourteen steps below. The steps laid out in the precise order are: (1) Databases-- eg. ERIC, PsycINFO and Sociological Abstracts (2) Shorten the reference list if it's too long (make revisions based on a sample search from the databases), (3) “Increase the size of the reference list, if necessary” by using "descriptors"--eg., teacher-hiring AND disparate-impact (4) “consider searching for unpublished studies--eg., Web of Knowledge, PsychINFO, Dissertation Abstract International (5) With the first draft of the topic statement. This should be a “descriptive phrase”. (6) Become acquainted with online database (7) Pick out the database relevant to the field of study (8) Become acquainted with the established databases (9) Start with general "keywords", then limit it--eg., school AND segregation, teacher AND diversity (10) Narrow down the topic (11) Select the most current research and work backwards (12) Search for theoretical articles (13) Search for “review” articles (14) Identify Seminal works and theories such as "stereotype threat" (Galvin, pp.17-22).

After identifying the first set of articles and texts that are supposed to constitute the literature review, each piece should then be analyzed individually. A working draft of the list of works should be done. Then, for each article or work there should be a set of index cards with relevant details (annotations) about the pieces of literature collected. Following this, the researcher should read the titles of each article, their abstracts, the first couple of paragraphs of two or three of the articles and identify the problem in each piece. The researcher should, then, read the last paragraph prior to the “method”. At this point, he or she should state his or her hypotheses, and/or research questions. Actually, this is the so-called section of the research which will give the researcher the tool to “pre-read”. And thus, the researcher will be able to break down the collected articles into categories.

The major headings one should expect to find in a journal article are:

Title: followed by the authors name and institution

abstract

method

Participants

Measures (Instrumentation)

Results

Discussion

In almost all such articles, “discussion” will be the final heading. From then, the

articles should be organized into categories. Before the researcher begins the actual writing, he should assemble all his tools including a computer, a pack of index cards, together with self-adhesive flags. He should, then, summarize the articles, Next, he should locate definitions of key terms, identify statistical information to be used at the beginning of the review, please a heading on the index card, and finally, pull out the most pertinent pieces (Galvin, pp.30-'4).

In reading the pieces, the researcher should distinguish between mere assertions

and evidence. He should identify the main trends or patterns in past studies. All gaps in each piece of literature should be identified as well as the manner in which parallel or opposing points are expressed from one to the other. It is also recommended that, with the exception of seminal works, or trends that are needed to support the historical basis of the problem (background), the pieces should be selected from literature within the last five years (Galvin, pp.34-41).

First, the reader should be able to determine if an article is quantitative simply by

recognizing whether or not the "results" section deals primarily with statistical data. Over the past century, quantitative research recognizable by the way it reduces data to statistics, has been the dominant strain of the two main types of research. And, because of the more rigid scientific process required of quantitative research than of qualitative research, one should expect the writer to show a similar obedience to the "order of operations" convention as a mathematician would. As a result, the research conscious reader should expect to see in the literature that the researcher had adhered strictly to the order below:

1) Hypotheses or Research questions

2) Select a random sample of 30 or less

3) Utilize qualitative measures

a. multiple choice achievement tests

b. forced-choice questionnaire

c. attitude scales

d. presentation

4) Presentation of statistical data drawn from direct sources as well as from

inference (Galvin, p. 45).

Works Cited

Hoskin, Tanya (n.d.). A statistician in the Mayo Clinic Department of Health Sciences

Research who provides consultations through the Mayo Clinic CTSA BERD

Resources.

Galvin, Jose L. and Galvin, Melisa C. (2014). Writing literature review. A Guide for Students

of the Social and Behavioral Sciences. Taylor & Francis Group.

http://taylorfrancis.com