Critical Review of Amanda S. Williams Article: “Worry, Intolerance of Uncertainty, And Statistics Anxiety”
Summary of the Article
The study conducted by Amanda S. Williams is to research and analyze how intolerance of uncertainty and worry are related to the six factors of statistics anxiety. These factors are defined by Cruise, Cash, & Bolton (1985) and include worth of statistics, interpretation anxiety, test and class anxiety, computational self-concept, fear of asking for help, and fear of statistics teacher. Williams (2013) concentrates her research on the three hypotheses:
- Intolerance of uncertainty is significantly correlated with worry in statistics students at pretest;
- Worry is significantly correlated with six types of statistics anxiety at pretest;
- Student level of intolerance of uncertainty, worry, and statistics anxiety will be significantly reduced from pretest to posttest.
To test these hypotheses, Williams administered pretest and posttest questionnaires to a group of 97 graduate-level students taking an introductory statistics course during the 2010 fall and spring semesters in a large southwestern university. The demographic of volunteers was comprised of predominantly white female students halfway through their degree programs– majoring in various fields from educational psychology, to mass communications. The volunteers were issued a questionnaire in efforts to examine how they felt about statistics as well as their self-perceptions in regard to worry, and uncertainty.
Based on the study, Williams concludes that intolerance of uncertainty and worry are significantly correlated. Also, while there is a correlation between worry and statistics anxiety, only three out of six dimensions of anxiety proves to have a strong correlation. The exceptions include worth of statistic, fear of asking for help and fear of statistics teachers. Finally, the study shows that while statistics anxiety is significantly reduced from pretest to posttest, the intolerance of uncertainty and worry is not significantly different. In conclusion, Williams recommends generalizing the results of her study with caution and suggests continuing the investigation of additional variables.
In-depth critique of the article
William’s did an excellent job in differentiating and defining the topics of study and organized it in a simple way to allow for effortless transitions throughout the study. William’s problem is clearly defined and carried throughout the article. It is initially mentioned in the abstract and introduction; supported by literature review; then distinctly stated in the purpose of the study section of the article; reinforced in the methods, instruments, procedures; and summarized in results, discussion and conclusions. This makes it easy to determine that the researcher intends to study the relationship between intolerance of uncertainty, worry and the six dimensions of statistics anxiety.
Williams provides a logically organized literature review. The author starts with the definition of statistics anxiety provided by Cruise et al., and then explains its multi-dimensional construct. She continues with the review of the relationship between anxiety and worry discussed by Onwuegbuzie (1997)., Then Williams completes the literature review with the studies on how intolerance of uncertainty appears to be inseparable from anxiety and worry conducted by Koerner & Dugas (2006), Buhr & Dugas (2002). Thus, Williams offers a balanced critical analysis of the literature ranging from 1983 up to the time of her study in 2010. While some of the references are not recent, it still supports her research and provides valid insights. William’s uses this to compares her findings to existing statistics analyses discussed in her literature review. Thus, Williams was able to develop the research topic, identify the methods of data collection and define any gaps in the existing research and formulate current study questions based on these gaps.
The author makes sure that the focus and objectives of the study are consistent with literature review discussions. Williams defined each term she sought out to investigate at the beginning of the article, which was helpful in understanding her intentions. Each of her hypothesis was also clearly defined and easy to follow.
Ethical Standards Applied
Williams continues with the description of the method used in research. In the study, all 97 students are defined as volunteers. The author provided them with the purpose of the research and assurance that they will remain confidential and anonymous. The researcher achieved that by asking students to mark provided pretest questionnaire envelops with the last four digits of their phone number before returning sealed envelopes upon completion of the questionnaires. This was done to ensure that the same student completes the posttest questionnaire. Therefore, before returning the posttest instruments, the students were asked to destroy the part of the envelope that contained identification information to guarantee the confidentiality, anonymity, and protection from harm. This ensured that the ethical standards were appropriately followed.
The author defines the terms, concepts, and theories used in the research. Most of these are provided in the literature review and are supported with appropriate references. Williams also does a good job providing definitions for acronyms, explaining the scale ranking, and supporting her findings with data tables with proper instructions.
Williams is using correlational research design because it is intended to measure the relationship between variables. While the author does not identify the research design, the reader can define it by examining the research purpose (correlation between variables), analyses and statistical measurements used (Pearson’s r correlation coefficient) and results discussed (correlation between variables). For data collection purposes the author used pretest and posttest questionnaires. Instead of creating new instruments, Williams uses three instruments previously designed by the authors defined in the literature review and described in detail in the instruments section of the article. These instruments are Intolerance of Uncertainty Scale-12 (IUS-12), The Penn State Worry Questionnaire (PSWQ), Statistics Anxiety Rating Scale (STARS) and Multivariate analysis of variance (MANOVA). Besides providing details on the instruments’ origin, Williams also offers sample questions, scale definition, and explains why these questions are relevant to her study and how they can help to achieve the research goal. In addition, the researcher has undertaken the reliability and validity testing and consistently specifies the internal consistency reliability coefficients, Cronback’s alpha reliability coefficient and Pearson’s r coefficients for both pretest and posttest. While given article does not mention a pilot study, Williams is using the instruments that were previously implemented and tested by other researchers. Thus, she compares the results of her validity and reliability testing to the existing results. Finally, the researcher provided an explicit method, instruments, and easy to follow steps of data collection and analyzes.
Williams clearly identified the statistical tests that were undertaken, explained why she used these tests and presented the results in easy to read tables. The author used descriptive statistics to calculate means and standard deviations for research variables. She used Pearson’s r correlation coefficient and applied Bonferroni adjustment to ensure that only significant correlations were defined as significant. These tests helped the researcher to support hypothesis one and partially support hypothesis two. The third hypothesis was tested with multivariate analysis of variance (MANOVA) and was only partially supported due to the intolerance of uncertainty and worry not being significantly reduced from pretest to posttest results. While the author identified a couple of questionnaire items that could skew the results, the overall results were appropriate to support the research question and provide instruments for further analyses and recommendations. Finally, there was 100 percent of the sample who participated in the study which helped to avoid bias and to generalize the results.
The discussion section of the study provided a link between the purpose, literature review and put the study in context. The means and standard deviations, consistency intervals, correlation and MANOVA were calculated among the variables. The results illustrated internal consistency reliability coefficients between 0.85 and 0.91 which indicates a good to excellent internal consistency among variables. The only factor that shows acceptable internal consistency is the relationship between worry and fear of statistics teachers as it is at 0.77 which is below 0.80. The correlation is evaluated on the scale from 0 to 1, where correlation above 0.7 is considered a strong correlation, 0.6 – 0.3 is a moderate correlation, and anything below .2 is considered a weak correlation. Thus, based on the study results, while the first hypothesis was fully supported, the second hypotheses was partially supported as only 3 out of 6 dimensions have the correlation above 0.3. As for the third hypothesis, since the adjusted results indicate the evidence of 4 out of 6 dimensions of statistics anxiety significantly reduced from pretest to posttest, the third hypothesis is also supported only partially.
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The exceptions identified during the study were provided and explained as being related to attitude construct rather than direct construct, and social apprehension construct rather than anxiety construct. While this study provides the start for valuable research, it may need to include other factors not measured in the current study. The author also suggests that the results should be used with caution. Some of the adjustments to the study sample can include more narrowed specific groups to analyze if there is any correlation between group demographic and statistics anxiety. While the sample group is more or less evenly distributed, the majority of the participants are female, white master students. Thus, testing if the standard deviation reduces with the more evenly distributed group can be beneficial. Some other factors that can skew the results can be the field of study, the number of research questions as well as the verbiage. These can be updated, and the study piloted to see if that impacts the results and how. Finally, Williams recommends continuing the research with fewer variables and inclusion of other variables over multiple studies along with the addition of a control group.
Based on all the evaluation categories, the article can be considered well researched. It provides a clear purpose, balanced critical analysis of the literature that is linked to the research methodology, discussion and conclusions. The author follows ethical standards and provides a clear description of the data gathering instruments and analyses. While there are some limitations to this study, recommendations for the further research are provided and foster future research.
The research study concluded with the list of reports, journal articles, books and other media used in the study to support and clarify the research material. All sources were cited adequately including in-text citations and reference page
- Buhr, K., & Dugas, M.J. (2002). The intolerance of uncertainty scale: psychometric properties of the English version. Behavior Research and Therapy, 40(8), 931-945. doi: 10.1016/S0005-7967(01)00092-4
- Coughlan, M., Cronin, P. & Ryan, F. (2008). Step-by-step guide to critiquing research. Part 1: quantitative research. Retrieved from https://lancashirecare.files.wordpress.com/2008/03/step-by-step-guide-to-criti-research-part-1-quantitative-reseawrch.pdf
- Cruise, R.J., Cash, R.W., & Bolton, D.L. (1985). Development and validation of an instrument to measure statistical anxiety. Proceedings of the Joint Statistical Meetings, Section on Statistical Education (pp. 92-97). Alexandria, VA: American Statistical Association.
- Koerner, N., & Dugas, M. J. (2006). A cognitive model of generalized anxiety disorder: The role of intolerance of uncertainty. Retrieved from https://onlinelibrary.wiley.com/doi/abs/10.1002/9780470713143.ch12
- Onwuegbuzie, A. J. (1997). Writing a research proposal: The role of library anxiety, statistics anxiety, and composition anxiety. Library and Information Science Research, 19(1), 5-33.
- Williams, A.S. (2013). WORRY, INTOLERANCE OF UNCERTAINTY, AND STATISTICS ANXIETY. Retrieved from https://iase-web.org/documents/SERJ/SERJ12(1)_Williams.pdf
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