Chi-Square Tests: Advantages, Disadvantages, and Applications

This assignment delves into the Chi-square test, a nonparametric statistical method used to analyze categorical data. The student provides examples of scenarios where transforming numerical data into categories is beneficial, such as categorizing light wavelengths and grading scales. The assignment then explores a hypothetical situation involving an ANOVA test and explains the necessary changes to apply a Chi-square test, including recategorizing continuous variables like satisfaction levels. It further discusses the advantages and disadvantages of using a Chi-square approach compared to a parametric approach like ANOVA, highlighting the robustness and ease of computation of the Chi-square test while acknowledging its limitations regarding the loss of continuous variable information. The student concludes by suggesting that ANOVA is the more appropriate method for the given hypothesis due to the detailed information it provides, which is supported by the assumptions required to perform ANOVA analysis. References supporting the concepts are also provided.

Chi-square tests are nonparametric tests that examine nominal categories as opposed to
numerical values. Consider a situation in which you may want to transform numerical
scores into categories. Provide a specific example of a situation in which categories are
more informative than the actual values.
Nonparametric test is a statistical branch is mainly based on single family of parameterized of
probability distribution. It is based on free distribution or specified distribution but under
unspecified distribution parameter.
The first example of numerical data to categories data would be light: Light have different color
based on their wavelength, from the wavelength there are others that would have quality of
wavelength while others would have hues wavelength. We can generalize the range as either red
or blue. The red wavelength is categorized as light that would have a wavelength of about 622
nanometers and 780 nanometers, whereas the blue wavelength would have 455 nanometers and
492 nanometers. According to a common person or physical deprived person blue and red would
mean something different from wavelength of light. Therefore, a categorical description would
be of special thoughts and meaning in such context.
The second example involves grading scales. We would arrange the grading ranges as A, B, C
and so on. Suppose the grading is done for secondary students who were enrolled in a particular
university. Students who scored either A or B grade would have a higher chance of being
admitted to the university as compared to other grades who had insignificant chance of enrolling
into the university.
Suppose we had conducted an ANOVA, with individuals grouped by political affiliation
(Republican, Democrat, and Other), and we were interested in how satisfied they were with
the current administration. Satisfaction was measured on a scale of 1-10, so it was
measured on a continuous scale. Explain what changes would be required so that you
could analyze the hypothesis using a chi-square test. For instance, rather than looking at
test scores as a range from 0 to 100, you could change the variable to low, medium, or high.
Anova method is used in determining whether there is any existence of statistical significance
difference between three or more independent groups.
Example, if we start with a numerical stores that measures self –esteem and we create 3 levels of
categories which includes high esteem, medium esteem and low esteem. In most cases a
preferred parametric test would be done to help detect easily the difference in reality or real
relationship (Gravetter and Wallnau, 2014).

Political affiliation is an independent variable and has three levels. The continuous dependent
variable would now be the satisfaction with the existing administration. Chi-square test
performance would require breaking up the measured satisfaction into categories like, high, low
and medium.
What advantage and disadvantage do you see in using this approach?
The following are the advantage of Chi-square method
 Chi-square method is a robust method with respect to data distribution
 Chi-square method is easier to compute
 Chi-square method is normally used in studies where parametric assumptions would not
be possible to be met
 Chi-square method is flexible on data handling either in two or more groups that would
require studies
The following are the demerits of chi-square method
 Chi-square method is independent on frequency size and observation
 The continuous difference function change of independent variable would not be seen
while using Chi-square method
 When using Chi-square method it would be Difficult to interpreting effect of correlation
on samples taken on the boundaries containing two satisfaction categories
In this case it would be appropriate to break the data flow if the independent variable would be
measured in continuous scale
Which is the better option for this hypothesis, the parametric approach or nonparametric
approach? Why?
ANOVA method is used in determining whether there is any existence of statistical significance
difference between three or more independent groups.
ANOVA method in this case would be the appropriate approach.
Advantage of ANOVA
 ANOVA method provides a restrictive and detailed information that would provide less
deciphered

Parametric tests are also referred as statistical procedure. In this test a statistical sample would be
obtained in order to estimate a given population parameter. Since the process of estimation
would require sampling distribution then assumptions would be required to ensure there is
compatibility between each data. For example ANOVA analysis would require three
assumptions (Norman, 2010);
 The observation should be independent
 The sample data should be distributed normally
 The scores would have homogeneous variances
Non parametric method would not deal with any population estimation parameters unlike
parametric; hence they are regarded as free methods. If the sample populations are normally
distributed then a method of parametric would always be used. Categorical scale data would
require the use of non-parametric method.
References
Gravetter, F. J., & Wallnau, L. B. (2014). Introduction to the t statistic. Essentials of statistics for
the behavioral sciences, 8, 252.
Norman, G. (2010). Likert scales, levels of measurement and the “laws” of statistics. Advances
in health sciences education, 15(5), 625-632.
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