Chi-square tests are nonparametric tests that examine nominal categories as oppo

Question

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. 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. What advantages and disadvantages do you see in using this approach? Which is the better option for this hypothesis, the parametric approach or nonparametric approach? Why?

Explanation / Answer

1)

An example for numerical to categorical data off the top of my head: Light of different color has different wavelengths, but certain ranges of wavelengths qualify as certain shades/hues/tints/etc. You can generalize and say a certain range can be called "blue" or "red". Red is usually attributed to light that has a wavelength between 780 and 622 nanometers, whereas blue light is between 492 and 455 nm. To the average (physics-deprived) person, "red" and "blue" obviously mean more than a given wavelength of light, so a categorical/qualitative description might be of more use in such a context. Another example would be grading scales. Certain ranges of scores will qualify as an A, a B, and so on. Suppose you want to examine the grades of high school students admitted into a prestigious university. Students that fall in the A/B range tend to have a better chance of being admitted, while those at the other end of the spectrum are "significantly" less likely to enroll. ("Significant" here can take on either the statistical or colloquial meaning of the word. The former could be established with an actual statistical test.)

2)

The independent variable is political affiliation, and it has 3 levels. The dependent variable is satisfaction of the current administration, and it is continuous. For performing a Chi-square test on these variables, we have to break satisfaction measurement to categories like low, medium, and high. The advantage of doing chi-square is that it is easier to compute. The disadvantage is that we could not see the continuous change of difference as a function of independent variables. Also, for people fall at the boundaries between two categories of satisfaction, it will be difficult to interpret the correlation effect on this sample. To me, if a dependent variable is measured in continuous scale, we should not break the data flow. In this case, ANOVA is a better approach. The advantages I find in utilizing this methodology is that it can give you restrictive convincing information that is effortlessly deciphered. However the burden might be that the information isn't sufficiently particular as numerical information might be.
   Conventional statistical procedures are also called parametric tests. In a parametric test a sample statistic is obtained to estimate the population parameter. Because this estimation process involves a sample, a sampling distribution, and a population, certain parametric assumptions are required to ensure all components are compatible with each other. For example, in Analysis of Variance (ANOVA) there are three assumptions:

•   Observations are independent.
•   The sample data have a normal distribution.
•   Scores in different groups have homogeneous variances.
   Parametric methods deal with the estimation of population parameters (like the mean) while the non-parametric are distribution free methods. They rely on ordering (ranking) of observations. More specifically, the data distribution is significant in the choice between parametric and non-parametric procedures.If we believe that the populations are normally distributed then we use parametric methods. If we are not sure or we suspect that they do not behave normally then we use non-parametric methods.Similarly the scale of the data is important. That is categorical (nominal) or ordinal scale data demand the use of non-parametric methods while in the case of interval and ratio scale data where we cannot assume population normality then again non-parametric methods have to be used.

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