Weekly Discussion: T Or Chi-Square Test Study Background

Weekly Discussion 1z T Or Chi Square Test Studybackgroundduring This

Weekly Discussion 1z T Or Chi Square Test Studybackgroundduring This

During this week, you will identify a research question created in Week 1 that would be best answered by any of the following statistical tests: z test, t test for single sample, independent samples t test, repeated measures t test, or Chi-Square test. This discussion will help you work towards your “Week 3 Assignment 2.” If there are no research questions that fit any of these types of statistical analyses, decide on a new question before moving forward with the assignment.

Initial Posting Requirements:

  • Identify an appropriate research question that would require the use of a z-, t-, or Chi-Square test to answer.
  • Pick the question from the list created in Week 1 or identify a new question if there are no appropriate ones from Week 1.
  • Describe why this question is appropriate for the selected statistical test.
  • Identify the variables in this study and each of their attributes: discrete or continuous, quantitative or categorical, scale of measurement (nominal, ordinal, interval, or ratio), and independent or dependent.
  • Explain how the variables do or do not fit the qualifications for the selected statistical test.
  • Provide a written explanation for the null and alternative hypotheses.
  • Describe the types of errors that could occur.

Paper For Above instruction

The choice of appropriate statistical tests is fundamental in research to ensure valid and reliable conclusions. For the purpose of this discussion, I have selected a research question suitable for the use of a Chi-Square test, which is typically employed for categorical data analysis. The research question I propose is: "Is there an association between gender (male or female) and preference for a specific brand of beverage (Brand A, Brand B, or Brand C)?"

This question is appropriate for the Chi-Square test because it examines the relationship between two categorical variables: gender and beverage preference. The Chi-Square test assesses whether the observed distribution of preferences differs significantly from what would be expected if there were no association between the variables. Since both variables are nominal and categorical, the Chi-Square test is suitable for analyzing the frequency or count data obtained from survey responses.

The variables in this study are as follows:

  • Gender: Discrete, categorical, nominal, independent variable, with attributes being male and female.
  • Beverage Preference: Discrete, categorical, nominal, dependent variable, with attributes being Brand A, Brand B, and Brand C.

Both variables are qualitative, nominal, and discrete, fitting the conditions for a Chi-Square test that compares observed and expected frequencies across different categories. Since gender and beverage preference are independent attributes, the Chi-Square test can determine if a significant association exists between these variables.

The null hypothesis (H0) for this study is: "There is no association between gender and beverage preference," meaning the distribution of beverage preference is independent of gender. The alternative hypothesis (H1) is: "There is an association between gender and beverage preference," indicating that preference varies significantly between males and females.

Potential errors in this analysis include Type I error—incorrectly rejecting the null hypothesis when it is true, leading to a false claim of an association—and Type II error—failing to reject the null hypothesis when it is false, missing a real association between gender and beverage preference. Proper sampling and data collection procedures help mitigate these errors, but they remain considerations in interpreting statistical results.

References

  • Agresti, A. (2018). Categorical Data Analysis (3rd ed.). Wiley.
  • Fisher, R. A. (1922). On the interpretation of χ² from contingency tables, and the calculation of P. Journal of the Royal Statistical Society, 85(1), 87-94.
  • McHugh, M. L. (2013). The Chi-square test of independence. Biochemia Medica, 23(2), 143–149.
  • Tabachnick, B. G., & Fidell, L. S. (2013). Using Multivariate Statistics (6th ed.). Pearson.
  • Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Routledge.
  • Siegel, S., & Castellan, N. J. (1988). Nonparametric statistics for the behavioral sciences (2nd ed.). McGraw-Hill.
  • Sheskin, D. J. (2011). Handbook of parametric and nonparametric statistical procedures (5th ed.). CRC Press.
  • Laerd Statistics. (2018). Chi Square Test of Independence. Retrieved from https://statistics.laerd.com
  • Munro, B. (2005). Statistical Methods for Health Care Research. Lippincott Williams & Wilkins.
  • Keppel, G., & Wickens, T. D. (2004). Design and Analysis: A Researcher's Handbook (4th ed.). Pearson.

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