Quantitative Research Methods: Chi Square, T-Test, and ANOVA Analysis
ATTACHED ARE "Case assignment instructions", "week 1-4 discussions", "Chi Square, T-Test and ANOVA analysis" (Please use these in writing the paper)', "paper writing guidelines by the professor", and other supporting attachments.
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In this assignment you will revisit your analyses that you presented in the Week 1-4 discussion postings. In 5 to 8 pages please provide a short presentation of each test you performed to include a research question and both a null and alternative hypothesis. There should be a separate paragraph for each of your analyses to include your Chi Square, t-test, and ANOVA analysis followed by a presentation of the results in APA format.
For instance, the presentation of independent sample t-test results would look something like what is below for a hypothetical example (not included in your data set), that considered accounting proficiencies scores for individuals who attended online training as compared to those who did not:
RQ: To what extent does having a CPA influence accounting proficiency scores of individuals with equivalent experience?
Hnull: There is no difference in accounting proficiency scores for those who have a CPA as compared to those who do not.
Halt: There is a difference in accounting proficiency scores for those who hold a CPA as compared to those who do not.
An independent samples t-test revealed a statistically significant difference in accounting proficiency scores between individuals who hold a CPA M= 96.6 (.80) and those who do not M= 94.5 (1.2), with t (43) = 2.10, p = .034. The 95% CI of the mean difference 2.1 is (1.2, 3.0). Those who hold a CPA outperformed those who do not. Hence, we reject he null hypothesis.
Make sure you indicate whether you accepted or rejected your null hypothesis. Also, please provide an introduction and conclusion to your paper and in your conclusion discuss any insights you might have gained from the results of your statistical tests. That is, do your findings seem to make sense?
Writing Guidelines: - • Running head and pagination. • The length of this paper should be between 5-8 pages (not including the title page, table of contents, reference page and Appendices page). • APA style formatting (7th edition), double spaced, with 1-inch margins and 12 point Times New Roman font. • The paper must have an EXECUTIVE SUMMARY/Statement of purpose (including THESIS statement), INTRODUCTION and CONCLUSION paragraphs. • Please include TITLE PAGE, TABLE OF CONTENTS PAGE, REFERENCE PAGE, and any APPENDICES. • Please submit in a word document and NOT pdf version. • Please use HEADINGS AND SUBHEADINGS to organize your paper. • Use at least 10 academic, peer-reviewed, library trade publications, scholarly or professional practitioner sources, and minimum 36 in-text CITATIONS. • You must cite and reference all texts used, including page numbers as applicable to avoid plagiarism. • Please provide verifiable links/web address for each academic reference used. • Paper should be proofread for spelling and grammar mistakes. • Write your paper in an integrated fashion, weaving theory and application. In other words, do not merely respond to each bullet above as a checklist. -------------------------------------------------------------------------------------------- Professor’s Additional instructions – Please: - Use third person in writing. - Do not use quotes. - Use APA formatting (7TH Edition) of references and in text citations is required. - the following resources are NOT ACCEPTABLE as citations for this paper: • Wikipedia.com • Ehow.com • Dictionary.com • About.com • Smallbusiness.chron.com • Diffen.com • Yourbusiness.azcentral.com • Tjmarino.com • Investopedia.com • Boundless.com and Lumen • CourseHero.com • Chegg.com • Difference between • Answers.com • Any student essay website ----------------------------------------------------------------------------------------------------------- .
Quantitative Research Methods
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Date of Submission Table of Contents Executive summary. 3 Chi-Square Analysis Presentation. 4 Hypotheses. 4 Results. 5 T-Test Analysis Presentation. 8 Research Question. 8 Hypotheses: 8 Methodology: 8 Results: 8 Table 1: Group Statistics. 8 Table 2: T-test Analysis. 9 Insights: 10 Anova Analysis. 11 Research Question. 11 Hypotheses. 11 Methodology. 11 Results. 12 Educational Attainment Level Mean Income ($) Standard Deviation ($) 12 Discussion. 15
Executive summary
This paper discusses three quantitative research methods: Chi-square analysis, t-test analysis, and ANOVA analysis. The Chi-square analysis results from testing the relationship between ownership and product mix options, which shows a statistically significant association between the two variables. The t-test analysis shows a significant difference in customer satisfaction scores between rural and urban stores. Lastly, ANOVA analysis explores the relationship between educational attainment levels and mean income, which shows a significant association between the two variables. The article provides insights into the use of these research methods and highlights the importance of statistical significance in making informed decisions.
Quantitative Research Methods
Introduction
Quantitative research methods involve the collection and analysis of numerical data. It is a systematic approach to research that uses statistical techniques to measure and analyze relationships between variables. This type of research is commonly used in social sciences, business, and natural sciences, among others. Some of the key tools used in quantitative research include surveys, experiments, and statistical analysis. This paper presents the results of three quantitative research analyses: chi-square analysis, t-test analysis, and ANOVA analysis. These analyses aim to explore the relationship between different variables and provide insights that can be used to inform decision-making.
Quantitative Research Methods
Chi-Square Analysis Presentation
Chi-square analysis is a statistical tool commonly used to determine the association between two nominal variables (Kent State University, 2020b; Lund Research, 2018). It involves comparing the observed frequencies of the variables with the expected frequencies to determine if there is a significant relationship between them (Martin, 2019). In this paper, we will present the results of a chi-square test of independence that was undertaken on two nominal variables in the dataset: ownership and product mix. The test aimed to determine if there is a significant association between these variables.
Hypotheses
The null hypothesis stated that the product mix options are not dependent on the ownership type. In contrast, the alternative hypothesis stated that the product mix options depend on the ownership type. A chi-square test of independence was undertaken on the two nominal variables in the dataset to test these hypotheses (Kent State University, 2020b). The purpose was to determine if there is a significant relationship between the ownership type and product mix options.
The null hypothesis formulated in this case was:
H0: The product mix options are not dependent on the ownership type.
The alternative hypothesis was:
H1: The product mix options are dependent on the ownership type.
Results
Table SEQ Table \* ARABIC 1: Cross tabulation of Ownership and Product Mix
Corporate or Franchise * Product Mix CrosstabulationProduct MixTotalABCCorporate or FranchiseCorporateCount9476125295% within Corporate or Franchise31.9%25.8%42.4%100.0%% within Product Mix28.7%27.3%47.3%33.9%% of Total10.8%8.7%14.4%33.9%FranchiseCount233202139574% within Corporate or Franchise40.6%35.2%24.2%100.0%% within Product Mix71.3%72.7%52.7%66.1%% of Total26.8%23.2%16.0%66.1%TotalCount327278264869% within Corporate or Franchise37.6%32.0%30.4%100.0%% within Product Mix100.0%100.0%100.0%100.0%% of Total37.6%32.0%30.4%100.0%
Table 1 summarizes the distribution of ownership (Corporate & Franchise) against the different product mixes (A, B & C). The table shows that most of the products are owned by franchisees, with product mix C being the most popular among the franchises.
Table SEQ Table \* ARABIC 2: Chi-Square Tests
Chi-Square TestsValuedfAsymp. Sig. (2-sided)Pearson Chi-Square30.505a2.000Likelihood Ratio29.8132.000Linear-by-Linear Association20.8461.000N of Valid Cases869a. 0 cells (0.0%) have an expected count less than 5. The minimum expected count is 89.62.
Table 2 shows the results of the chi-square test conducted in SPSS. The Pearson Chi-square value is 30.505 with a significance value of 0.000. This indicates a statistically significant association between ownership and product mix options (Franke et al., 2012). Consequently, we reject the null hypothesis and conclude that the product mix options depend on the ownership type (Barcelу, 2018).
Table SEQ Table \* ARABIC 3: Symmetric Measures
Symmetric MeasuresValueApprox. Sig.Nominal by NominalPhi.187.000Cramer's V.187.000N of Valid Cases869a. Not assuming the null hypothesis.b. Using the asymptotic standard error assuming the null hypothesis.
Table 3 illustrates the strength of the association between the variables using the Phi and Cramer's V tests. The Cramer’s V test value shows that the strength of association is weak but statistically significant since p = 0.000 at the 0.05 level of significance. This means there is a significant association between ownership and product mix options. However, the strength of the association is weak.
In conclusion, the results of the chi-square test indicate that there is a significant association between ownership and product mix options (Sharpe, 2015). Franchises tend to have a higher proportion of product mix C than corporations (Turhan, 2020). The findings of this study provide insights into the relationship between ownership and product mix options, which can be useful for business owners in making strategic decisions (Martin, 2020). Although the strength of the association is weak, it is still statistically significant and should not be ignored. Future research could investigate the reasons behind the association and explore ways to strengthen it.
T-Test Analysis Presentation
This analysis aims to investigate if there is a significant difference in customer satisfaction scores between urban and rural stores (Collins, 2020). In this study, we used an independent t-test to compare the mean scores of customer satisfaction between two groups: rural and urban stores.
Research Question
To what extent does the setting of a store (rural vs. urban) affect customer satisfaction scores?
Hypotheses:
H0: There is no significant difference in customer satisfaction scores between rural and urban stores.
H1: There is a significant difference in customer satisfaction scores between rural and urban stores.
Methodology:
We collected data from 869 customers who visited stores in rural and urban settings. We used an independent t-test to compare rural and urban stores' mean customer satisfaction scores. The analysis was conducted at a 0.05 significance level.
Results:
The group statistics in Table 1 show that the mean customer satisfaction score is higher in urban stores (M=27.19, SD=2.904) than in rural stores (M=22.47, SD=3.456). This suggests that there might be a difference in customer satisfaction scores between the two groups.
Table 1: Group Statistics
Urban or RuralNMeanStd. DeviationStd. Error MeanCustomer SatisfactionRural39622.473.456.174Urban47327.192.904.134
Urban or Rural N Mean Std. Deviation Std. Error Mean Customer Satisfaction Rural 396 22.47 3.456 .174 Urban 473 27.19 2.904 .134
Table 2 shows the results of the independent t-test. The results show that the t-value is -21.870, with a p-value of 0.000. This suggests that the difference in customer satisfaction scores between rural and urban stores is statistically significant. The mean difference in customer satisfaction scores between the two groups is -4.718, with a 95% confidence interval of (-5.142, -4.295).
Table 2: T-test Analysis
Levene's Test for Equality of Variancest-test for Equality of MeansFSig.tdfSig. (2-tailed)Mean DifferenceStd. Error Difference95% Confidence Interval of the DifferenceLowerUpperCustomer SatisfactionEqual variances assumed2.499.114-21.870867.000-4.718.216-5.142-4.295Equal variances not assumed-21.538773.700.000-4.718.219-5.149-4.288
Levene's Test for Equality of Variances t-test for Equality o...