Understanding Hypothesis Testing and Managerial Significance

1 Review Questions: Answer the following questions in detail. 1. Explain the notions of mathematical differences, managerially important differences, and statistical significance. Can results be statistically significant and yet lack managerial importance. Explain your answer. 2. Describe the steps in the procedure for testing hypotheses. Discuss the difference between a null hypothesis and an alternative hypothesis. 3. What purpose does a scatter diagram serve? 4. The following ANOVA summary data are the result of a regression with sales per year (dependent variable)as a function of promotion expenditures per year (independent variable) for a toy company. F = MSA = 34,276 MSE 4,721 The degrees of freedom are 1 for the numerator and 19 for the denominator. Is the relationship statistically significant at " = .05? Comment on your answer. Deliverable length 3-5 body page in APA format with the incorporation and citation of reference material

2 Hypothesis Testing and Data Analysis Student Name MKTG400: Marketing Research Dr. Thomas Schaefer November 12 th , 2023

3 Hypothesis Testing and Data Analysis Explain the notions of mathematical differences, managerially important differences, and statistical significance. Can results be statistically significant and yet lack managerial importance. Explain your answer. Marketing research is an effective tool for decision makers and management teams to make the best possible decision. There are many problems day to day that should be solved effectively and efficiently, and each problem has many different solutions. Marketing research helps provide information to identify the best alternative solutions, thus implementing sound decision-making. Marketing decisions are very important to the business as they affect every step of the business process – product design and creation, pricing, promotion, and distribution. Consumer buying behavior and the decision to purchase a product are what determines the success of a business, which means the marketing decisions are more difficult. In order to find the best alternative to choose from, research is conducted to determine the nature of the market and its characteristics. Statistics help understand the significance of marketplace characteristics by reducing the uncertainty of management decisions by identifying measured variables that are managerially significant and statistically significant from one other (Silver & Wrenn, 2013, pp.207). Using statistical analysis methods provides decision-makers with several methods to test theories and innovative ideas with alternative solutions. Statistical tests include sample size, variability and reliability of data, and confidence levels desired in the results. Mathematical differences occur when a number (constant value of a variable) is subtracted from another number representing the same physical quantity. Measuring statistical significance in marketing can be an important tool. Statistical significance is defined by Silver & Wrenn (2013, pp.207) as “when a difference (e.g.,

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4 between two market segments, attitudes, likelihood of purchase between two products, etc.) is big enough that it is unlikely that to have occurred due to chance”. This essentially determines whether the results of an experiment or study are due to chance or are actually meaningful and can illustrate if the result was due to testing the change or if it was happenstance. Understanding if test results are statistically significant or not will help marketers determine whether the change being tested will impact the marketing campaign or not and can improve confidence in marketing decisions. Although a test result is statistically significant, it doesn’t necessarily mean that it is managerially significant. Managerially significant differences are defined by Silver & Wrenn (2013, pp.207) as “when any observed difference in findings is considered significant enough to influence managerial decisions”. A statistically significant difference should be meaningful enough to influence a business decision and give confidence to management that a new strategy or campaign is worth implementing. Results of a test can be statistically significant, but not important to management making marketing decisions. Statistical analysis on collected data will reduce the uncertainty of management decisions because it identifies the variables that are statistically significant and significant to marketing managers that are making marketing decisions. Describe the steps in the procedure for testing hypotheses. Discuss the difference between a null hypothesis and an alternative hypothesis. A hypothesis is an assumption that can either be proved or disproved. The hypothesis states what a researcher is looking for and is a proposition that can be tested to determine its validity (Sontakki, 2010). In order to test a hypothesis, there are five steps: 1. State the research hypothesis as a null hypothesis and alternate hypothesis.

5 2. Collect data in a way designed to test the hypothesis. 3. Perform an appropriate statistical test. 4. Decide whether to reject or fail the null hypothesis. 5. Present the findings in the results and discussion section. The first step to test a hypothesis indicates finding a null hypothesis and an alternate hypothesis. This means to set up two hypotheses instead of one where if one hypothesis is true, the other is false. An alternate hypothesis is typically the initial hypothesis that predicts a relationship between variables. Null means ‘invalid’ or ‘nothing,’ meaning that the null hypothesis is a prediction of no relationship between the variables you are interested in. The test will determine a statistical decision based on the acceptance or rejection of the null hypothesis. What purpose does a scatter diagram serve? Once research is completed, it is important for researchers to analyze the data and draw inferences or establish the cause-and-effect relations. In statistics, correlation is the relationship between two variables (Sontakki, 2010, pp.194). Measuring correlation between variables can illustrate the degree of relationships between them. In marketing, correlation can help a decision- maker estimate cost, sales, or even prices. To determine the relationship between two variables, a scatter diagram may be used. A scatter diagram studies possible relationships between two variables, and it displays what happens to one variable when another variable is changed (CEC, n.d.). The following ANOVA summary data are the result of a regression with sales per year (dependent variable)as a function of promotion expenditures per year (independent variable) for a toy company.

6 F = MSA = 34,276 MSE 4,721 The degrees of freedom are 1 for the numerator and 19 for the denominator. Is the relationship statistically significant at " = .05? Comment on your answer. Analysis of variance (ANOVA) is a test used to determine if samples come from two or more populations with equal means (Silver & Wrenn, 2013, pp.211). ANOVA examines: (1) two factors of interest on the dependent variable, and (2) the interaction between the different levels or the two factors. In the example given, the relationship at “ =.05 is not statistically significant. Since the numbers are minimal, a mathematical difference is more likely chance and getting .05. A larger number would be statistically significant.

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7 References Clinical Excellence Commission. (n.d.). Scatter plot . CEC. https://www.cec.health.nsw.gov.au/CEC-Academy/quality-improvement-tools/scatter- plot#:~:text=The%20purpose%20of%20the%20scatter,the%20two%20variables%20are %20related . McShane, B. B., Gal, D., Gelman, A., Robert, C., & Tackett, J. L. (2019). Abandon Statistical Significance. The American Statistician , 73 , 235–245. https://doi.org/10.1080/00031305.2018.1527253 Silver, L. S., & Wrenn, Bruce. (2013). The essentials of marketing research (3rd ed.). Routledge. https://doi.org/10.4324/9780203182598 Sontakki, C. N. (2010). Marketing research (Rev. ed.). Himalaya Pub. House.

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