Unit 5 Discussion Topic 1

This week’s discussion focuses on various forms of statistical hypothesis testing and challenges associated with data gathering.

Discussion Topic 1: Statistical Hypothesis Testing

Discussion 1: For each of the five scenarios listed in the PDF below, choose the most appropriate statistical test from the list, also included in the PDF, and explain your choice.

Please include the following as part of your reply

“Response: Scenario 1 relates to the Pearson correlation statistical test because…..,

Scenario 2 relates to the ………..because…”

In our textbook, review Figure 14.6 (Classification of Univariate Techniques), Figure 14.7 (Classification of Multivariate Techniques), and Figure 15.9 (Hypothesis Tests Related to Differences).

The following 10 statistical tests are used commonly used to test hypotheses in marketing research studies:

- Pearson correlation (r) – also known as the coefficient of correlation. This method measure the relationship (“strength of association” between variables; it allows comparison of an observed set of frequencies with an expected set of frequencies – and this method can be used for nominal, ordinal, interval or ratio measurements
- t test for independent samples – we use t (instead of z) when the sample is less than 30 and we don’t know the population standard deviation)
- t test for paired samples
- t test for a single sample
- Chi square test of best fit – this method is used for nominal and ordinal data
- Chi square test of independence
- One-way ANOVA – Analysis of Variance means the data must be interval or ratio because ANOVA compares sample means through their variances
- Two-way ANOVA – as above but considers additional variables.
- Simple regression – requires interval or ratio data and compares the relationship between one independent variable and one dependent variable
- Multiple regression – requires interval or ratio data and examines the influence of two or more independent variables on one dependent variable

When deciding on which statistical test best applies to the five scenarios presented in this assignment, first ask yourself the following:

- Are the “variables of interest” (data) available on an interval (meaning it is scaled and zero is a point on the scale, such as temperature) or ratio (meaning differences between two numbers are meaningful and zero means absence of condition, like number of patients visiting an emergency room), or are they nominal or ordinal (nominal observations can only be classified and counted; ordinal observations are typically ranked or ordered).
- Are the samples drawn randomly (“independent”) or do the samples come from the same group of respondents (“dependent”)? There are two types of dependent samples: one is characterized by a measurement followed by an intervention of some kind, and then another measure (such as a before and after study), the second is characterized by matching or pairing observations.
- Sample size matters when determining the appropriate method to test hypotheses, so check to see the number of samples.
- Is it univariate, single measurement of each element in the sample or there are several measurement of each element but each variable is analyzed in isolation, or is it multivariate (two or more measurement on each element AND the variables are analyzed simultaneously to determine relationships between the variables).

- Choose one of the statistical tests listed above and explain your choice for the following scenario: The director of a college’s food services is considering the addition of new items to the cafeteria menu. One of the new items is a green salad topped with strips of grilled chicken breast. After tasting the salad, the college’s students, faculty, and administrators who eat at the cafeteria are asked to indicate their preference by circling one of the following options:

(a) Add it to the menu, (b) Do not add it to the menu, and (c) No opinion. The director of food services analyzes the data to determine if there are differences in the numbers of students, faculty, and administrators who chose each of the three response options. Here we have one salad and multiple tasters. We do not know our sample size. We know there are three sample groups (students, faculty and administrators).

Each sample group has three choices.

- Choose one of the statistical tests listed above and explain your choice for the following scenario: A research course instructor at a business college has noticed that accounting and finance students seem to have more positive attitudes toward statistics compared with management and marketing students. The professor administers the Statistics Attitudes Inventory (SAI) scale to all students on the first day of the fall semester. The inventory contains 20 Likert-scale items with responses ranging from Strongly Disagree to Strongly Agree. The responses of accounting, finance, management, and marketing students are then compared to determine if there are significant differences in attitudes between the four groups of students. Here we have four samples giving feedback using a scaled method approach: there is meaningful information between each of the intervals.
- Choose one of the statistical tests listed above and explain your choice for the following scenario: The engineers in a large multinational corporation claim that the salespeople get paid more than employees in other departments. The CEO assures the employees that there is no significant difference in annual salaries between employees from different departments. The CEO conducts a study to compare the annual salaries of the 32 salespeople to the mean of the annual salaries of all the 530 employees of the company. Here there is no dependency (cause/effect) between variables; this represents gathered information.
- Choose one of the statistical tests listed above and explain your choice for the following scenario: Many people view television as a major contributor to the shopping habits of teenagers. A marketing researcher decides to investigate whether there is a relationship between the number of hours children watch television and the amount of money they spend shopping. For two weeks, teenagers record the number of hours they watch television and how much they spend shopping. The researcher can now analyze the data (TV viewing hours and money spent shopping) and determine whether there is a relationship between these two variables.

5. Choose one of the statistical tests listed above and explain your choice for the following scenario: A product manager is trying to determine whether to use a higher or lower price on a new product. She decides to test market the higher price in one city and the test market the lower price in another city. The two cities chosen to test the prices are similar in terms of their demographics and other factors. For four weeks the manger kept track of the sales volume in each of the two test cities. The manager compares the mean sales volume for each test city to determine which price is more successful. Here we have a small sample size

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