Give your outlook on each post about 5 sentences minimum.

POST A:

When testing the mean for business data, statisticians sometimes get confused about when to use the independent-samples t-tests, and one-sample t-tests. State when it is appropriate to use each of the three t-tests. This could be for business-related problems or questions relating to your dissertation topic. Give a brief description of a business-related problem, then state which of the t-tests you would use and why? Finally, select what you would propose to be the best statistical test to address that problem and provide an explanation as to why you believe that would be best.

The three most used t-tests are the single-sample t-test, independent-samples t-test, and the paired-samples t-test (Gronk 2019). An independent-samples T-test is used when comparing the means of two unrelated groups. There are two types of independent samples t-test. The first is the Student’s T-test, where distribution is assumed to be normal, the common variance between groups is divided by two and assigned equal weight. The second is the Welch’s t-test, where unequal sample sizes and/or unequal variances exists or are assumed (Hae-Young, 2019).

A one-sample t-test may be used when comparing a single group to a known mean or known variable. Ross & Wilson (2017) use the example of comparing the test scores of all of the freshman in a college class on a particular test against a known value of 70. In this case the value of 70 is selected as the control value and in SPSS is input into the “test value” box, under One-sample t-test, and the students scores would be entered under the test variable section.

A paired sample t-test compares samples from a single subject at different times (Kent State, 2023). An illustration of this would be comparing the test scores of a subject before and after prep course. This before and after comparison evaluates the effectiveness of the preparatory course.

A business case for using a one-sample t-test would be evaluating the effectiveness of an advertising campaign. Sales of Widget Co. products during a predetermined timeframe prior to the advertising campaign would serve as a control or known mean. For the sake of argument, let’s choose 90 days. The sales over the 90 day period after the advertising campaign could then be collected and a one-sample t-test be conducted to compare the means of sales values.

The purpose behind using the one-sample t-test is to evaluate the effectiveness of the advertising campaign. Since businesses operate on return on investment (ROI), it is important to determine if the money spent on advertising is affecting the bottom line in a positive manner. I believe this test is the best because it is a straightforward comparison of two data sets relative to one another under defined and controlled conditions.

References

Cronk, B. C. (2019). How to use SPSS®: A step-by-step guide to analysis and interpretation. Routledge

Kent State. (2023). LibGuides: SPSS tutorials: Paired samples T test. LibGuides at Kent State University. https://libguides.library.kent.edu/spss/pairedsamplesttest

Ross, A., & Wilson, V. (2017, January 1). One-sample T-test. Brill. https://brill.com/display/book/9789463510868/BP000003.xml

Hae-Young, K. (2019). Statistical notes for clinical researchers: The independent samples T-Test. PubMed Central (PMC). https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6713081/

POST B:

According to Gronk (2019), the three most used t-tests are the single-sample t-test, independent-samples t-test, and the paired-samples t-test. The single-sample t-test compares the mean of a single sample to a known population mean (p. 71). The independent-samples t-test compares the means of two independent samples (p.74), meaning there is no relationship between the samples. The paired-sample t-test compares the means of two measurements from related samples (p.78).

McCrum-Gardner (2008) points out that the first step to take when deciding which test to use is to determine the scale of measurement (nominal, ordinal, or interval), which helps determine the best test to use. The second step McCrum-Gardner recommends is to have a clear understanding of the purpose of the analysis.

Based on the information from McCrum-Gardner (2008) and looking at my dissertation topic, the business-related problem is how reliable new technologies are and if it is worth investing in technology that may not function as designed. I would use a single-sample t-test if I want to measure a manufacturer’s claim of how clear an image or video from a License Plate Reader camera really is. It will be an ordinal scale with 1 being not very clear to 5 meaning a clear image and then compared it with the industry standard. Image quality is important when using LPR technology to identify wanted or stolen vehicles.

The independent-sample test for this example will be to determine if image quality is better using electrical power or solar power. Some LPR may have to be placed in areas where no power is available; therefore, so solar power is used. Will the cameras perform the same way if powered by a direct electrical source or by solar power? Making sure clear images are provided 24 hours a day is important for crime prevention.

Finally, the paired samples T-test can be used to determine the effects of LPR cameras by measuring the number of stolen vehicles before the implementation of LPR and after. This is one of the key statistics required to present a strong business case for purchasing real-time crime analysis technology.

**Conclusion**

T-tests will play a major role in my dissertation. Paired-sample t-test will be the primary statistic technique I will use because the goal of my dissertation is to compare the data of several crimes before and after the implementation of various real-time crime analysis and command technologies. The main purpose of my dissertation is to expand on the Plural Policing Theory to include real-time technology. Showing positive results will help support my hypothesis.

**References**

Cronk, B. C. (2019). How to use SPSS®: A step-by-step guide to analysis and interpretation. Routledge

McCrum-Gardner, E. (2008). Which is the correct statistical test to use? British Journal of Oral and Maxillofacial Surgery, 46(1), 38–41. https://doi.org/10.1016/j.bjoms.2007.09.002

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